Transport of Topological Semimetals

In the paper

“This relativistic effect is attributed to the positron or electron emission by a potential barrier when the barrier is sufficiently high (254)(255)(256).”

What the sources say

• ?Not checked — no full text of the sourcecites [254] 254. Dombey N, Calogeracos A. 1999. Seventy years of the Klein paradox. Phys. Rep. 315:41-58 257. source
• Disputed

  The paper acknowledges that a sufficiently strong barrier can emit particles, but it rejects emission as the explanation for Klein tunnelling. In E. Emission Dynamics (p. 15), it says tunnelling is independent of emission and occurs even when the barrier is subcritical; the Conclusions (p. 18) likewise call them separate phenomena. (LLM, conf=0.91)

  Checked by a reasoning model — may be wrong.

  cites [255] 255. Katsnelson MI, Novoselov KS, Geim AK. 2006. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2:620-25 258. sourceExperimental — accuracy not yet measured
• Partly supported

  In the main text (page unavailable), the paper identifies Klein tunnelling as relativistic electrons passing through a potential barrier and describes perfect transmission at normal incidence. It does not attribute that effect to positron or electron emission by a sufficiently high barrier; its explanation concerns transmission and the absence of backscattering in graphene p–n junctions. (LLM, conf=0.84)

  cites [256] 256. Young AF, Kim P. 2009. Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5:222-26 259. sourceExperimental — accuracy not yet measured

In the paper

“This was interpreted as the dynamic mass generation accompanied by density wave formation, which is due to the nesting of the zeroth LL driven by enhanced electron correlation (272).”

What the sources say

• Disputed

  In “Discussion and Theoretical Explanation” (page not supplied), the paper says the observed oscillations do not agree with a density-wave transition and interprets them instead as arising from two-body quasi-bound states. It does not interpret the observations as dynamic mass generation caused by nesting of the zeroth Landau level. (LLM, conf=0.89)

  Checked by a reasoning model — may be wrong.

  cites [272] 272. Wang H, Liu H, Li Y, Liu Y, Wang J, et al. 2018. Discovery of log-periodic oscillations in ultra-quantum topological materials. Sci. Adv. 4:eaau5096 275. sourceExperimental — accuracy not yet measured

In the paper

“An alternative proposition is that the linear MR in Cd 3 As 2 may arise from spatial fluctuations of the magnitude and direction of local current density in disordered systems (172), and this interpretation appears to be applicable for other topological semimetals with linear MR.”

What the sources say

• Disputed

  Split into 2 atoms — 1 confirmed, 0 partially supported, 1 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Checked by a reasoning model — may be wrong.

  cites [172] 172. Novak M, Sasaki S, Segawa K, Ando Y. 2015. Large linear magnetoresistance in the Dirac semimetal TlBiSSe. Phys. Rev. B 91:041203 175. sourceExperimental — accuracy not yet measured

In the paper

“Given the strongly titled Weyl cones in such WSMs, Landau quantization sensitively depends on the orientation of magnetic field, and the Landau spectrum is gapped for some field directions.”

What the sources say

• Supported

  The main text (p. 2) explains that the tilt defining a type-II Weyl point makes the chiral anomaly depend on magnetic-field direction: outside the relevant cone, the Landau spectrum is gapped and has no chiral zero mode. The supplementary discussion (p. 5) likewise contrasts field directions with and without a chiral Landau level. (LLM, conf=0.93)

  cites [28] 28. Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M, et al. 2015. Type-II Weyl semimetals. Nature 527:495-98 sourceExperimental — accuracy not yet measured
• Disputed

  The Discussion and Conclusions (p. 4) says that field orientation affects Landau levels in a linearized model, but for angles beyond a threshold all Landau levels disappear; it does not describe a gapped Landau spectrum. The authors call that disappearance a pathology of the model. They also find anomaly-induced longitudinal magnetoconductivity at all field angles (p. 5), contrary to an orientation-restricted anomaly. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  cites [306] 306. Sharma G, Goswami P, Tewari S. 2017. Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals. Phys. Rev. B 96:045112 309. sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [307] 307. Burkov AA. 2017. Giant planar Hall effect in topological metals. Phys. Rev. B 96:041110 310.

In the paper

“Different from WTe 2 , which is a type II topological WSM in the bulk form (28,(111)(112)(113)117), bulk WHM is predicted to be a weak topological insulator formed from the stacking of QSHIs (322,325); this is a long-sought topological quantum state (326).”

What the sources say

• Partly supported

  The citation is attached to the description of a “long-sought topological quantum state.” The paper describes quantum spin Hall insulators as a topologically distinct new state of matter (p. 3) and reports experimental evidence for that state in HgTe quantum wells (p. 8). It does not establish that a stacked weak topological insulator is the state in question or characterize that state as long-sought. (LLM, conf=0.81)

  cites [322] 322. König M, Wiedmann S, Brüne C, Roth A, Buhmann H, et al. 2007. Quantum spin Hall insulator state in HgTe quantum wells. Science 318:766-70 325. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [325] 325. Wang C, Hughbanks T. 1995. Main group element size and substitution effects on the structural dimen- sionality of zirconium tellurides of the ZrSiS type. Inorg. Chem. 34:5524-29 328. source
• Disputed

  Citation (326) is attached to the description of the proposed bulk WHM weak topological insulator as a long-sought state. On p. 1, the cited paper instead calls a chiral superconductor produced by coupling a quantum Hall state to a superconductor the “long sought after” state; it does not make that claim about a weak topological insulator. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  cites [326] 326. Qi X-L, Hughes TL, Zhang S-C. 2010. Chiral topological superconductor from the quantum Hall state. Phys. Rev. B 82:184516 329. sourceExperimental — accuracy not yet measured

In the paper

“Since a pair of degenerate Weyl nodes of opposite chiralities is in general unstable and may annihilate, additional crystalline point group symmetries are needed to realize a stable DSM phase (131).”

What the sources say

• Partly supported

  The Applications section says that the stability of Dirac cones in a diamond-lattice model arises from its nonsymmorphic space group. It does not discuss degenerate Weyl nodes of opposite chirality, their possible annihilation, or a general requirement for additional point-group symmetries. (LLM, conf=0.83)

  cites [131] 131. Watanabe H, Po HC, Vishwanath A, Zaletel M. 2015. Filling constraints for spin-orbit coupled insula- tors in symmorphic and nonsymmorphic crystals. PNAS 112:14551-56 134. sourceExperimental — accuracy not yet measured

In the paper

“An alternative explanation is that the backscattering at zero field is strongly suppressed by some protection mechanisms associated with nontrivial band topology but is significantly enhanced by magnetic fields (45).”

What the sources say

• Partly supported

  The paper reports that backscattering in Cd₃As₂ is strongly suppressed at zero field and that this protection is rapidly removed by a magnetic field (pp. 1, 5). It calls the protection mechanism unknown, however, and presents a link to field-induced changes in the Dirac Fermi surface as a possibility rather than establishing that nontrivial band topology causes the suppression. (LLM, conf=0.86)

  cites [45] 45. Liang T, Gibson Q, Ali MN, Liu M, Cava RJ, Ong NP. 2015. Ultrahigh mobility and giant magnetore- sistance in the Dirac semimetal Cd 3 As 2 . Nat. Mater. 14:280-84 sourceExperimental — accuracy not yet measured

In the paper

“Electron-hole compensation has been proposed to be a possible mechanism (46,48,171).”

What the sources say

• Supported

  The passage labeled Abstract (page not specified) explains that compensating electron and hole currents can increase longitudinal resistance and produce extremely high magnetoresistance. It also states that balancing electrons and holes enhances the MR effect, supporting the proposed mechanism. (LLM, conf=0.92)

  cites [46] 46. Shekhar C, Nayak AK, Sun Y, Schmidt M, Nicklas M, et al. 2015. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nat. Phys. 11:645-49 source
• ?Could not verify

  Our copy reports unusually large magnetoresistance and electron and hole pockets in WTe2 (p. 3), but does not propose electron-hole compensation as its mechanism. It describes the mechanism responsible for the effect as unidentified (p. 3) and calls for further work to understand it (p. 5). Searches for compensation and balanced electron and hole carriers found no passage making the attributed proposal. (LLM, conf=0.73)

  cites [48] 48. Ali MN, Xiong J, Flynn S, Tao J, Gibson QD, et al. 2014. Large, non-saturating magnetoresistance in WTe 2 . Nature 514:205-8 sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Conclusion (p. 13) discusses excitonic effects and a particle-hole response in massless Dirac fermions, not electron-hole compensation as a mechanism for magnetoresistance. Searches for electron-hole compensation and magnetoresistance found no passage addressing the claim. (LLM, conf=0.76)

  cites [171] 171. Wang K, Graf D, Lei H, Tozer SW, Petrovic C. 2011. Quantum transport of two-dimensional Dirac fermions in SrMnBi 2 . Phys. Rev. B 84:220401 174. sourceExperimental — accuracy not yet measured

In the paper

“The diverging Berry curvatures near the nodal points support distinct anomalous transport phenomena, including intrinsic anomalous Hall effects (AHEs) (54)(55)(56) and anomalous Nernst effects (57,58).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (54)(55)(56)
• Supported

  The Abstract (passage 2) says Berry curvature diverges around Weyl points and that the anomalous Nernst effect is enhanced when Berry curvature is large near the Fermi level. It also links anomalous Hall conductivity to Berry curvature, though the citation in the citing sentence is attached specifically to the Nernst-effect claim. (LLM, conf=0.91)

  cites [57] 57. Ikhlas M, Tomita T, Koretsune T, Suzuki M-T, Nishio-Hamane D, et al. 2017. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13:1085-90 source
• Supported

  The paper’s main text (page unavailable) says that intense Berry curvature near Weyl points can enhance the intrinsic anomalous Nernst effect. It also identifies large Berry curvature near Weyl points in the studied material. This supports the anomalous Nernst effect portion of the sentence, to which this source’s citation is attached. (LLM, conf=0.88)

  cites [58] 58. Sakai A, Mizuta YP, Nugroho AA, Sihombing R, Koretsune T, et al. 2018. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14:1119-24 source

In the paper

“First, Equations 3 and 4 are not applicable if there are open orbits, which occur when the Fermi surface is not closed in the momentum space (190).”

What the sources say

• ?Could not verify

  The Results and Discussions section discusses the LK formula (Eq. 2) and Berry-phase fitting, but does not say that equations fail for open orbits or define open orbits by a non-closed Fermi surface. Searches for “open orbits” and for the claimed limitation of Equations 3 and 4 found no passage addressing it; the paper’s reference to a closed cyclotron trajectory does not establish that limitation. No page number was supplied for these passages. (LLM, conf=0.72)

  cites [190] 190. Hu J, Liu JY, Graf D, Radmanesh SMA, Adams DJ, et al. 2016. π Berry phase and Zeeman splitting of Weyl semimetal TaP. Sci. Rep. 6:18674 193. sourceExperimental — accuracy not yet measured

In the paper

“We consider a 1D closed loop that interlinks the nodal line in k space (Figure 1c).The band structure is fully gapped and therefore allows for the definition of a topological invariant, i.e., the winding number (150).”

What the sources say

• ?Could not verify

  Section 1.2 describes nodal lines as one-dimensional band crossings, and Section 2.1 discusses InBi’s topology, but neither addresses a gapped closed loop interlinking a nodal line or a winding number defined on that loop. Searches for those terms and for a topological invariant on an enclosing loop found no passage supporting the attributed claim. No page numbers were provided in our copy. (LLM, conf=0.76)

  cites [150] 150. Ekahana SA, Shu-Chun W, Juan J, Kenjiro O, Dharmalingam P, et al. 2017. Observation of nodal line in non-symmorphic topological semimetal InBi. New J. Phys. 19:065007 153. sourceExperimental — accuracy not yet measured

In the paper

“In contrast, on a 2D closed surface that encloses the Weyl node in k space (Figure 1a), the band structure is fully gapped and therefore allows a topological invariant to be defined (19).”

What the sources say

• Supported

  In “Origin of Surface States” (p. 6), the paper describes a gapped two-dimensional subsystem on a torus in momentum space and defines its Chern number. It states that when the torus encloses a single node, the subsystem has unit Chern number. (LLM, conf=0.93)

  cites [19] 19. Wan X, Turner AM, Vishwanath A, Savrasov SY. 2011. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83:205101 source

In the paper

“The phase shift δ in Equation 9, which is determined by the dimensionality of the Fermi surface, is 0 for the 2D case and ±1/8 for the 3D case.”

What the sources say

• ?Not checked — no full text of the sourcecites [203] 203. McClure JW. 1956. Diamagnetism of graphite. Phys. Rev. 104:666-71 206. source
• ?Could not verify

  Section §3, “Topological anomaly and Berry’s phase” (page unavailable), discusses a Berry phase and its cancellation of a 1/2 factor in graphene’s Landau levels. Searches for the Lifshitz–Kosevich phase shift and ±1/8 found no passage in our copy assigning δ = 0 to two dimensions or δ = ±1/8 to three dimensions. (LLM, conf=0.76)

  cites [204] 204. Ando T. 2008. Physics of graphene: zero-mode anomalies and roles of symmetry. Prog. Theor. Phys. Suppl. 176:203-26 207. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [212] 212. Shoenberg D. 1984. Magnetization of a two-dimensional electron gas. J. Low Temp. Phys. 56:417-40 215. source

In the paper

“Earlier studies on graphene (205,206) established that the quantized energies of LLs for spinless 2D Dirac fermions are ε n = v F sgn(n) 2e |B n| (n = 0, ±1, ±2. . .), 5.”

What the sources say

• ?Not checked — no full text of the sourcecites [205] 205. Berry MV. 1984. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392:45-57 208. source
• Partly supported

  In “C. de Haas-van Alphen oscillation” (p. 33), the review derives graphene Landau-level energies near the Dirac point with square-root dependence on the level index and magnetic field. Its printed expression includes ℏ, which the cited formula omits, and the passage does not explicitly give the claimed sgn(n) form for negative-energy levels. (LLM, conf=0.84)

  cites [206] 206. Xiao D, Chang M-C, Niu Q. 2010. Berry phase effects on electronic properties. Rev. Mod. Phys. 82:1959- 2007 209. sourceExperimental — accuracy not yet measured

In the paper

“In some topological semimetals, a strong suppression of backscattering due to nontrivial band topology has also been proposed (45); such suppression would lead to enhanced transport relaxation time.”

What the sources say

• Partly supported

  The main text (pp. 4–5) links suppressed backscattering in Cd3As2 to an exceptionally long transport lifetime. But the paper calls the protection mechanism unknown (main text, p. 1; Supplementary Section S5, p. 11); it does not propose nontrivial band topology as its cause. (LLM, conf=0.88)

  cites [45] 45. Liang T, Gibson Q, Ali MN, Liu M, Cava RJ, Ong NP. 2015. Ultrahigh mobility and giant magnetore- sistance in the Dirac semimetal Cd 3 As 2 . Nat. Mater. 14:280-84 sourceExperimental — accuracy not yet measured

In the paper

“Most topological semimetals reported so far are 3D in nature [such as Cd 3 As 2 (14, 127-130), Na 3 Bi (13,126), and the TaAs family (22,23,25,27,39,86,87,211)], and 3D is necessarily required for a Weyl state (10).”

What the sources say

• Supported

  The citation (10) is attached to the requirement for a Weyl state, not to the claim about most reported semimetals. In “Topological aspects of Weyl semimetals” (p. 5), the paper says that Weyl-node band crossings require three independent variables—that is, three spatial dimensions. (LLM, conf=0.93)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 source

In the paper

“Such a dependence has indeed been observed in a number of topological semimetals (48,183,(191)(192)(193), but linear or even sublinear MR has also been observed in a variety of samples (107, 171, 172, 174-180, 182, 183, 191, 194).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (48,183,(191)(192)(193)
• ?Could not verify

  The paper discusses the temperature dependence of resistivity in RPdBi (Fig. 2E) and the temperature dependence of its superconducting upper critical field (Fig. 4B), but neither establishes a quadratic, linear, or sublinear field dependence of ρxx. Searches for magnetoresistance and field-dependent resistivity found only a reference title mentioning linear magnetoresistance, not a finding reported in this paper. (LLM, conf=0.76)

  cites [107] 107. Nakajima Y, Hu R, Kirshenbaum K, Hughes A, Syers P, et al. 2015. Topological RPdBi half-Heusler semimetals: a new family of noncentrosymmetric magnetic superconductors. Sci. Adv. 1:e1500242 109. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction (p. 1) and Conclusion (p. 13) discuss Coulomb interactions, density response, and Friedel oscillations in two-dimensional massless Dirac fermions. Searches for magnetoresistance, ρxx, and quadratic, linear, or sublinear magnetic-field dependence found no passage addressing the claimed observations in topological semimetals. (LLM, conf=0.76)

  cites [171] 171. Wang K, Graf D, Lei H, Tozer SW, Petrovic C. 2011. Quantum transport of two-dimensional Dirac fermions in SrMnBi 2 . Phys. Rev. B 84:220401 174. sourceExperimental — accuracy not yet measured
• Supported

  The paper reports linear magnetoresistance in the Dirac semimetal TlBiSSe at high magnetic fields (p. 1), making it an example supporting the cited sentence’s linear-MR clause. It also reports ordinary quadratic field dependence below about 0.1 T (p. 2); the linear behavior is field-dependent, not universal across fields. (LLM, conf=0.92)

  cites [172] 172. Novak M, Sasaki S, Segawa K, Ando Y. 2015. Large linear magnetoresistance in the Dirac semimetal TlBiSSe. Phys. Rev. B 91:041203 175. source
• Supported

  The paper reports linear field dependence of ρxx in the Dirac semimetal Na₃Bi. On p. 2, it describes B-linear magnetoresistance as robust across eight samples, supporting its use as an example of the linear-MR observations in the citing sentence. (LLM, conf=0.94)

  cites [174] 174. Xiong J, Kushwaha S, Krizan J, Liang T, Cava RJ, Ong NP. 2016. Anomalous conductivity tensor in the Dirac semimetal Na 3 Bi. Europhys. Lett. 114:27002 177. source
• Supported

  The Results and Discussion (Fig. 2C) report that EuMnBi₂ has a strikingly field-linear ρxx profile at 50 K, without saturation up to 35 T. This supports the cited paper’s role as an example of linear magnetoresistance; it need not establish the separate claim about quadratic dependence in other semimetals. (LLM, conf=0.92)

  cites [175] 175. Masuda H, Sakai H, Tokunaga M, Yamasaki Y, Miyake A, et al. 2016. Quantum Hall effect in a bulk antiferromagnet EuMnBi 2 with magnetically confined two-dimensional Dirac fermions. Sci. Adv. 2:e1501117 178. source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [176] 176. He LP, Hong XC, Dong JK, Pan J, Zhang Z, et al. 2014. Quantum transport evidence for the three- dimensional Dirac semimetal phase in Cd 3 As 2 . Phys. Rev. Lett. 113:246402 179.
• Supported

  The NbP results (p. 2) report non-saturating quasi-linear magnetoresistance in all measured crystals and say its magnitude is sample dependent. This supports the cited paper as an example of the linear-MR observations; it does not need to establish the other observations covered by the sentence’s remaining citations. (LLM, conf=0.91)

  cites [177] 177. Wang Z, Zheng Y, Shen Z, Lu Y, Fang H, et al. 2016. Helicity-protected ultrahigh mobility Weyl fermions in NbP. Phys. Rev. B 93:121112 180. source
• Partly supported

  On p. 2, the paper reports that magnetoresistance in its NbAs single crystal is quite linear above 1.5 T, supporting the linear-MR part of the citing sentence. Our copy does not report quadratic or nearly quadratic field dependence, sublinear MR, or findings across a variety of samples. (LLM, conf=0.86)

  cites [178] 178. Yang X, Liu Y, Wang Z, Zheng Y, Xu Z-a. 2015. Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs. arXiv:1506.03190 [cond-mat.mtrl-sci] 181. sourceExperimental — accuracy not yet measured
• Supported

  The Abstract (p. 4) reports linear field-dependent magnetoresistance in TaP and NbP below 75 K, supporting this paper as an example of the linear-MR samples cited. It also describes a crossover from parabolic to linear dependence; the claim does not require this particular paper to show sublinear MR. (LLM, conf=0.91)

  cites [179] 179. Zhang C, Guo C, Lu H, Zhang X, Yuan Z, et al. 2015. Large magnetoresistance over an extended tem- perature regime in monophosphides of tantalum and niobium. Phys. Rev. B 92:041203(R) 182. source

In the paper

“Although most topological semimetals are 3D, there are also some materials with layered structure and that thus display a quasi-2D electronic structure, such as ZrSiTe ( 156) and (Sr/Ba)Mn(Bi/Sb) 2 (143, 173, 177, 213).”

What the sources say

• ?Could not verify

  The citation is attached to ZrSiTe, not to (Sr/Ba)Mn(Bi/Sb)2. Our copy mentions ZrSiTe only in the title of another work in References and notes (p. 8); its discussion of a layered crystal structure concerns HfSiS (p. 3). A search for ZrSiTe and quasi-two-dimensional electronic structure found no passage establishing the claimed properties for ZrSiTe. (LLM, conf=0.76)

  cites [156] 156. Chen C, Xu X, Jiang J, Wu SC, Qi YP, et al. 2017. Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M = Hf, Zr). Phys. Rev. B 95:125126 159. sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [143] 143. Bian G, Chang T-R, Zheng H, Velury S, Xu S-Y, et al. 2016. Drumhead surface states and topological nodal-line fermions in TlTaSe 2 . Phys. Rev. B 93:121113 146.
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [173] 173. Yi-Yan W, Qiao-He Y, Tian-Long X. 2016. Large linear magnetoresistance in a new Dirac material BaMnBi 2 . Chin. Phys. B 25:107503 176.
• ?Could not verify

  The paper’s discussion of NbP and the TaAs family (pp. 1–2) does not address ZrSiTe or (Sr/Ba)Mn(Bi/Sb)2. Searches for those compounds and for layered or quasi-two-dimensional electronic structure found no passage supporting the attributed claim. (LLM, conf=0.76)

  cites [177] 177. Wang Z, Zheng Y, Shen Z, Lu Y, Fang H, et al. 2016. Helicity-protected ultrahigh mobility Weyl fermions in NbP. Phys. Rev. B 93:121112 180. sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [213] 213. Champel T, Mineev VP. 2001. de Haas-van Alphen effect in two-and quasi-two-dimensional metals and superconductors. Philos. Mag. B 81:55-74 216.

In the paper

“Linear MR may be a classical effect due to strong current inhomogeneity (172) or may have a quantum mechanical interpretation (195) (see Section 3.2.8),while sublinear MR may be attributed to the weak antilocalization caused by strong SOC (196).”

What the sources say

• Supported

  The citation to this paper is attached to the quantum-mechanical interpretation, not the classical-inhomogeneity explanation. On p. 3, the paper describes Abrikosov’s proposed quantum interpretation of linear MR, while noting that its temperature data argue against that model for the TlBiSSe sample studied. (LLM, conf=0.86)

  cites [172] 172. Novak M, Sasaki S, Segawa K, Ando Y. 2015. Large linear magnetoresistance in the Dirac semimetal TlBiSSe. Phys. Rev. B 91:041203 175. source
• ?Not checked — no full text of the sourcecites [195] 195. Chen YL, Chu J-H, Analytis JG, Liu ZK, Igarashi K, et al. 2010. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329:659-62 198. source

In the paper

“Given several damping factors, the general formula of the magnetization oscillations for a 3D system, derived by Lifshitz & Kosevich (the LK formula) (203,204,212), is (in SI units)”

What the sources say

• ?Not checked — no full text of the sourcecites [203] 203. McClure JW. 1956. Diamagnetism of graphite. Phys. Rev. 104:666-71 206. source
• ?Could not verify

  Section §4, “Singular diamagnetism” (page unavailable), derives magnetization and susceptibility for graphene but does not discuss the Lifshitz–Kosevich formula or a general formula for three-dimensional magnetization oscillations. Searches for “Lifshitz Kosevich” and “de Haas van Alphen three dimensional oscillatory magnetization” found no passage addressing the claim. (LLM, conf=0.72)

  cites [204] 204. Ando T. 2008. Physics of graphene: zero-mode anomalies and roles of symmetry. Prog. Theor. Phys. Suppl. 176:203-26 207. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [212] 212. Shoenberg D. 1984. Magnetization of a two-dimensional electron gas. J. Low Temp. Phys. 56:417-40 215. source

In the paper

“For a perfectly 2D system, the above LK formula has been modified by Shoenberg and others (203,204,214,215):”

What the sources say

• ?Not checked — no full text of the sourcecites [203] 203. McClure JW. 1956. Diamagnetism of graphite. Phys. Rev. 104:666-71 206. source
• ?Could not verify

  The passages on magnetic susceptibility (§4, page unavailable) discuss graphene’s susceptibility but do not address a two-dimensional modification of the LK formula. Searches for Shoenberg, the LK formula, and two-dimensional magnetic oscillations found no passage in our copy stating the attributed claim. (LLM, conf=0.74)

  cites [204] 204. Ando T. 2008. Physics of graphene: zero-mode anomalies and roles of symmetry. Prog. Theor. Phys. Suppl. 176:203-26 207. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [214] 214. Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, et al. 2005. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438:197-200 217. source
• ?Not checked — no full text of the sourcecites [215] 215. Das Sarma S, Stern F. 1985. Single-particle relaxation time versus scattering time in an impure electron gas. Phys. Rev. B 32:8442-44 218. source

In the paper

“Such an unconventional Weyl orbit manifests itself by an additional frequency in quantum oscillations (Figure 4e,f ), with 2D character that can be verified by the measurement of the field orientation dependence of oscillation frequency (i.e., F ∝ 1/ cos θ ).”

What the sources say

• Supported

  In “Distinguishing surface and bulk contributions” (page not specified), the paper says surface-arc oscillations can coexist with bulk oscillations and be separated by their different 1/B periodicity. Its field-direction analysis says only the field component normal to the surface drives motion along the arc; neglecting arc curvature, this gives the stated 1/cos θ frequency dependence. The paper also notes that the orbit is not purely two-dimensional because it depends on slab thickness. (LLM, conf=0.88)

  cites [43] 43. Potter AC, Kimchi I, Vishwanath A. 2014. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5:5161 source
• Supported

  The Results sections “Extra-quantum oscillation from Weyl orbit” and “Two-dimensional feature of Weyl orbit” report an extra oscillation frequency and use its field-angle dependence to identify the orbit as 2D. The formula is missing from our copy’s extracted text, but the discussion gives the corresponding 1/cos θ field scaling. Page numbers are unavailable in our copy. (LLM, conf=0.90)

  cites [260] 260. Li P, Wen Y, He X, Zhang Q, Xia C, et al. 2017. Evidence for topological type-II Weyl semimetal WTe 2 . Nat. Commun. 8:2150 263. source

In the paper

“the Klein paradox, which states that the tunneling barrier is nearly”

What the sources say

• Partly supported

  The Introduction (p. 3) says fermions can pass through strong repulsive potentials without the exponential damping expected in ordinary tunnelling. But the square-barrier discussion (pp. 15–16) specifies V > 2m, not merely a height exceeding the electron rest energy, and says transmission is not exponentially small—not that the barrier is generally nearly transparent. Complete transparency occurs at particular transmission resonances (p. 8). (LLM, conf=0.90)

  cites [253] 253. Calogeracos A, Dombey N. 1999. History and physics of the Klein paradox. Contemp. Phys. 40:313-21 256. sourceExperimental — accuracy not yet measured

In the paper

“This method was previously used for the LaAlO 3 /SrTiO 3 heterostructure (246) and was first employed for analyzing the SdH oscillations of TaP (Figure 4c) in the study of topological semimetals (192) and was then proven to be effective in characterizing topological fermion properties for many other multiband topological semimetals (143,156,221,226,230,245,(247)(248)(249).”

What the sources say

• Supported

  The passage labeled ABSTRACT (p. 6) says the authors fitted five overlapping oscillation modes in PdTe₂ with a multiband LK formula and extracted transport parameters. This paper therefore supports its citation as an example of the method used in a multiband topological semimetal. The LaAlO₃/SrTiO₃ and TaP statements carry separate citations and are not attributed to this source. (LLM, conf=0.91)

  cites [246] 246. Fei F, Bo X, Wang R, Wu B, Jiang J, et al. 2017. Nontrivial Berry phase and type-II Dirac transport in the layered material PdTe 2 . Phys. Rev. B 96:041201 249. source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [192] 192. Ghimire NJ, Yongkang L, Neupane M, Williams DJ, Bauer ED, Ronning F. 2015. Magnetotransport of single crystalline NbAs. J. Phys. Condens. Matter 27:152201 195.
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (143,156,221,226,230,245,(247)(248)(249)

In the paper

“Such analysis has been reported for ZrSiS (221) and WTe 2 (250).”

What the sources say

• ?Could not verify

  The paper reports Landau-level spectroscopy and spin splitting in Cd3As2 (p. 1), not spin-zero analysis in ZrSiS or WTe2. Searches for those materials and for spin-zero g-factor extraction found no passage addressing the attributed claim. (LLM, conf=0.76)

  cites [221] 221. Jeon S, Zhou BB, Gyenis A, Feldman BE, Kimchi I, et al. 2014. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd 3 As 2 . Nat. Mater 13:851-56 224. sourceExperimental — accuracy not yet measured
• Partly supported

  The Results section (‘Irregularities in S(B)’, page not available) calculates a Landé g factor for ZrSiS from spin-split Fermi surfaces. It does not describe this as spin-zero analysis, so it supports the g-factor extraction but not the specified method. WTe2 has a separate citation and is not assessed here. (LLM, conf=0.85)

  cites [250] 250. Matusiak M, Cooper JR, Kaczorowski D. 2017. Thermoelectric quantum oscillations in ZrSiS. Nat. Commun. 8:15219 253. sourceExperimental — accuracy not yet measured

In the paper

“The literature contains various definitions for integer LL indices, including resistivity minimum (141, 178, 234, 235), resistivity maximum (171,179,183,191,193,232,233,(236)(237)(238)(239), and conductivity minimum (143,172,213).”

What the sources say

• ?Not checked — no full text of the sourcecites [141] 141. Liu JY, Hu J, Zhang Q, Graf D, Cao HB, et al. 2017. A magnetic topological semimetal Sr 1-y Mn 1-z Sb 2 (y, z < 0.10). Nat. Mater 16:905-10 144. source
• Supported

  The citation falls in the resistivity-maximum group. On p. 4, the paper assigns integer Landau-level indices to peaks in the oscillatory resistivity Δρ, so it is an example of that indexing convention; it need not document the other conventions listed with separate citations. (LLM, conf=0.93)

  cites [178] 178. Yang X, Liu Y, Wang Z, Zheng Y, Xu Z-a. 2015. Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs. arXiv:1506.03190 [cond-mat.mtrl-sci] 181. source
• Supported

  In Results, under “Magnetotransport under high magnetic fields,” the paper says its Landau fan diagrams assign integers to peaks and half-integers to valleys of longitudinal resistivity. This supports the resistivity-maximum convention for which this source is cited; the other conventions are attributed to other references. (LLM, conf=0.93)

  cites [234] 234. Cao J, Liang S, Zhang C, Liu Y, Huang J, et al. 2015. Landau level splitting in Cd 3 As 2 under high magnetic fields. Nat. Commun. 6:7779 237. source
• Supported

  The citation to this paper appears in the resistivity-maximum group of the citing sentence. In the Sample structure section, the paper assigns integer Landau-level indices to resistivity maxima and half-integer indices to minima; it therefore supports the part attributed to it, without needing to establish the other conventions listed. (LLM, conf=0.93)

  cites [235] 235. Zhao Y, Liu H, Zhang C, Wang H, Wang J, et al. 2015. Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional Dirac semimetal Cd 3 As 2 . Phys. Rev. X 5:031037 238. source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (171,179,183,191,193,232,233,(236)(237)(238)(239)
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [143] 143. Bian G, Chang T-R, Zheng H, Velury S, Xu S-Y, et al. 2016. Drumhead surface states and topological nodal-line fermions in TlTaSe 2 . Phys. Rev. B 93:121113 146.
• Partly supported

  Figure 4(a) (p. 3) marks maxima in Hall resistivity oscillations and identifies a first Landau level. But the paper’s Landau-level index plot uses conductivity extrema, assigning N + 1/4 to maxima and N + 3/4 to minima (Fig. 4(d), p. 3); it does not define integer indices by resistivity maxima, the part of the citing sentence to which this source appears attached. (LLM, conf=0.83)

  cites [172] 172. Novak M, Sasaki S, Segawa K, Ando Y. 2015. Large linear magnetoresistance in the Dirac semimetal TlBiSSe. Phys. Rev. B 91:041203 175. sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [213] 213. Champel T, Mineev VP. 2001. de Haas-van Alphen effect in two-and quasi-two-dimensional metals and superconductors. Philos. Mag. B 81:55-74 216.

In the paper

“Generally, the total Hall resistivity ρ xy in a FM material has an anomalous contribution proportional to sample magnetization M (ρ xy AH = R s M) (284).”

What the sources say

• Supported

  The introduction (p. 2) describes the Hall resistivity in ferromagnets as having a contribution due to spontaneous magnetization and identifies Rs as its coefficient. The Early experiments section (p. 8) likewise says Hall resistivity comprises ordinary and anomalous terms involving the sample magnetization. (LLM, conf=0.91)

  cites [284] 284. Berger L. 1970. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2:4559-66 287. source

In the paper

“The recent studies on TaP have shown that the two counterpropagating chiral modes of the lowest LL (represented by χ = ±1 in Equation 16) may hybridize and open up an energy gap, leading to a magnetic tunnelinginduced Weyl node annihilation in TaP that manifests as a sharp reversal of the Hall signal (Figure 6a) (273).”

What the sources say

• ?Could not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  cites [273] 273. Liu H, Jiang H, Wang Z, Joynt R, Xie XC. 2018. Discrete scale invariance in topological semimetals. arXiv:1807.02459 [cond-mat.mtrl-sci] 276. sourceExperimental — accuracy not yet measured

In the paper

“AHE, the enhanced Hall signal that couples with the magnetization of magnetic materials, has been intensively studied, as discussed in previous reviews (e.g., 284).”

What the sources say

• Supported

  The brief history (p. 2) says Hall observed a tenfold stronger effect in ferromagnetic iron than in non-magnetic conductors. The review also describes the anomalous Hall contribution as associated with spontaneous magnetization, supporting the paraphrase’s description of an enhanced Hall signal coupled to magnetization. (LLM, conf=0.93)

  cites [284] 284. Berger L. 1970. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2:4559-66 287. source

In the paper

“Anomalous Hall resistivity can originate from extrinsic mechanisms such as skew scattering (285) and side jumps (286) and from intrinsic mechanisms due to the topological properties of bands (56,(287)(288)(289).”

What the sources say

• ?Not checked — no full text of the sourcecites [285] 285. Onoda M, Nagaosa N. 2002. Topological nature of anomalous Hall effect in ferromagnets. J. Phys. Soc. Jpn. 71:19-22 288. source
• Supported

  The citation is attached to the intrinsic-mechanism part of the sentence. The paper describes an anomalous Hall contribution arising from the Berry phase of Bloch-band wavefunctions (p. 1) and identifies its conductivity with k-space Berry curvature rather than scattering (pp. 1–2). (LLM, conf=0.93)

  cites [286] 286. Jungwirth T, Niu Q, MacDonald AH. 2002. Anomalous Hall effect in ferromagnetic semiconductors. Phys. Rev. Lett. 88:207208 289. source
• Supported

  The citation is attached to the intrinsic-mechanism portion of the sentence; separate citations accompany skew scattering and side jumps. The opening passage (p. 1) links the intrinsic anomalous Hall effect to Berry phases and describes them as a topological ingredient. The paper discusses Hall conductivity rather than resistivity, but supports the attributed intrinsic mechanism. (LLM, conf=0.91)

  cites [56] 56. Haldane FDM. 2004. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93:206602 source

In the paper

“One approach is to pursue their 2D nanostructures, but only the integer QHE has been observed so far in nanostructures of Cd 3 As 2 and WTe 2 (261,267,268), probably due to the quantum confinement effect, which gaps the Dirac cone (267).”

What the sources say

• ?Could not verify

  The paper reports a half-integer quantum Hall effect in graphene (pp. 1–2), not observations in Cd3As2 or WTe2 nanostructures. Searches for those materials and for confinement gapping the Dirac cone found no passage addressing either part of the attributed claim. (LLM, conf=0.76)

  cites [261] 261. Zhang Y, Tan Y-W, Stormer HL, Kim P. 2005. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438:201-4 264. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The introduction discusses Cd3As2 as a three-dimensional Dirac semimetal, and the Electronic structure section discusses gaps in YbMnBi2. Neither addresses integer QHE in Cd3As2 or WTe2 nanostructures or says that quantum confinement gaps their Dirac cones (searched for both points). (LLM, conf=0.76)

  cites [267] 267. Borisenko S, Evtushinsky D, Gibson Q, Yaresko A, Kim T, et al. 2015. Time-reversal symmetry breaking type-II Weyl state in YbMnBi 2 . arXiv:1507.04847 [cond-mat.mes-hall] 270. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s introduction (p. 1) discusses quantum Hall observations in graphene, while its account of α-(BEDT-TTF)₂I₃ says no quantum Hall effect was observed up to 15 T. Searches for Cd₃As₂, WTe₂, integer QHE in their nanostructures, and confinement-induced gapping of a Dirac cone found no passage addressing the attributed claim. (LLM, conf=0.77)

  cites [268] 268. Tajima N, Sugawara S, Kato R, Nishio Y, Kajita K. 2009. Effect of the zero-mode Landau level on interlayer magnetoresistance in multilayer massless Dirac fermion systems. Phys. Rev. Lett. 102:176403 271. sourceExperimental — accuracy not yet measured

In the paper

“The concept for QHE for 2D Dirac fermions has already been established for graphene and topological insulators (216,(263)(264)(265).”

What the sources say

• ?Could not verify

  The Introduction (p. 1) restricts the paper to scattering and relaxation times in doped graphene, while Theory and Results (p. 3) compares those times with ordinary 2D systems. Searches for QHE, the quantum Hall effect, and topological insulators found no passage establishing the claimed concept for graphene or topological insulators. (LLM, conf=0.76)

  cites [216] 216. Hwang EH, Das Sarma S. 2008. Single-particle relaxation time versus transport scattering time in a two-dimensional graphene layer. Phys. Rev. B 77:195412 219. sourceExperimental — accuracy not yet measured
• Supported

  The main text (p. 1) reports a quantized Hall effect from the two-dimensional, Dirac-type surface states of strained HgTe, a three-dimensional topological insulator. On p. 2, it explains the Dirac-fermion Hall plateaus and notes a corresponding zero mode in graphene. This supports the cited sentence’s point about QHE in graphene and topological insulators. (LLM, conf=0.92)

  cites [263] 263. Brüne C, Liu CX, Novik EG, Hankiewicz EM, Buhmann H, et al. 2011. Quantum Hall effect from the topological surface states of strained bulk HgTe. Phys. Rev. Lett. 106:126803 266. source
• Partly supported

  Section V (p. 6) compares the quantum Hall plateaus in zero-gap HgTe wells with those observed in graphene, supporting the graphene part. But the paper does not establish the quantum Hall effect for topological insulators: its Introduction (p. 1) places the HgTe Dirac system at the transition between trivial and quantum spin Hall phases, and note 9 (p. 18) says topological-insulator surface samples had not yet been suitable for high-resolution transport experiments. (LLM, conf=0.86)

  cites [264] 264. Büttner B, Liu CX, Tkachov G, Novik EG, Brüne C, et al. 2011. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nat. Phys. 7:418-22 267. sourceExperimental — accuracy not yet measured

In the paper

“This causes a surprising strong peak centered at θ = 90° in AMR, which can be well fitted by the model that includes tunneling of the zeroth LL's carriers (Figure 5f ) (270).”

What the sources say

• ?Could not verify

  The ‘Magnetotransport under high magnetic fields’ section reports a large resistance peak around 8 T and interprets it in terms of the first Landau level and dynamical mass generation. Although it discusses angular-dependent magnetoresistance and the zeroth Landau level, our copy does not describe a peak centered at θ = 90° or fit such a peak with a model of zeroth-Landau-level carrier tunneling (searched: tunneling, θ = 90°, angular magnetoresistance). No page number is available in the indexed passages. (LLM, conf=0.74)

  cites [270] 270. Liu Y, Yuan X, Zhang C, Jin Z, Narayan A, et al. 2016. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe 5 . Nat. Commun. 7:12516 273. sourceExperimental — accuracy not yet measured

In the paper

“Such linear MR was discovered in a number of materials (276-280) before the establishment of the theory for topological quantum states.”

What the sources say

• ?Not checked — no full text of the sourcecites [276] 276. Hu J, Rosenbaum TF. 2008. Classical and quantum routes to linear magnetoresistance. Nat. Mater 7:697- 700 279. source
• Partly supported

  The Results (p. 6) report linear magnetoresistance in BaFe₂As₂ over a wide field range, making this paper an example of the phenomenon cited. The paper does not establish that this observation preceded the theory of topological quantum states; that timing qualifier is unsupported by our copy. (LLM, conf=0.82)

  cites [277] 277. Kuo H-H, Chu J-H, Riggs SC, Yu L, McMahon PL, et al. 2011. Possible origin of the nonmonotonic doping dependence of the in-plane resistivity anisotropy of Ba(Fe 1-x T x ) 2 As 2 (T = Co, Ni, and Cu). Phys. Rev. B 84:054540 280. sourceExperimental — accuracy not yet measured
• Partly supported

  The discussion on p. 2 says that linear magnetoresistance had been reported in several materials, including Bi and InSb. The paper does not establish when the theory of topological quantum states was developed, so it does not support the claim that those discoveries preceded it. (LLM, conf=0.82)

  cites [278] 278. Huynh KK, Tanabe Y, Tanigaki K. 2011. Both electron and hole Dirac cone states in Ba(FeAs) 2 con- firmed by magnetoresistance. Phys. Rev. Lett. 106:217004 281. sourceExperimental — accuracy not yet measured

In the paper

“This half-integer quantization can also be understood in terms of a Berry phase of π for relativistic fermions and has been observed in graphene (216, 263), zero-gap HgTe quantum wells (266), and 3D topological insulators (264,265).”

What the sources say

• ?Could not verify

  The Introduction (p. 1) discusses graphene’s chiral symmetry, and Theory and Results (p. 3) discusses its effect on impurity scattering. Neither passage addresses half-integer quantization, a Berry phase of π, or observation of that quantization in graphene. Searches for those terms found no supporting passage; the HgTe and topological-insulator observations have separate citations in the citing sentence. (LLM, conf=0.76)

  cites [216] 216. Hwang EH, Das Sarma S. 2008. Single-particle relaxation time versus transport scattering time in a two-dimensional graphene layer. Phys. Rev. B 77:195412 219. sourceExperimental — accuracy not yet measured
• Supported

  The paper reports quantized Hall conductance in a strained 3D HgTe topological insulator (Summary, p. 3). It also gives the half-integer Hall conductance of each Dirac surface state and explains that the two surfaces produce the observed odd-integer plateaus (p. 2). This supports the part of the citing sentence attributed to this source: the observation in a 3D topological insulator. (LLM, conf=0.91)

  cites [263] 263. Brüne C, Liu CX, Novik EG, Hankiewicz EM, Buhmann H, et al. 2011. Quantum Hall effect from the topological surface states of strained bulk HgTe. Phys. Rev. Lett. 106:126803 266. source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [266] 266. Schumann T, Galletti L, Kealhofer DA, Kim H, Goyal M, Stemmer S. 2018. Observation of the quan- tum Hall effect in confined films of the three-dimensional Dirac semimetal Cd 3 As 2 . Phys. Rev. Lett. 120:016801 269.

In the paper

“The topological nontrivial states in half-Heusler compounds attracted significant attention even before the discoveries of topological semimetals (108,(295)(296)(297).”

What the sources say

• Partly supported

  The reference list (p. 6) cites a 2014 study of GdBiPt as a candidate topological insulator, preceding the 2015 Weyl-semimetal discovery cited there. This supports earlier interest in a half-Heusler topological state, but the paper does not establish that such states had attracted significant attention across half-Heusler compounds. (LLM, conf=0.76)

  cites [108] 108. Hirschberger M, Kushwaha S, Wang Z, Gibson Q, Liang S, et al. 2016. The chiral anomaly and ther- mopower of Weyl fermions in the half-Heusler GdPtBi. Nat. Mater 15:1161-65 110. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [295] 295. Al-Sawai W, Lin H, Markiewicz RS, Wray LA, Xia Y, et al. 2010. Topological electronic structure in half-Heusler topological insulators. Phys. Rev. B 82:125208 298. source
• ?Not checked — no full text of the sourcecites [296] 296. Suzuki T, Chisnell R, Devarakonda A, Liu YT, Feng W, et al. 2016. Large anomalous Hall effect in a half-Heusler antiferromagnet. Nat. Phys. 12:1119-23 299. source

In the paper

“In condensed matter, this charge pumping process is finally relaxed by inter-Weyl node scattering, and a steady state is reached, with a chiral current j c ∝ BE • Bτ int , where τ int is the internode relaxation time (10,11,53).”

What the sources say

• Supported

  Section 2, “The chiral anomaly,” says that pumping between Weyl nodes is balanced by inter-Weyl-node scattering, producing a finite steady-state density difference. It then gives the resulting chiral current as j_c ∝ B(E·B)τ_a, with τ_a governing internode relaxation. No page number is provided in the supplied passage. (LLM, conf=0.95)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 source
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source
• Supported

  On p. 1, the paper defines τ as the inter-valley scattering time and says the collision integral includes only inter-valley scattering. On p. 2 it describes anomaly-driven pumping proportional to E·B and a stationary solution; on p. 3 it says the resulting current is proportional to τ, parallel to B, and responds only to the component of E parallel to B. Together these support the stated proportionality. (LLM, conf=0.88)

  cites [53] 53. Son DT, Spivak BZ. 2013. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88:104412 source

In the paper

“Such electric field-driven motion leads to electron pumping between Weyl nodes with a rate ∝ -E • B (10,11,53), which results in imbalanced population of carriers between the two zeroth LLs of the paired Weyl cones.”

What the sources say

• Supported

  In “The chiral anomaly” (pp. 11–12), the paper describes opposite Weyl nodes as sources and sinks of electrons under electric and magnetic fields. It explains that their zeroth Landau levels carry electrons in opposite directions and that chiral pumping produces a density imbalance proportional to E·B. The sign of the pumping rate depends on which node’s population is being tracked. (LLM, conf=0.92)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 source
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source
• Supported

  On p. 2, the paper describes spectral flow carrying electrons between Dirac points and identifies an E·B-proportional term in the valley particle-number equation. On p. 3, it says electric and magnetic fields create an imbalance of electron populations and identifies the two valleys with opposite chiral branches of the zeroth Landau level. The prose in our copy does not specify a universal minus sign; the pumping direction depends on the valley convention. (LLM, conf=0.87)

  cites [53] 53. Son DT, Spivak BZ. 2013. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88:104412 source

In the paper

“A large intrinsic AHE and a giant anomalous Hall angle were recently reported in FM Co 3 Sn 2 S 2 (94,292), for which the existence of Weyl fermions has been demonstrated by the observation of surface Fermi arcs (93).”

What the sources say

• ?Could not verify

  Citation (93) is attached to the claim that surface Fermi arcs demonstrate Weyl fermions in Co3Sn2S2. The paper instead reports topological line nodes and drumhead surface states in Co2MnGa (Abstract, pp. 2, 4). Searches for Co3Sn2S2 and its surface Fermi arcs found no passage addressing that claim. (LLM, conf=0.75)

  cites [94] 94. Belopolski I, Sanchez DS, Chang G, Manna K, Ernst B, et al. 2017. A three-dimensional magnetic topo- logical phase. arXiv:1712.09992 [cond-mat.mtrl-sci] sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [292] 292. Felser C, Hirohata A, eds. 2016. Heusler Alloys: Properties, Growth, Applications. Cham, Switz.: Springer Int. 295.
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [93] 93. Wang Q, Xu Y, Lou R, Liu Z, Li M, et al. 2018. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co 3 Sn2S 2 with magnetic Weyl fermions. Nat. Commun. 9:3681

In the paper

“These anomalous transport features have been ascribed to a magnetic Weyl state, which was subsequently demonstrated both theoretically (102) and experimentally (103).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [102] 102. Kuroda K, Tomita T, Suzuki MT, Bareille C, Nugroho AA, et al. 2017. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16:1090-95 104.
• Partly supported

  The paper reports experimental evidence for magnetic Weyl fermions in Mn₃Sn, including transport measurements it describes as strong evidence for a chiral anomaly (p. 1). But it also says strong correlation effects prevented a clear spectroscopic observation of Weyl points and Fermi arcs (p. 7), so calling the magnetic Weyl state experimentally demonstrated is stronger than the source’s conclusion. Citation (103) is attached to the experimental part of the sentence, not the theoretical part. (LLM, conf=0.85)

  cites [103] 103. Cano J, Bradlyn B, Wang Z, Hirschberger M, Ong NP, Bernevig BA. 2017. Chiral anomaly factory: creating Weyl fermions with a magnetic field. Phys. Rev. B 95:161306 105. sourceExperimental — accuracy not yet measured

In the paper

“Aside from this quantum mechanical interpretation based on only the zeroth LL, a semiclassical approach based on the Boltzmann equation also yields the same result; with this approach, this formulism can also be generalized to the semiclassical regime that involves multiple LLs (10,11,53).”

What the sources say

• Supported

  Split into 2 atoms — 2 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 source
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source
• Supported

  Split into 2 atoms — 2 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [53] 53. Son DT, Spivak BZ. 2013. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88:104412 source

In the paper

“The mechanism of this phenomenon is well established (10,11,52,53).”

What the sources say

• Partly supported

  The chiral-anomaly discussion (p. 42) explains a mechanism: parallel electric and magnetic fields pump charge between Weyl nodes, with internode scattering relaxing the imbalance. But the citing sentence does not identify what “this phenomenon” is, and the review cautions (p. 43) that alternative effects can complicate interpretation of the observed magnetoresistance. The copy therefore does not support an unqualified claim that the mechanism of the unspecified phenomenon is well established. (LLM, conf=0.72)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source
• Supported

  The Introduction (p. 1) explains the chiral-anomaly mechanism for enhanced longitudinal magnetoconductivity in Weyl metals. Section III (p. 3) calls the resulting negative magnetoresistance a known result, supporting the claim if that is the phenomenon the citing sentence refers to. (LLM, conf=0.83)

  cites [52] 52. Jho Y-S, Kim K-S. 2013. Interplay between interaction and chiral anomaly: anisotropy in the electrical resistivity of interacting Weyl metals. Phys. Rev. B 87:205133 source

In the paper

“In this case, the AHE is purely intrinsic and tunable by the separation of paired Weyl nodes (54).”

What the sources say

• Supported

  The paper states that the AHE in a ferromagnetic Weyl metal is purely intrinsic when the Fermi energy is sufficiently close to the Weyl nodes (p. 1). It also identifies K as the distance between the paired nodes in its expression for the Hall conductivity and says the conductivity takes that value under the stated Fermi-energy condition (p. 4). (LLM, conf=0.92)

  cites [54] 54. Burkov AA. 2014. Anomalous Hall effect in Weyl metals. Phys. Rev. Lett. 113:187202 source

In the paper

“An incomplete list includes Co-based Heusler alloys Co 2 XZ (X = IVB or VB; Z = IVA or IIIA) (95)(96)(97)(98)(99), half-metallic Co 3 Sn 2 S 2 (93,94,292), half-Heusler compounds RPtBi (R = Gd and Nd) with AFM orders (108-110), and the chiral antiferromagnets MnSn 3 and MnGe 3 (102, 103).”

What the sources say

• Supported

  The citation is attached to the Co-based Heusler-alloy item, not the other materials in the list. The paper’s Abstract identifies Co2TiX (X = Si, Ge, or Sn) as full Heusler compounds, providing an example of the cited Co2XZ family. (LLM, conf=0.93)

  cites [95] 95. Chang G, Xu S-Y, Zheng H, Singh B, Hsu C-H, et al. 2016. Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half-metallic Heusler Co 2 TiX (X = Si, Ge, or Sn). Sci. Rep. 6:38839 source
• Supported

  The citation to this paper is attached to the Co-based Heusler-alloy entry, not the later entries in the list. On p. 2, the paper proposes XCo₂Z compounds with X = IVB or VB and Z = IVA or IIIA as Weyl-metal candidates; this matches the cited entry despite the citing sentence's different ordering of the formula. (LLM, conf=0.91)

  cites [96] 96. Wang Z, Vergniory MG, Kushwaha S, Hirschberger M, Chulkov EV, et al. 2016. Time-reversal- breaking Weyl fermions in magnetic Heusler alloys. Phys. Rev. Lett. 117:236401 source
• Supported

  The citation is attached to the Co₂XZ entry, not to the other materials in the list. The Introduction identifies Co₂TiSn as a Co₂-based Heusler compound, providing an example with Ti as X and Sn as Z. (LLM, conf=0.92)

  cites [97] 97. Ernst B, Sahoo R, Sun Y, Nayak J, Muechler L, et al. 2017. Manifestation of the Berry curvature in Co 2 TiSn Heusler films. arXiv:1710.04393 [cond-mat.mtrl-sci] source

In the paper

“The intrinsic AHE current is dissipationless (55,56,284,289) and fully spin polarized (289-291) and therefore has great potential for spintronic applications.”

What the sources say

• ?Not checked — no full text of the sourcecites [55] 55. Karplus R, Luttinger JM. 1954. Hall effect in ferromagnetics. Phys. Rev. 95:1154-60 source
• Partly supported

  On p. 1, Haldane describes the intrinsic Hall conductivity as dissipationless, supporting that part of the sentence. The paper does not say the current is fully spin polarized or discuss its potential for spintronic applications. (LLM, conf=0.88)

  cites [56] 56. Haldane FDM. 2004. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93:206602 sourceExperimental — accuracy not yet measured
• Partly supported

  The discussion of symmetry and Hall response (p. 26) says the Hall response does not produce dissipation, and Future challenges and perspectives (p. 49) says the dissipationless nature of anomalous Hall current will manifest in the quantized AHE. The cited review does not establish that intrinsic AHE current is fully spin polarized; its spin-current discussion (p. 50) instead describes the spin Hall effect as a generalization of AHE. (LLM, conf=0.84)

  cites [284] 284. Berger L. 1970. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2:4559-66 287. sourceExperimental — accuracy not yet measured

In the paper

“As mentioned in Section 3.3, these materials are zerogap semiconductors, and their Weyl points are believed to be caused by external field-induced Zeeman splitting (109) or by the exchange field from 4f electrons (110).”

What the sources say

• Supported

  The Abstract links magnetism in GdPtBi and NdPtBi to their 4f electrons and says exchange-field band splitting forms Weyl points. The discussion ('A B') attributes the effect to field-aligned antiferromagnetic magnetization producing a large exchange field, rather than simple external-field-induced Zeeman splitting. This supports the mechanism attributed to citation (110). (LLM, conf=0.92)

  cites [109] 109. Shekhar C, Nayak AK, Singh S, Kumar N, Wu S-C, et al. 2016. Observation of chiral magneto-transport in RPtBi topological Heusler compounds. arXiv:1604.01641 [cond-mat.mtrl-sci] 111. source
• ?Could not verify

  The introduction (p. 1) discusses predicted Weyl points in WTe₂, and the summary (p. 4) reports Fermi arcs. Neither passage describes these materials as zero-gap semiconductors or attributes their Weyl points to Zeeman splitting or a 4f-electron exchange field; searches for both proposed mechanisms found no supporting passage in our copy. (LLM, conf=0.77)

  cites [110] 110. Wu Y, Mou D, Jo NH, Sun K, Huang L, et al. 2016. Observation of Fermi arcs in type-II Weyl semimetal candidate WTe 2 . Phys. Rev. B 94:121113(R) 112. sourceExperimental — accuracy not yet measured

In the paper

“However, a saturation behavior is seen in Na 3 Bi (Figure 8c), which is attributed to the field-dependent internode relaxation time in the quantum limit (105).”

What the sources say

• ?Could not verify

  The Results section (Negative MR under B//E; page unavailable) mentions negative magnetoresistance in Na3Bi, but does not describe its saturation or attribute it to a field-dependent internode relaxation time. The Discussion (page unavailable) addresses the quantum limit in Cd3As2 nanowires, not that proposed explanation for Na3Bi. Searches for saturation and internode relaxation found no passage addressing the claim. (LLM, conf=0.74)

  cites [105] 105. Li C-Z, Wang L-X, Liu H, Wang J, Liao Z-M, Yu D-P. 2015. Giant negative magnetoresistance induced by the chiral anomaly in individual Cd 3 As 2 nanowires. Nat. Commun. 6:10137 107. sourceExperimental — accuracy not yet measured

In the paper

“The PHE, a well-known phenomenon observed in ferromagnets, is due to the resistivity anisotropy caused by anisotropic magnetization (316).”

What the sources say

• ?Could not verify

  The paper discusses the quantum spin Hall effect in graphene (p. 1) and spin-filtered edge transport (p. 3). Searches for the planar Hall effect and anisotropic magnetoresistance found no passage addressing resistivity anisotropy caused by magnetization in ferromagnets. (LLM, conf=0.76)

  cites [316] 316. Kane CL, Mele EJ. 2005. Z 2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95:146802 319. sourceExperimental — accuracy not yet measured

In the paper

“Although topological semimetals have the same in-plane angular dependence in Hall resistivity ρ xy as do ferromagnets, the PHE in topological semimetals occurs in the absence of magnetic order, with a significantly enhanced amplitude (309,310).”

What the sources say

• Supported

  On p. 3, Burkov says the topological-metal PHE has the standard form known from ferromagnetic metals. The same passage states that it requires no magnetic order and that its magnitude can be extremely large, whereas the effect in ferromagnets is typically very weak. (LLM, conf=0.91)

  cites [309] 309. Li P, Zhang CH, Zhang JW, Wen Y, Zhang XX. 2018. Giant planar Hall effect in the Dirac semimetal ZrTe 5-δ . Phys. Rev. B 98:121108(R) 312. source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [310] 310. Li H, Wang H-W, He H, Wang J, Shen S-Q. 2018. Giant anisotropic magnetoresistance and planar Hall effect in the Dirac semimetal Cd 3 As 2 . Phys. Rev. B 97:201110 313.

In the paper

“[which was predicted to be 100 meV (72) and found to be 55 ± 20 meV for MBE-grown samples (73)].”

What the sources say

• Supported

  The citation to this paper (73) is attached to the measured value, not the separate 100 meV prediction cited as (72). The paper reports a 55 ± 20 meV bulk bandgap in intrinsic monolayer 1T′-WTe₂, and its Thin-film growth section states that the films were grown by MBE. (LLM, conf=0.94)

  cites [72] 72. Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z, et al. 2017. Quantum spin Hall state in monolayer 1T -WTe 2 . Nat. Phys. 13:683-87 source
• ?Could not verify

  Citation (73) is attached to the reported 55 ± 20 meV measurement in MBE-grown samples; the 100 meV prediction has a separate citation. The Methods description (p. 2) says this paper used exfoliated WTe2, and its discussion (p. 7) considers a possible small bulk gap without giving a measured value. Searches for “55 ± 20 meV,” “MBE,” and “band gap” found no passage reporting the attributed measurement. (LLM, conf=0.76)

  cites [73] 73. Fei Z, Palomaki T, Wu S, Zhao W, Cai X, et al. 2017. Edge conduction in monolayer WTe 2 . Nat. Phys. 13:677-82 sourceExperimental — accuracy not yet measured

In the paper

“However, the extension of the 2D Chern insulator to 3D cannot produce a strong 3D Chern insulator.Instead, this development results in a metallic phase: the topological semimetal (76).”

What the sources say

• Partly supported

  Section 2 (page unavailable) describes a multilayer that becomes a Weyl semimetal when time-reversal symmetry is broken near a phase transition. But it also says that, at higher spin splitting, the resulting state is a 3D quantum anomalous Hall insulator. The paper therefore supports a conditional route to a semimetal, not the claim that extending a 2D Chern insulator to 3D necessarily produces one; it does not address the stated impossibility of a strong 3D Chern insulator. (LLM, conf=0.84)

  cites [76] 76. Burkov AA. 2015. Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27:113201 sourceExperimental — accuracy not yet measured

In the paper

“From the experimental aspect, QSHIs and QAHIs are expected to display unusual nonlocal transport (320,321).”

What the sources say

• Partly supported

  The Introduction (p. 2) describes helical edge states in quantum spin Hall systems and the resulting nondissipative electronic transport. It does not say that transport is nonlocal or extend that expectation to quantum anomalous Hall insulators. (LLM, conf=0.72)

  cites [320] 320. Xu Q, Song Z, Nie S, Weng H, Fang Z, Dai X. 2015. Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure. Phys. Rev. B 92:205310 323. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [321] 321. Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS. 2012. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol 7:699-712 324. source

In the paper

“With TRS, the Chern number must vanish, but another topological invariant, the Z 2 number, can be introduced to clarify the 2D insulators, becoming 0 for trivial insulators and 1 for a symmetry-protected topological insulator (QSHI) (318).”

What the sources say

• Partly supported

  The discussion of the quantum spin Hall state (p. 1) distinguishes a trivial insulator from a topologically nontrivial QSH insulator whose edge states are protected by time-reversal symmetry. Our copy does not state that time-reversal symmetry forces the Chern number to vanish or that a Z₂ invariant assigns these phases the values 0 and 1; searches for those terms found no such passage. (LLM, conf=0.85)

  cites [318] 318. Roth A, Brüne C, Buhmann H, Molenkamp LW, Maciejko J, et al. 2009. Nonlocal transport in the quantum spin Hall state. Science 325:294-97 321. sourceExperimental — accuracy not yet measured

In the paper

“Apparently, the magnetic field necessary to produce an integer quantum Hall system is no longer needed for a QSHI system (76,79), as the magnetic field is cancelled out when the time-reversal copies of integer quantum Hall systems are brought together.”

What the sources say

• ?Could not verify

  The passages in §3.3 (page unavailable) describe cancellation between Landau-level contributions in a Weyl semimetal, not cancellation of magnetic fields when time-reversal copies of integer quantum Hall systems are combined. Searches for quantum spin Hall insulators, QSHI, and time-reversal copies found no passage in our copy addressing the attributed explanation. (LLM, conf=0.74)

  cites [76] 76. Burkov AA. 2015. Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27:113201 sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction (p. 2) discusses quantum spin Hall materials, and section IIIB (p. 9) describes a time-reversal-symmetry-breaking quantum anomalous Hall state. Neither passage explains a quantum spin Hall insulator as combined time-reversal copies of integer quantum Hall systems whose magnetic fields cancel. Searches for that mechanism and for the claimed lack of a required magnetic field found no passage addressing it. (LLM, conf=0.67)

  cites [79] 79. Bansil A, Lin H, Das T. 2016. Topological band theory. Rev. Mod. Phys. 88:021004 sourceExperimental — accuracy not yet measured

In the paper

“For a rhombohedral 1T phase with ABC stacking (Figure 10e), the structure is unstable and undergoes a spontaneous lattice distortion to the 1T phase (Figure 10f ), which consequently leads to a QSHI state in the presence of SOC (72).”

What the sources say

• Supported

  The crystal-structure passage (indexed as Abstract; page not provided) describes ABC-stacked 1T-WTe₂ as unstable in free-standing form and says it spontaneously distorts. Figure 1 and the accompanying band-structure discussion identify the resulting phase as 1T′-WTe₂ and explain that distortion induces band inversion while spin-orbit coupling opens the bulk gap associated with the quantum spin Hall state. (LLM, conf=0.90)

  cites [72] 72. Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z, et al. 2017. Quantum spin Hall state in monolayer 1T -WTe 2 . Nat. Phys. 13:683-87 source

In the paper

“Although the interlayer coupling in WHMs is not van der Waals type (322, 327), the weak coupling strength in some WHMs allows for mechanical exfoliation, as has been demonstrated (156).”

What the sources say

• ?Could not verify

  The cited portion of the sentence concerns mechanical exfoliation of weakly coupled WHMs. Our copy instead reports measurements of the quantum spin Hall state in HgTe quantum wells (p. 1); searches for mechanical exfoliation, weak interlayer coupling, and van der Waals bonding found no passage addressing that demonstration. (LLM, conf=0.76)

  cites [322] 322. König M, Wiedmann S, Brüne C, Roth A, Buhmann H, et al. 2007. Quantum spin Hall insulator state in HgTe quantum wells. Science 318:766-70 325. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction (p. 1) discusses quantum anomalous Hall models and superconducting proximity effects, not mechanical exfoliation of WHMs. A search for mechanical exfoliation, WHMs, and van der Waals interlayer coupling found no passage addressing the claim; the paper’s discussion of interlayer tunneling (section B, p. 4) concerns a different model. (LLM, conf=0.77)

  cites [327] 327. Liu X, Wang Z, Xie XC, Yu Y. 2011. Abelian and non-Abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect. Phys. Rev. B 83:125105 330. sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [156] 156. Chen C, Xu X, Jiang J, Wu SC, Qi YP, et al. 2017. Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M = Hf, Zr). Phys. Rev. B 95:125126 159.

In the paper

“Such gap closing leads to a topological phase transition to a trivial phase; this transition occurs very rapidly and can thus be used for topological field effect transistors (72).”

What the sources say

• ?Could not verify

  The discussion of Figure 1 (section labeled Abstract; page unavailable) describes a lattice-distortion-driven transition from a trivial to a nontrivial phase, followed by a gap opening due to spin-orbit coupling. Searches for electric-field-induced gap closing and rapid transistor switching found no passage addressing the claimed transition to a trivial phase. (LLM, conf=0.76)

  cites [72] 72. Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z, et al. 2017. Quantum spin Hall state in monolayer 1T -WTe 2 . Nat. Phys. 13:683-87 sourceExperimental — accuracy not yet measured

In the paper

“For example, upon sweeping the gate voltage, a conductance plateau associated with the 1D edge state of a QSHI is observed in a WTe 2 monolayer (Figure 10g) but is absent in bilayer or few-layer samples (74,75).”

What the sources say

• Partly supported

  The main text (p. 2) reports a gate-voltage-dependent conductance plateau in monolayer WTe2 and attributes it to edge conduction. The introduction (p. 1) says the monolayer’s insulating interior and conducting edges differ from its multilayer counterparts, but our copy does not establish that the plateau is absent specifically in bilayer or few-layer samples. (LLM, conf=0.86)

  cites [74] 74. Wu S, Fatemi V, Gibson QD, Watanabe K, Taniguchi T, et al. 2018. Observation of the quantum spin Hall effect up to 100 Kelvin in a monolayer crystal. Science 359:76-79 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [75] 75. Weng H, Yu R, Hu X, Dai X, Fang Z. 2015. Quantum anomalous Hall effect and related topological electronic states. Adv. Phys. 64:227-82 source

In the paper

“Furthermore, under one proposal, the horizontal electric field may break the inversion symmetry and may induce strong Rashba splitting of the bands near E F , which closes the bulk gap at some critical electric fields.”

What the sources say

• ?Could not verify

  The band-structure passage (section labelled Abstract; page unavailable) attributes symmetry breaking to lattice distortion and bulk-gap opening to spin–orbit coupling. Searches for electric fields, Rashba splitting, and critical-field gap closure found no passage addressing the proposed field-induced mechanism. The reported gap under the studied conditions does not contradict a possible closure under an applied field. (LLM, conf=0.76)

  cites [72] 72. Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z, et al. 2017. Quantum spin Hall state in monolayer 1T -WTe 2 . Nat. Phys. 13:683-87 sourceExperimental — accuracy not yet measured

In the paper

“However, for a QSHI with time-reversed spin-polarized edge states, the spin of the emitted electrons has half probability to be reversed, corresponding to the back-moving edge channel with opposite spin.Therefore, a finite resistance depending on the number and configuration of contacts can be expected (320, 321).”

What the sources say

• Partly supported

  Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

  cites [320] 320. Xu Q, Song Z, Nie S, Weng H, Fang Z, Dai X. 2015. Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure. Phys. Rev. B 92:205310 323. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [321] 321. Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS. 2012. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol 7:699-712 324. source

In the paper

“For the material aspect, such a system should be stable in the ambient environment and have minimal defects (10,11).”

What the sources say

• Partly supported

  The discussion of Dirac semimetals (p. 30) warns that disorder can introduce additional effects, supporting a preference for fewer defects. The design criteria (p. 20) call for a stable lattice structure, but do not say that the material should remain stable in the ambient environment. (LLM, conf=0.76)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source

In the paper

“An ideal model system should contain only the topological band(s), with the same types of Dirac or Weyl points being symmetrically related, located at the Fermi energy level, and well separated in momentum space.”

What the sources say

• Partly supported

  In “Non-centrosymmetric Weyl semimetals” (p. 27), the review favors simpler systems with Weyl nodes at the Fermi level and large momentum and energy separations from other bands; it also says non-symmetry-equivalent sets complicate measurements. This supports much of the proposed ideal, but the passage concerns Weyl semimetals and does not say an ideal Dirac or Weyl system should contain only topological bands. (LLM, conf=0.84)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source

In the paper

“As previous reviews have noted (10,11), one challenge in this field is the experimental realization of ideal model systems like graphene (10) or the hydrogen atom (11) for various types of topological semimetal phases.”

What the sources say

• Supported

  The Concluding Remarks (p. 53) explicitly identify finding a truly ideal Weyl semimetal—the ‘graphene’ of Weyl semimetals—as an outstanding goal, and say all known realizations fall short. The ‘hydrogen atom’ analogy is attributed to the other citation, not this source. (LLM, conf=0.92)

  cites [10] 10. Armitage NP, Mele EJ, Vishwanath A. 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001 source
• ?Not checked — no full text of the sourcecites [11] 11. Bernevig A, Weng H, Fang Z, Dai X. 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001 source

In the paper

“As mentioned above, a QAHI system is in principle similar to the integer quantum Hall system, but the former occurs without an external magnetic field and LLs (76,79) and thus carries great promise for possible applications in spintronics.”

What the sources say

• Partly supported

  Section 2 (page unavailable) identifies a three-dimensional quantum anomalous Hall insulator with quantized Hall conductivity, supporting the claim's basic characterization. The passages found do not make the comparison with the integer quantum Hall system, explicitly say that the insulator occurs without an external magnetic field or Landau levels, or discuss spintronics applications. (LLM, conf=0.79)

  cites [76] 76. Burkov AA. 2015. Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27:113201 sourceExperimental — accuracy not yet measured
• Partly supported

  Section IIIB (p. 9) describes a quantum anomalous Hall insulator as a state driven by magnetic exchange energy, consistent with a Hall state that does not require an external field. Our copy does not explicitly compare it with the integer quantum Hall system or state that it occurs without Landau levels. The spintronics promise follows the citation in the citing sentence and appears to be the citing authors’ own conclusion. (LLM, conf=0.78)

  cites [79] 79. Bansil A, Lin H, Das T. 2016. Topological band theory. Rev. Mod. Phys. 88:021004 sourceExperimental — accuracy not yet measured

In the paper

“The topological Dirac semimetals (DSMs) (12)(13)(14) and Weyl semimetals (WSMs) (2,(15)(16)(17)(18)(19)(20)(21)(22)(23) are crystalline solids whose low-energy electronic excitations resemble the Dirac (24) and Weyl (15) fermions in high-energy particle physics, respectively.”

What the sources say

• ?Not checked — no full text of the sourcecites [24] 24. Dirac PAM. 1928. The quantum theory of the electron. Proc. R. Soc. A 117:610-24 source
• ?Not checked — no full text of the sourcecites [15] 15. Weyl H. 1929. Elektron und Gravitation. I. Z. Phys. 56:330-52 source

In the paper

“The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermions.”

In the paper

“The compensating electron and hole carriers further cause nonsaturating magnetoresistance (MR) (46)(47)(48) and magnetothermopower (49)(50)(51).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (46)(47)(48)
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites (49)(50)(51)

In the paper

“Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated.”

In the paper

“High mobility is another signature accompanied with large MR in topological semimetals.”

In the paper

“In a DSM, two doubly degenerate bands cross to form a Dirac node and disperse linearly in all three momentum directions away from the node.”

In the paper

“Large MR is a common signature often seen in most DSMs and WSMs.”

In the paper

“Equation 3indicates that ρ xx tends to saturate at high fields where the B 2 terms dominate.Only when n e = n h , i.e., the case of electron-hole compensation, ρ xx ∝ B 2 without saturation.”

In the paper

“In a WSM, two singly degenerate bands cross at discrete points, i.e., Weyl nodes, and disperse linearly in all three momentum space directions away from each Weyl node (Figure 1a).”

In the paper

“The relativistic nature of the Dirac and Weyl fermions in topological semimetals manifests in many distinct transport properties, including extremely large MR, high mobility, light effective mass, nontrivial Berry phase, the chiral anomaly, and the AHE.”

In the paper

“Weyl fermions have distinct chiralities that are either left handed or right handed.”

In the paper

“In fact, the two-band model already yields reasonable results for a variety of material systems, so it is reasonable to extend its application to topological semimetals.”

In the paper

“Type I WSMs have untilted or weakly tilted Weyl cones with a point-like Fermi surface when the chemical potential is placed at the Weyl node.”

In the paper

“Each Dirac node can be viewed as a pair of degenerate Weyl nodes of opposite chiralities.”

In the paper

“The chiralities of the Weyl nodes give rise to chiral charges, which can be understood as monopoles and antimonopoles of Berry flux in momentum space.”

In the paper

“According to current theoretical understanding, Dirac nodes are not associated with any nontrivial topological invariant (i.e., they have zero chiral charge) (144).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [144] 144. Fang C, Chen Y, Kee H-Y, Fu L. 2015. Topological nodal line semimetals with and without spin-orbital coupling. Phys. Rev. B 92:081201 147.

In the paper

“Such high transport mobility is consistent with the ultralow residual resistivity at the zero-temperature limit (∼n to a few μ ; see Table 1) as well as with the high quantum mobility revealed by quantum oscillation studies (discussed in Section 3.2.2).”

In the paper

“Quantum oscillation originates from the quantized cyclotron motion of charge carriers under magnetic fields, i.e., the Landau quantization of the energy states.”