Transport of Topological Semimetals

In the paper

“Further studies also found that, in the classical limit characterized by ω c τ 1 (as opposed to the quantum limit or semiclassical limit, where ω c τ 1, where ω c is the cyclotron frequency and τ is the transport relaxation time), negative longitudinal MR in type II WSMs becomes isotropic, similar to that in type I semimetals (303, 308).”

What the sources say

• ?Not matched

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

  cites [303] 303. Reis RDd, Ajeesh MO, Kumar N, Arnold F, Shekhar C, et al. 2016. On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance. New J. Phys. 18:085006 306.
• Disputed

  The paper finds negative longitudinal magnetoresistance in type-II Weyl semimetals for magnetic fields in any direction, but it does not find it isotropic. Section III (p. 4) reports a direction-dependent response in the low-field quasiclassical regime: magnetoconductivity is approximately linear in the field along the tilt axis and quadratic perpendicular to it, for both type-I and type-II semimetals. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  cites [308] 308. Nandy S, Sharma G, Taraphder A, Tewari S. 2017. Chiral anomaly as the origin of the planar Hall effect in Weyl semimetals. Phys. Rev. Lett. 119:176804 311. sourceExperimental — accuracy not yet measured

In the paper

“Because of linear dispersion and spin (pseudospin) momentum locking, low-energy electrons in topological semimetals are highly robust against crystalline disorder and imperfections, leading to very high electron mobilities (45,46).”

What the sources say

• Partly supported

  The main text (p. 1) reports that suppressed backscattering in Cd3As2 produces ultrahigh mobility, and the supplement (S5, p. 11) says lattice disorder has little effect on forward drift. But the authors call the protection mechanism unknown; they do not establish linear dispersion or spin/pseudospin momentum locking as its cause, or show the result generally for topological semimetals. (LLM, conf=0.90)

  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
• Partly supported

  The Abstract says Weyl and Dirac semimetals usually have very high mobilities and suggests a link to their electronic dispersion. The transport discussion (section labelled “14.5 T; refs”; page unavailable) attributes NbP’s ultrahigh mobility to large Fermi velocity and low effective mass. Our copy does not attribute that mobility to spin or pseudospin momentum locking or establish robustness against crystalline disorder and imperfections. (LLM, conf=0.87)

  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 sourceExperimental — accuracy not yet measured

In the paper

“The Fermi arcs also lead to unusual quantum cyclotron orbits (the Weyl orbits) as observed in quantum oscillation measurements (43,44).”

What the sources say

• Partly supported

  The Abstract describes unusual closed magnetic orbits involving Fermi arcs, and the Quantum oscillations section predicts that they produce periodic oscillations. The paper presents semiclassical analysis and numerical simulation, not an observation in quantum oscillation measurements; the Discussion calls the signatures experimentally testable. (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 sourceExperimental — accuracy not yet measured
• Partly supported

  The paper reports Shubnikov–de Haas oscillations in Cd3As2 consistent with Weyl orbits involving Fermi-arc surface states (p. 1), and says the measured oscillation frequency agrees with the Weyl-orbit prediction (p. 2). But it does not establish an unqualified observation of Weyl orbits: on p. 4, it says the experiments cannot rule out another origin for the oscillations. (LLM, conf=0.84)

  cites [44] 44. Moll PJW, Nair NL, Helm T, Potter AC, Kimchi I, et al. 2016. Transport evidence for Fermi-arc- mediated chirality transfer in the Dirac semimetal Cd 3 As 2 . Nature 535:266-70 sourceExperimental — accuracy not yet measured

In the paper

“The application of parallel electric and magnetic fields can break the apparent conservation of the chiral charge (10,11,52,53).”

What the sources say

• Supported

  In §2, “The chiral anomaly,” the paper says parallel electric and magnetic fields pump charge between opposite Weyl nodes, so the electron density at each node is not conserved. It distinguishes this loss of nodal—or chiral—charge conservation from total electric charge, which remains conserved. (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
• ?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

  Section II (p. 2) explicitly states that when electric fields are applied parallel to magnetic fields, the chiral current is not conserved. The Introduction (p. 1) explains that this is the chiral anomaly: a classically conserved current ceases to be conserved at the quantum level. (LLM, conf=0.95)

  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
• Supported

  On p. 2, the paper states that in electric and magnetic fields the particle number in an individual valley is not conserved, even without inter-valley scattering, and identifies this as the chiral anomaly. It specifies a term proportional to E · B, which applies when the fields are parallel. The claim concerns chiral charge, not total electric charge. (LLM, conf=0.93)

  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

“In contrast to high-energy physics, solid-state crystals can support band crossings beyond the Dirac/Weyl paradigm (31)(32)(33)(34)(35)(36).These band crossings, broadly referred as unconventional fermions, include three-, four-, six-, and eightfold degeneracies (31).”

What the sources say

• ?Not matched

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

  cites (31)(32)(33)(34)(35)(36)
• Supported

  The paper’s A. Notation section (p. 11) explicitly describes fermions beyond the Weyl and Dirac paradigm and identifies 3-, 6-, and 8-band crossings with time-reversal symmetry, as well as 4-band crossings without it. This supports the cited list of degeneracies, with the symmetry condition qualifying the fourfold case. (LLM, conf=0.92)

  cites [31] 31. Bradlyn B, Cano J, Wang Z, Vergniory MG, Felser C, et al. 2016. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353:aaf5037 source

In the paper

“The transverse MR, measured with the field perpendicular to the current direction, can reach up to 0.1-1 million percent at low temperatures (0.5-5 K) and a field of 9 T (see Table 1), without any sign of saturation up to 30-100 T in WSMs/DSMs such as Cd 3 As 2 , PtBi 2 , WTe 2 , and NbP (46,48,171,172).”

What the sources say

• Supported

  The NbP measurements in the “14.5 T; refs” section report transverse MR of 8.5 × 10⁵% at 1.85 K and 9 T. The same section reports that MR continued to increase without a tendency to saturate through 62 T, supporting the part of the multi-citation sentence attributable to this NbP paper. (LLM, conf=0.93)

  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
• Partly supported

  The WTe2 results (p. 3) support a very large transverse magnetoresistance at low temperature, still increasing without saturation at 45 T. They report 452,700% at 4.5 K and 14.7 T, however, not the claimed magnitude at 9 T. This paper does not provide evidence for the other named materials. (LLM, conf=0.88)

  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 paper’s Conclusion (p. 13) discusses density response and Friedel oscillations in two-dimensional Dirac-fermion models, not transverse magnetoresistance. Searches for magnetoresistance, the named materials, and the quoted field strengths and percentages 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
• Partly supported

  The paper reports transverse, nonsaturating magnetoresistance in the Dirac semimetal TlBiSSe (pp. 2, 4) and mentions gigantic magnetoresistance in Cd3As2 (p. 4). It does not support the claimed 0.1–1 million percent at 9 T, nonsaturation up to 30–100 T, or the claims about PtBi2, WTe2, and NbP. For TlBiSSe, it reports almost 10,000% at 14 T and 1.8 K (p. 4). (LLM, conf=0.89)

  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

“However, reports also indicate that carrier compensation is not achieved in some topological semimetals (188,189).”

What the sources say

• ?Not matched

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

  cites [188] 188. Chamber RG. 1990. Electrons in Metals and Semiconductors. New York: Chapman and Hall 191.
• ?Could not verify

  The Introduction (p. 1) and Conclusion (p. 7) describe electron–hole compensation in NbAs. I searched the paper’s discussion of other topological semimetals and carrier densities, but found no passage reporting a topological semimetal in which compensation is not achieved. The NbAs finding does not rule out the claim about other materials. (LLM, conf=0.72)

  cites [189] 189. Luo Y, Ghimire NJ, Wartenbe M, Choi H, Neupane M, et al. 2015. Electron-hole compensation effect between topologically trivial electrons and nontrivial holes in NbAs. Phys. Rev. B 92:205134 192. sourceExperimental — accuracy not yet measured

In the paper

“By contrast, type II WSMs have strongly tilted Weyl cones (Figure 1b) (28).”

What the sources say

• Supported

  The Type II Weyl Semimetals section (p. 2) says the kinetic term tilts the cone-like spectrum and that a Weyl point is type II when the tilt becomes large enough to produce touching electron and hole pockets. Appendix A (p. 4) likewise describes type-II Weyl points as type-I nodes tilted enough along a direction. (LLM, conf=0.94)

  cites [28] 28. Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M, et al. 2015. Type-II Weyl semimetals. Nature 527:495-98 source

In the paper

“DSMs host Dirac fermions as low-energy quasiparticle excitations (12-14, 38, 126-131).”

What the sources say

• Supported

  On p. 1, the paper defines a Dirac semimetal by its linearly dispersing bands at Dirac points and says its Fermi surface consists of those point-like degeneracies. It also describes the effective Hamiltonian around a 3D Dirac point as a Dirac Hamiltonian, supporting the claim about low-energy Dirac excitations. (LLM, conf=0.91)

  cites [12] 12. Young SM, Zaheer S, Teo JCY, Kane CL, Mele EJ, Rappe AM. 2012. Dirac semimetal in three dimen- sions. Phys. Rev. Lett. 108:140405 source
• ?Not matched

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

  cites [13] 13. Wang Z, Sun Y, Chen X-Q, Franchini C, Xu G, et al. 2012. Dirac semimetal and topological phase transitions in A 3 Bi (A = Na, K, Rb). Phys. Rev. B 85:195320
• ?Not matched

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

  cites [14] 14. Wang Z, Weng H, Wu Q, Dai X, Fang Z. 2013. Three-dimensional Dirac semimetal and quantum transport in Cd 3 As 2 . Phys. Rev. B 88:125427
• ?Not checked — no full text of the sourcecites [38] 38. Xu S-Y, Liu C, Kushwaha SK, Sankar R, Krizan JW, et al. 2015. Observation of Fermi arc surface states in a topological metal. Science 347:294-98 source
• Supported

  The paper’s opening section (p. 1) states that topological Dirac semimetals possess 3D Dirac fermions in the bulk. It also reports linear dispersions in Na3Bi, supporting the description of those fermions as low-energy electronic excitations. (LLM, conf=0.92)

  cites [126] 126. Liu ZK, Jiang J, Zhou B, Wang ZJ, Zhang Y, et al. 2014. A stable three-dimensional topological Dirac semimetal Cd 3 As 2 . Nat. Mater 13:677-81 129. source
• Supported

  The paper defines 3D Dirac semimetals by linear energy–momentum dispersions crossing at the Fermi level (main text; page unavailable). That supports the paraphrase that their low-energy electronic excitations are Dirac fermions. (LLM, conf=0.90)

  cites [127] 127. Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava RJ. 2014. Experimental real- ization of a three-dimensional Dirac semimetal. Phys. Rev. Lett. 113:027603 130. source
• ?Not checked — no full text of the sourcecites [128] 128. Yi H, Wang Z, Chen C, Shi Y, Feng Y, et al. 2014. Evidence of topological surface state in three- dimensional Dirac semimetal Cd 3 As 2 . Sci. Rep. 4:6106 131. source
• Supported

  The paper defines 3D Dirac semimetals by linear band dispersions that cross at the Fermi level (main text; page not provided). That description supports the paraphrase that their low-energy quasiparticle excitations are Dirac fermions. (LLM, conf=0.90)

  cites [129] 129. Yang B-J, Nagaosa N. 2014. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5:4898 132. source
• Supported

  The paper describes Dirac points in the bulk electronic spectra of proposed three-dimensional materials (p. 1) and gives a low-energy theory at the Fermi surface using Dirac matrices (p. 5). This supports the general statement that Dirac semimetals host Dirac-like low-energy quasiparticle excitations. (LLM, conf=0.91)

  cites [130] 130. Steinberg JA, Young SM, Zaheer S, Kane CL, Mele EJ, Rappe AM. 2014. Bulk Dirac points in distorted spinels. Phys. Rev. Lett. 112:036403 133. source
• Supported

  The Applications section describes a Dirac semimetal whose electronic structure has Dirac cones at the Brillouin-zone face centers. That supports the claim that Dirac semimetals host low-energy Dirac excitations; the copy provides no page number for this passage. (LLM, conf=0.88)

  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. source

In the paper

“while sublinear MR may be attributed to the weak antilocalization caused by strong SOC (196).”

What the sources say

• ?Could not verify

  The paper’s discussion of backscattering and localization in its main text does not connect weak antilocalization to sublinear magnetoresistance or strong spin-orbit coupling. Searches for those terms and for magnetoresistance found no passage in our copy making the claimed attribution; weak antilocalization appears in a reference title, not as the paper’s explanation of sublinear MR. (LLM, conf=0.73)

  cites [196] 196. Beidenkopf H, Roushan P, Seo J, Gorman L, Drozdov I, et al. 2011. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nat. Phys. 7:939-43 199. sourceExperimental — accuracy not yet measured

In the paper

“While both arise from the scattering by static impurities and defects, these two quantities are essentially different (217, 218):”

What the sources say

• ?Could not verify

  Section V (p. 5) defines a lifetime through the Dingle temperature and uses it to estimate surface mobility, but does not distinguish quantum from transport relaxation time. Section III (p. 3) discusses defects and carrier density, not whether both times arise from scattering by static impurities and defects. Searches for the two relaxation times and scattering did not locate the attributed comparison. (LLM, conf=0.72)

  cites [217] 217. Xiong J, Luo Y, Khoo Y, Jia S, Cava RJ, Ong NP. 2012. High-field Shubnikov-de Haas oscillations in the topological insulator Bi 2 Te 2 Se. Phys. Rev. B 86:045314 220. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Fermi-surface discussion (p. 4) reports a Dingle temperature from oscillation damping, but does not compare quantum and transport relaxation times. Searches for relaxation time, scattering, and the claimed distinction found no passage in our copy that addresses it. (LLM, conf=0.74)

  cites [218] 218. Pariari A, Dutta P, Mandal P. 2015. Probing the Fermi surface of three-dimensional Dirac semimetal Cd 3 As 2 through the de Haas-van Alphen technique. Phys. Rev. B 91:155139 221. sourceExperimental — accuracy not yet measured

In the paper

“Such a zero energy can be understood in terms of the Berry phase arising from the cyclotron motion of carriers in momentum space (206).”

What the sources say

• Supported

  In “C. de Haas-van Alphen oscillation” (p. 33), the review explains that a cyclotron orbit near graphene’s Dirac point acquires a Berry phase of π. That phase cancels the usual 1/2 term in the Landau-level quantization rule, yielding a level at zero energy. (LLM, conf=0.93)

  cites [206] 206. Xiao D, Chang M-C, Niu Q. 2010. Berry phase effects on electronic properties. Rev. Mod. Phys. 82:1959- 2007 209. source

In the paper

“Klein tunneling has been demonstrated in graphene, with a potential barrier created by a local gate (257, 258).”

What the sources say

• ?Not checked — no full text of the sourcecites [257] 257. O'Brien TE, Diez M, Beenakker CWJ. 2016. Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal. Phys. Rev. Lett. 116:236401 260. source
• ?Could not verify

  The Methods and Abstract discuss quantum oscillations in Weyl semimetals, not a graphene tunneling experiment. Searches for Klein tunneling and for graphene with a locally gated potential barrier found no passage addressing the claim; page numbers are unavailable in our copy. (LLM, conf=0.76)

  cites [258] 258. Zhang Y, Bulmash D, Hosur P, Potter AC, Vishwanath A. 2016. Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals. Sci. Rep. 6:23741 261. sourceExperimental — accuracy not yet measured

In the paper

“The additional frequencies ascribed to magnetic breakdown have been observed in high-field quantum oscillation studies on several topological semimetals (171,226,252).”

What the sources say

• ?Could not verify

  The paper’s opening summary (p. 1) describes theoretical calculations of excitonic effects, and its Conclusion (p. 13) discusses density response and Friedel oscillations. Searches for magnetic breakdown, high-field quantum oscillations, and topological semimetals found no passage reporting the claimed experimental observations. (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
• Partly supported

  The ZrSnTe results (p. 5) report multiple frequencies in high-field quantum oscillations, supporting the observation of additional frequencies in a topological semimetal. The paper attributes the measured frequencies to topological bands, not magnetic breakdown; a search for “magnetic breakdown” found no passage making that attribution. This source alone also does not establish observations in several semimetals. (LLM, conf=0.84)

  cites [226] 226. Hu J, Zhu Y, Gui X, Graf D, Tang Z, et al. 2018. Quantum oscillation evidence of a topological semimetal phase in ZrSnTe. Phys. Rev. B 97:155101 229. sourceExperimental — accuracy not yet measured
• ?Not matched

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

  cites [252] 252. Ru-Keng S, Siu GG, Xiu C. 1993. Barrier penetration and Klein paradox. J. Phys. A Math. Gen. 26:1001 255.

In the paper

“It has been predicted that under magnetic fields, electrons can transport on a cyclotron orbit that connects one surface Fermi arc to the opposite Fermi arc by coupling to bulk states (Figure 4d) (43,260).”

What the sources say

• Supported

  The Semiclassical analysis passage describes an electron moving along the top-surface Fermi arc, entering a bulk chiral Landau level, reaching the bottom-surface arc, and returning through another bulk mode to complete the orbit. This directly supports the attributed prediction under a magnetic field; the passage does not specify a page number. (LLM, conf=0.94)

  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 Introduction’s Fig. 1b description depicts a magnetic-field-induced Weyl orbit joining Fermi arcs on the top and bottom surfaces through bulk paths. The Results section (‘Extra-quantum oscillation from Weyl orbit’) likewise says bulk Landau levels connect the arcs in type-II WTe2. (LLM, conf=0.93)

  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

“However, multiple oscillation frequencies are often observed in most topological semimetals, such as those of the TaAs family (179, 180, 182, 183, 191-193, 227, 243) and WHM materials with PbFCl-type structure (W = Zr or Hf; H = Si, Ge, or Sn; M = S, Se, or Te) (156,221,222,226,228,232,233,241,242,244,245).”

What the sources say

• Partly supported

  The paper reports Shubnikov–de Haas oscillations in TaP and NbP (p. 4) and FFT-derived frequencies for those TaAs-family materials (p. 6). But the Fig. 4 caption (p. 11) assigns F1 and F2 to different samples; the copy does not establish that multiple frequencies occur in each material or that this is common across most topological semimetals. The WHM example has a separate citation group and is not attributed to this source. (LLM, conf=0.79)

  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. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The NbAs results (pp. 2–4) report Shubnikov–de Haas oscillations and identify a principal frequency of 25 T, but do not establish multiple frequencies. The paper also does not address how often multiple frequencies occur across the TaAs family or WHM materials (searched: multiple oscillation frequencies, 25 T, WHM and PbFCl). (LLM, conf=0.72)

  cites [180] 180. Zhang C-L, Yuan Z, Jiang Q-D, Tong B, Zhang C, et al. 2017. Electron scattering in tantalum monoarsenide. Phys. Rev. B 95:085202 183. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The discussion on p. 4 mentions quantum-oscillation measurements only to compare electron and hole carrier densities in WTe₂. The introduction (p. 1) mentions TaAs but does not discuss its oscillation frequencies. Searches for multiple frequencies and PbFCl-type WHM materials found no passage addressing the attributed claim. (LLM, conf=0.76)

  cites [182] 182. Wang YL, Thoutam LR, Xiao ZL, Hu J, Das S, et al. 2015. Origin of the turn-on temperature behavior in WTe 2 . Phys. Rev. B 92:180402 185. sourceExperimental — accuracy not yet measured
• Supported

  The paper reports two sets of Shubnikov–de Haas oscillation frequencies in TaAs (passage [1], Abstract), supporting its citation as an example from the TaAs family. The separate WHM-materials clause has its own citations and is not attributed to this source. (LLM, conf=0.89)

  cites [183] 183. Zhao Y, Liu H, Yan J, An W, Liu J, et al. 2015. Anisotropic magnetotransport and exotic longitudinal linear magnetoresistance in WTe 2 crystals. Phys. Rev. B 92:041104 186. source
• ?Not matched

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

  cites [191] 191. Du J, Wang H, Mao Q, Khan R, Xu B, et al. 2016. Large unsaturated positive and negative magnetore- sistance in Weyl semimetal TaP. Sci. China Phys. Mech. Astron. 59:657406 194.
• ?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 checked — no full text of the sourcecites [193] 193. Abrikosov AA. 1998. Quantum magnetoresistance. Phys. Rev. B 58:2788-94 196. source
• Partly supported

  The Results report multiple quantum-oscillation frequencies in PdTe₂ and PtTe₂, supporting an example of the phenomenon. The paper does not establish that this is often observed in most topological semimetals; its Introduction mentions the TaAs family in connection with Weyl nodes, not oscillation frequencies, and the cited passages do not address PbFCl-type WHM materials. Page numbers are unavailable in our copy. (LLM, conf=0.86)

  cites [227] 227. Zheng W, Schönemann R, Aryal N, Zhou Q, Rhodes D, et al. 2018. Detailed study of the Fermi surfaces of the type-II Dirac semimetallic candidates XTe 2 (X = Pd, Pt). Phys. Rev. B 97:235154 230. sourceExperimental — accuracy not yet measured
• Supported

  The cited paper supports the WHM example to which this citation is attached: the Dirac Nodal Loop section (p. 3) identifies ZrSiS as having a PbFCl-type structure, and the Abstract (p. 3) reports many Shubnikov–de Haas oscillation frequencies in ZrSiS. It is evidence for this example, not a survey of how often multiple frequencies occur across all topological semimetals. (LLM, conf=0.92)

  cites [243] 243. Pezzini S, van Delft MR, Schoop LM, Lotsch BV, Carrington A, et al. 2018. Unconventional mass enhancement around the Dirac nodal loop in ZrSiS. Nat. Phys. 14:178-83 246. source
• Partly supported

  The paper identifies HfSiS as having the PbFCl structure type (p. 3) and discusses de Haas–van Alphen quantum oscillations in this material family (p. 6). It does not say that multiple oscillation frequencies were observed, so it does not support that part of the claim. (LLM, conf=0.84)

  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

In the paper

“In type II WSMs, the magnetic breakdown has been predicted to be associated with the Klein paradox, which states that the tunneling barrier is nearly”

What the sources say

• ?Could not verify

  The Introduction (p. 3) explains the Klein paradox as transmission through strong repulsive potentials without the usual exponential damping. Our copy does not address type II Weyl semimetals or predict an association between magnetic breakdown and the Klein paradox; searches for those terms found no relevant passage. (LLM, conf=0.76)

  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

“For example, for the NLSM ZrSiS, the effective mass obtained from the fit of the FFT amplitude is greatly increased when a narrower field range is used for the FFT analysis.”

What the sources say

• ?Could not verify

  The paper describes STM measurements of Cd3As2 (p. 1) and Fourier transforms used for quasiparticle-interference maps (p. 8). Searches for ZrSiS and for effective-mass fitting over narrower FFT field ranges found no passage addressing the claimed result. (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

In the paper

“Because the zeroth LL is pinned at E F (269), the quantum limit can be reached in relatively low fields in this material (247).”

What the sources say

• ?Not checked — no full text of the sourcecites [269] 269. Stormer HL, Tsui DC, Gossard AC. 1999. The fractional quantum Hall effect. Rev. Mod. Phys. 71:S298- 305 272. source
• ?Could not verify

  The paper discusses magnetotransport and quantum oscillations in ZrB₂ (pp. 1, 2, 4), but the passages do not address a low-field quantum limit in YbMnBi₂. Searches for YbMnBi₂, the quantum limit, and a zeroth Landau level pinned at the Fermi energy found no supporting passage in our copy. (LLM, conf=0.77)

  cites [247] 247. Wang Q, Guo P-J, Sun S, Li C, Liu K, et al. 2018. Extremely large magnetoresistance and high-density Dirac-like fermions in ZrB 2 . Phys. Rev. B 97:205105 250. sourceExperimental — accuracy not yet measured

In the paper

“Indeed, the magnetic torque anomaly, which has been observed in NbAs, can be quantitatively described by the topological character of the electronic dispersion ( 224).”

What the sources say

• ?Could not verify

  The quantum-oscillation section (pp. 4–5) discusses magnetic-torque measurements and topological bands in ZrSnTe, not a torque anomaly in NbAs. A search for NbAs and a quantitative explanation of its torque anomaly found only a NbAs magnetotransport citation in the references (p. 11). (LLM, conf=0.76)

  cites [224] 224. Hu J, Zhu YL, Graf D, Tang ZJ, Liu JY, Mao ZQ. 2017. Quantum oscillation studies of topological semimetal candidate ZrGeM (M = S, Se, Te). Phys. Rev. B 95:205134 227. sourceExperimental — accuracy not yet measured

In the paper

“In another structurally similar compound, YbMnBi 2 , the zeroth LL was probed via interlayer transport (247).”

What the sources say

• ?Could not verify

  The Introduction (p. 1) and Results and Discussion (pp. 2–5) discuss magnetotransport and electronic structure in TmSb, not YbMnBi2. Searches for YbMnBi2, the zeroth Landau level, and interlayer transport found no passage addressing the claimed probe. (LLM, conf=0.77)

  cites [247] 247. Wang Q, Guo P-J, Sun S, Li C, Liu K, et al. 2018. Extremely large magnetoresistance and high-density Dirac-like fermions in ZrB 2 . Phys. Rev. B 97:205105 250. sourceExperimental — accuracy not yet measured

In the paper

“This has been demonstrated in nanostructures of Cd 3 As 2 (Figure 4e,f ) (44,261) and WTe 2 (262).”

What the sources say

• Supported

  The introduction (p. 1) reports oscillations in focused-ion-beam-prepared Cd3As2 microstructures consistent with Weyl orbits involving chirality transfer. This supports the Cd3As2 nanostructure portion attributed to this source; the sentence cites a different source for WTe2. (LLM, conf=0.90)

  cites [44] 44. Moll PJW, Nair NL, Helm T, Potter AC, Kimchi I, et al. 2016. Transport evidence for Fermi-arc- mediated chirality transfer in the Dirac semimetal Cd 3 As 2 . Nature 535:266-70 source
• ?Could not verify

  The experimental report (p. 1) describes quantum Hall measurements in graphene, not Cd3As2 or WTe2 nanostructures. Searches for both materials in our copy found no passage addressing the attributed demonstrations; the preceding sentence needed to identify what “this” refers to was not provided. (LLM, conf=0.78)

  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 (p. 2) reports a quantum Hall effect in BiSbTeSe2, not in Cd3As2 or WTe2. Searches for Cd3As2, WTe2, and nanostructures found no passage in our copy addressing the claimed demonstrations in those materials. (LLM, conf=0.77)

  cites [262] 262. Xu Y, Miotkowski I, Liu C, Tian J, Nam H, et al. 2014. Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator. Nat. Phys. 10:956-63 265. sourceExperimental — accuracy not yet measured

In the paper

“Another phenomenon directly associated with electron condensation to the zeroth LL in topological semimetals is anomalous magnetization (224).”

What the sources say

• ?Could not verify

  The discussion on p. 2 mentions interlayer quantum tunneling from the zeroth Landau level, while p. 4 reports magnetic-torque oscillations in ZrSnTe. Neither passage links electron condensation into the zeroth Landau level to anomalous magnetization. Searches for that link and for magnetization at the quantum limit found no supporting passage in our copy. (LLM, conf=0.76)

  cites [224] 224. Hu J, Zhu YL, Graf D, Tang ZJ, Liu JY, Mao ZQ. 2017. Quantum oscillation studies of topological semimetal candidate ZrGeM (M = S, Se, Te). Phys. Rev. B 95:205134 227. sourceExperimental — accuracy not yet measured

In the paper

“Another example of unusual transport in the quantum limit due to degeneracy enhancement is the aforementioned quantum tunneling of relativistic fermions in YbMnBi 2 (247).”

What the sources say

• ?Could not verify

  The Introduction (p. 1) and Results and Discussion (p. 5) discuss magnetoresistance in TmSb, attributing it to electron–hole compensation and high carrier mobility. Searches for YbMnBi2, relativistic-fermion tunneling, and degeneracy enhancement in the quantum limit found no passage addressing the cited claim. (LLM, conf=0.76)

  cites [247] 247. Wang Q, Guo P-J, Sun S, Li C, Liu K, et al. 2018. Extremely large magnetoresistance and high-density Dirac-like fermions in ZrB 2 . Phys. Rev. B 97:205105 250. sourceExperimental — accuracy not yet measured

In the paper

“Linear MR has been widely observed in many of the recently reported topological semimetals (45,172,173,175,234,235,(281)(282)(283).”

What the sources say

• Supported

  This paper supplies one example for the sentence’s collective citations: it studies the Dirac semimetal Cd3As2 and reports linear magnetoresistance in its low-mobility samples (p. 2; p. 5). The citation need not establish the claim about many semimetals on its own. (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 source
• Supported

  The Summary (p. 4) reports large linear magnetoresistance in TlBiSSe, which it identifies as a 3D Dirac semimetal. This paper therefore supports the citing sentence as one example among its multiple citations; it need not establish the prevalence claim on its own. (LLM, conf=0.91)

  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 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.

In the paper

“Masuda et al. (177) reported a half-integer QHE in a bulk DSM EuMnBi 2 with a layered structure (Figure 5b).”

What the sources say

• ?Could not verify

  The paper describes Weyl fermions and quantum oscillations in NbP (pp. 1, 3–4). Searches for Masuda, EuMnBi2, and a half-integer quantum Hall effect found no passage addressing the attributed report. (LLM, conf=0.78)

  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

In the paper

“Indeed, a mass enhancement in the quantum limit has been observed for ZrTe 5 (272).”

What the sources say

• ?Could not verify

  The Materials and Methods section (“Calculation of QL”; page unavailable) estimates the quantum-limit field for the authors’ ZrTe5 crystals and says their observed oscillations occur beyond it. It does not report an observed mass enhancement. Searches for “mass enhancement” and enhanced effective mass in the quantum limit found no supporting passage in our copy. (LLM, conf=0.76)

  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

“In real materials, an integer factor may be applied for G 0 due to degeneracy, such as graphene with a factor of 4 that originates from spin and valley degeneracies (216,263).”

What the sources say

• Partly supported

  Section II (p. 4) defines g as the spin and valley degeneracy factor and says that, in general, g = 4 for graphene. The paper applies g to Fermi-wave-vector and screening expressions, but the passages do not say that a factor of 4 is applied to the conductance quantum G₀. (LLM, conf=0.85)

  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
• Partly supported

  Appendix C (p. 5) says that a twofold Landau-level degeneracy in HgTe affects which Hall plateaus appear, supporting the general point that degeneracy matters. The paper mentions graphene in the main text (p. 2), but does not state that graphene has a factor of four arising from spin and valley degeneracies; that specific example is unsupported by this source. (LLM, conf=0.84)

  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. sourceExperimental — accuracy not yet measured

In the paper

“The chiral magnetic effect was first observed in Dirac systems such as Bi 0.97 Sb 0.03 (301), Na 3 Bi (Figure 8c) (105), Cd 3 As 2 (45, 106), and ZrTe 5 (Figure 8d) (107) before the experimental discovery of WSMs.”

What the sources say

• ?Not matched

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

  cites [301] 301. Lv Y-Y, Li X, Zhang B-B, Deng WY, Yao S-H, et al. 2017. Experimental observation of anisotropic Adler-Bell-Jackiw anomaly in type-II Weyl semimetal WTe 1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118:096603 304.
• Partly supported

  The Abstract and Discussion report negative magnetoresistance in Cd3As2 nanowires as evidence of the chiral anomaly, supporting Cd3As2 as an example of the phenomenon. The paper does not establish that this observation preceded the experimental discovery of Weyl semimetals, and it does not explicitly call its Cd3As2 result an observation of the chiral magnetic effect. (LLM, conf=0.84)

  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
• Partly supported

  For the Cd3As2 part of the sentence, the paper reports a weak but distinct negative magnetoresistance term (p. 6). It says further experiments are needed to compare that term meaningfully with the predicted chiral term, so it does not establish an observation of the chiral magnetic effect. The paper also does not establish the sentence’s ‘first’ or pre-WSM chronology. (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

“A TRS-breaking Weyl state has also been predicted or established in many magnetic compounds.”

What the sources say

• Partly supported

  The discussion on p. 3 says Co₂TiSn and several other Heusler compounds had been proposed as candidates for a magnetic topological phase; the references on p. 12 identify predictions of magnetic Weyl states. But the paper does not establish a TRS-breaking Weyl state in many magnetic compounds: it reports line nodes in Co₂MnGa (p. 4) and says few topological magnets had been demonstrated (p. 8). (LLM, conf=0.86)

  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 sourceExperimental — accuracy not yet measured
• Supported

  The paper states on p. 1 that it predicts a series of magnetic Heusler compounds with Weyl points and identifies them as a family of time-reversal-breaking Weyl systems. This supports the claim's 'predicted or established' wording; the paper presents these compounds as predictions, not experimental confirmations. (LLM, conf=0.88)

  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 Introduction states that Co₂-based Heusler compounds were predicted to be ferromagnets with Weyl points and links their properties to broken time-reversal symmetry. The Abstract likewise describes various such compounds, supporting the citing sentence’s broad statement that this state has been predicted in magnetic compounds. (LLM, conf=0.87)

  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 recent observations of the chiral anomaly-a unique feature of Weyl fermions-together with band structure calculations suggest a magnetic field-driven Weyl state in AFM RPtBi (109,110).”

What the sources say

• Supported

  The A B section says applied fields align magnetization in AFM GdPtBi and NdPtBi, producing an exchange field that establishes Weyl nodes. It also links calculations of those nodes to chiral-anomaly-induced negative magnetoresistance. Together, these passages support the claimed field-driven Weyl state. (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
• ?Not checked — no full text of the sourcecites [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.

In the paper

“It has been theoretically predicted that the locations of the Weyl points of these compounds in momentum space can be tuned by the magnetization direction (96,97).”

What the sources say

• Supported

  The main text (p. 1) says the structure and direction of Weyl points depend on the magnetic field. The paper also calculates Weyl-point locations for [110] magnetization (p. 3) and a different [100] configuration (Supplementary Material, p. 9), supporting the claim that their momentum-space locations can be tuned by magnetization direction. (LLM, conf=0.92)

  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
• Partly supported

  The Berry curvature calculation section reports that, for Co₂TiSn with magnetization along z, two Weyl points emerge along k_z. It explains how that magnetization direction changes the crystal symmetries, but does not show that changing the direction tunes the Weyl points’ momentum-space locations; its calculations use the (001) direction. (LLM, conf=0.81)

  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] sourceExperimental — accuracy not yet measured

In the paper

“These properties, together with the predicted giant anomalous Hall conductivity (98,293), make these materials potentially useful for spintronic and thermoelectric applications.”

What the sources say

• Partly supported

  The Summary reports a calculated anomalous Hall conductivity of 100 S/cm for Co₂TiSn and identifies its potential for spintronics applications. It does not describe the predicted conductivity as giant or discuss thermoelectric applications. (LLM, conf=0.87)

  cites [98] 98. Kübler J, Felser C. 2016. Weyl points in the ferromagnetic Heusler compound Co 2 MnAl. Europhys. Lett. 114:47005 100. sourceExperimental — accuracy not yet measured
• ?Not matched

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

  cites [293] 293. Chadov S, Qi X, Kübler J, Fecher GH, Felser C, Zhang SC. 2010. Tunable multifunctional topological insulators in ternary Heusler compounds. Nat. Mater 9:541-45 296.

In the paper

“Other magnetic systems such as FM kagomé metal Fe 2 Sn 3 (299), FM spinel CuCr 2 Se 4-x Br x (289), and magnetic semiconductors (288, 291) have also been reported to display the intrinsic AHE.”

What the sources say

• ?Could not verify

  The Conclusion (page unavailable) discusses magnetoconductivity in Bi1-xSbx and the chiral anomaly, not intrinsic anomalous Hall effect in magnetic semiconductors. Searches for intrinsic AHE and the named magnetic materials found no passage in our copy reporting the claimed effect. (LLM, conf=0.73)

  cites [299] 299. Kim H-J, Kim K-S, Wang JF, Sasaki M, Satoh N, et al. 2013. Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111:246603 302. sourceExperimental — accuracy not yet measured
• Supported

  The Conclusions (p. 10) report a large anomalous Hall effect in Co-doped FeSi and say it is most likely intrinsic, arising from band structure rather than impurity scattering. This supports the cited sentence’s claim that a magnetic semiconductor has been reported to display intrinsic AHE; the source qualifies the proposed origin as “most likely.” (LLM, conf=0.92)

  cites [289] 289. Manyala N, Sidis Y, DiTusa JF, Aeppli G, Young DP, Fisk Z. 2004. Large anomalous Hall effect in a silicon-based magnetic semiconductor. Nat. Mater 3:255-62 292. source
• ?Not checked — no full text of the sourcecites [288] 288. Husmann A, Singh LJ. 2006. Temperature dependence of the anomalous Hall conductivity in the Heusler alloy Co 2 CrAl. Phys. Rev. B 73:172417 291. source

In the paper

“Furthermore, remarkable anomalous behavior has also been observed in this material's Nernst effect (57).”

What the sources say

• Supported

  The paper reports a large anomalous Nernst effect in Mn₃Sn. Its Abstract says the effect does not follow the conventional scaling relation with magnetization, supporting the citing sentence’s description of remarkable anomalous behavior. (LLM, conf=0.94)

  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

In the paper

“In experimental studies on DSMs and WSMs, an abnormal Hall signal under in-plane magnetic field was first reported in ZrTe 5 (317).”

What the sources say

• ?Could not verify

  The paper discusses theoretical topological-insulator phases and mentions bismuth as a possible material (pp. 1, 4). Searches for ZrTe5 and an abnormal Hall signal under an in-plane magnetic field found no passage addressing the claimed experimental report or its priority. (LLM, conf=0.78)

  cites [317] 317. Fu L, Kane CL, Mele EJ. 2007. Topological insulators in three dimensions. Phys. Rev. Lett. 98:106803 320. sourceExperimental — accuracy not yet measured

In the paper

“Since the experimental discoveries of the WSM state in materials such as TaAs class (type I) materials (22,23,25,27,39,(86)(87)(88)(89)(90)(91)(92) and (W/Mo)Te 2 (type II) materials (28,(111)(112)(113)(114)(115)(116)(117)(118)(119)(120)(121)(122), many research groups have reported observation of negative longitudinal MR in those materials and have attributed it to the chiral magnetic effect (109”

What the sources say

• Partly supported

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

  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. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [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.
• Partly supported

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

  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. sourceExperimental — accuracy not yet measured

In the paper

“However, in-plane Hall voltage can be generated in the presence of coplanar electric and magnetic fields (Figure 9a) due to the chiral anomaly, leading to the so-called PHE (309-315).”

What the sources say

• Supported

  The opening passage (p. 1) says the chiral anomaly leads to a giant planar Hall effect: a transverse voltage when the in-plane magnetic field is not aligned with the current. The discussion on p. 3 likewise identifies the planar Hall effect in topological metals as originating from the chiral anomaly. The field must be at an angle to the current, not merely coplanar with it. (LLM, conf=0.93)

  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.
• Supported

  The introduction (p. 1) defines the planar Hall effect as a Hall voltage with the electric and magnetic fields coplanar and says it is directly related to the chiral anomaly in Weyl semimetals. The same page reports a chiral-anomaly-induced planar Hall effect in GdPtBi. The claim is supported in that Weyl-semimetal context. (LLM, conf=0.93)

  cites [311] 311. Kumar N, Guin SN, Felser C, Shekhar C. 2018. Planar Hall effect in the Weyl semimetal GdPtBi. Phys. Rev. B 98:041103 314. source
• ?Not matched

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

  cites [312] 312. Singha R, Roy S, Pariari A, Satpati B, Mandal P. 2018. Planar Hall effect in the type II Dirac semimetal VAl 3 . Phys. Rev. B 98:081103(R) 315.
• Supported

  The introduction (p. 1) describes the planar Hall effect as a coplanar Hall voltage, electric field, and magnetic field, and says it is directly related to the chiral anomaly in Weyl semimetals. The same page reports a large chiral-anomaly-induced planar Hall effect in GdPtBi. (LLM, conf=0.94)

  cites [313] 313. Wang YJ, Gong JX, Liang DD, Ge M, Wang JR, et al. 2018. Planar Hall effect in type-II Weyl semimetal WTe 2 . arXiv:1801.05929 [cond-mat.mtrl-sci] 316. source
• ?Not checked — no full text of the sourcecites [314] 314. West FG. 1963. Rotating-field technique for galvanomagnetic measurements. J. Appl. Phys. 34:1171-73 317. source
• Supported

  The Results and Discussion (p. 5) describe the planar Hall effect in topological semimetals as a transverse voltage when an in-plane magnetic field is not aligned with the current, and attribute the measured effect in WTe2 to the chiral anomaly. The measurement geometry (p. 4) places the magnetic field in the plane of the electric current. (LLM, conf=0.93)

  cites [315] 315. Liang T, Lin J, Gibson Q, Kushwaha S, Liu M, et al. 2018. Anomalous Hall effect in ZrTe 5 . Nat. Phys. 14:451-55 318. source

In the paper

“A strict sin 2ϕ dependence was later observed in a number of materials, including ZrTe 5 , Cd3As 2 , GdPtBi, WTe 2 , and VAl 3 (311)(312)(313)(314)(315).”

What the sources say

• Supported

  The citation supports the GdPtBi example in the multi-citation sentence, not the other listed materials. On p. 3, the authors fit GdPtBi’s measured angular dependence with a planar Hall resistivity proportional to sin φ cos φ, equivalent to ½ sin 2φ; their added orbital-magnetoresistance term changes the amplitude, not that angular form. (LLM, conf=0.90)

  cites [311] 311. Kumar N, Guin SN, Felser C, Shekhar C. 2018. Planar Hall effect in the Weyl semimetal GdPtBi. Phys. Rev. B 98:041103 314. source
• ?Not matched

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

  cites [312] 312. Singha R, Roy S, Pariari A, Satpati B, Mandal P. 2018. Planar Hall effect in the type II Dirac semimetal VAl 3 . Phys. Rev. B 98:081103(R) 315.
• Supported

  For GdPtBi, the paper reports measured planar Hall resistivity with extrema at 45° and 135° (p. 2). Its fitted angular dependence is proportional to sin φ cos φ (p. 3), which is proportional to sin 2φ. The other materials in the citing sentence are associated with other citations, not this paper. (LLM, conf=0.91)

  cites [313] 313. Wang YJ, Gong JX, Liang DD, Ge M, Wang JR, et al. 2018. Planar Hall effect in type-II Weyl semimetal WTe 2 . arXiv:1801.05929 [cond-mat.mtrl-sci] 316. sourceExperimental — accuracy not yet measured

In the paper

“Unlike the conventional Hall effect, the PHE does not satisfy antisymmetry; i.e., ρ xy = -ρ yx .”

What the sources say

• Supported

  On p. 3, the paper explicitly states that the planar Hall effect’s off-diagonal resistivity does not satisfy the antisymmetry property of a true Hall effect, ρxy = −ρyx. The equation names the property that PHE does not satisfy, rather than an equality that holds for PHE. (LLM, conf=0.94)

  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

“At a small angle, the angular dependence of magnetoconductivity has a Lorentzian profile with angular width (309): ϕ ≈ ε F v F /l B 2 τ τ c ,19.”

What the sources say

• Partly supported

  On p. 4, the paper explicitly says the small-angle magnetoconductivity has a Lorentzian form with angular width Δθ ∼ Lₐ/L꜀. The equation that would express this width in terms of εF, vF, ℓB, τ, and τc is not decoded in our copy, so the specific formula attributed to it cannot be verified. (LLM, conf=0.84)

  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. sourceExperimental — accuracy not yet measured

In the paper

“This is because the PHE does not originate from the Lorentz force (309, 310).”

What the sources say

• Supported

  The discussion of Eq. (15) (p. 3) explicitly says that the off-diagonal resistivity called the planar Hall effect does not originate from the Lorentz force. (LLM, conf=0.95)

  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

“With rotating inplane field (Figure 9a) and out-of-plane field (Figure 9b), the twofold anisotropy of the PHE (Figure 9c) clearly differs from the onefold symmetry seen for the conventional Hall effect (Figure 9d) (313).”

What the sources say

• Supported

  The measurement discussion (p. 2) distinguishes in-plane rotation for the planar Hall effect from rotation between in-plane and out-of-plane orientations for the usual Hall effect. It reports different angular extrema for the two signals, consistent with the cited contrast in symmetry. (LLM, conf=0.91)

  cites [313] 313. Wang YJ, Gong JX, Liang DD, Ge M, Wang JR, et al. 2018. Planar Hall effect in type-II Weyl semimetal WTe 2 . arXiv:1801.05929 [cond-mat.mtrl-sci] 316. source

In the paper

“Therefore, their negative longitudinal MR is strongly anisotropic (28,306,307); this has been observed in WTe 2 (302,303).”

What the sources say

• Partly supported

  In “Novel chiral anomaly in type-II Weyl semimetals” (p. 5), the paper says the chiral anomaly depends on magnetic-field direction and has immediate consequences for transport. It does not specifically state that negative longitudinal magnetoresistance is strongly anisotropic; that is an inference from its result, not a reported finding. (LLM, conf=0.83)

  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
• Partly supported

  The lattice-model results (p. 4) show direction-dependent longitudinal magnetoconductivity, supporting anisotropy in the corresponding negative magnetoresistance. But the paper describes *strong* anisotropy with a vanishing perpendicular response as an earlier suggestion that its own results challenge: it finds a nonzero response at all angles (Discussion and Conclusions, p. 5). (LLM, conf=0.83)

  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

“Therefore, with increasing magnetic field, the voltage drop between voltage contacts may even decrease for asymmetric point-like electrical contacts and irregular sample shape, leading to negative longitudinal MR (10,304,305).”

What the sources say

• Supported

  In “The chiral anomaly” (p. 44), the review explains that small contacts, non-ideal sample geometry and strong conductivity anisotropy can produce current jetting, making the measured voltage difference depend on contact position rather than intrinsic resistance. It also describes apparent negative longitudinal MR from this effect (pp. 44–45), consistent with a voltage drop decreasing as the field increases. (LLM, conf=0.89)

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

  Section II (page unavailable) describes small current contacts that accentuate field-induced current jetting. The passage on case 1 says the edge-contact voltage decreases as the magnetic field increases, yielding a spurious negative longitudinal magnetoresistance. The paper does not establish the claim’s specific conditions of asymmetric contacts and irregular sample shape; it describes platelike samples with contacts placed along the spine and edge. (LLM, conf=0.84)

  cites [304] 304. Udagawa M, Bergholtz EJ. 2016. Field-selective anomaly and chiral mode reversal in type-II Weyl ma- terials. Phys. Rev. Lett. 117:086401 307. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s Optical Conductivity discussion (p. 3) addresses magnetic-field effects on optical absorption, not voltage measured between contacts. Searches for asymmetric contacts, irregular sample shape, voltage drop, and negative longitudinal magnetoresistance found no passage addressing the claimed mechanism. (LLM, conf=0.75)

  cites [305] 305. Yu Z-M, Yao Y, Yang SA. 2016. Predicted unusual magnetoresponse in type-II Weyl semimetals. Phys. Rev. Lett. 117:077202 308. sourceExperimental — accuracy not yet measured

In the paper

“Another unusual property that can be derived from Equation 18is the narrowing of the AMR peak at high magnetic field (309).”

What the sources say

• Partly supported

  On p. 4, the paper derives angular narrowing of the longitudinal magnetoconductivity peak using Eq. (15), not Eq. (18). It reports that the angular width decreases roughly as 1/B at low fields but appears to saturate at higher fields. Thus the narrowing is supported, but its attribution to Eq. (18) and its unqualified description as a high-field effect are not. (LLM, conf=0.84)

  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. sourceExperimental — accuracy not yet measured

In the paper

“Current jetting is also expected to be weak in materials with small transverse MR [e.g., GdPtBi (304)] due to reduced-conductance anisotropy under magnetic fields.”

What the sources say

• ?Could not verify

  The paper discusses field-dependent chiral modes (p. 2) and optical conductivity (pp. 3–4), not current jetting. Searches for GdPtBi, small transverse magnetoresistance, and conductance anisotropy found no passage addressing the cited claim. (LLM, conf=0.76)

  cites [304] 304. Udagawa M, Bergholtz EJ. 2016. Field-selective anomaly and chiral mode reversal in type-II Weyl ma- terials. Phys. Rev. Lett. 117:086401 307. sourceExperimental — accuracy not yet measured

In the paper

“For example, a quadratic field dependence of negative MR anticipated for a non-quantum limit regime has been observed for most of the above materials (107, 110, 301).”

What the sources say

• ?Could not verify

  The passages on charge transport and electrical resistivity (section labeled Abstract; page unavailable) discuss temperature dependence and Hall carrier density, not negative magnetoresistance. Searches for quadratic negative MR and its field dependence in the non-quantum limit found no passage addressing the claim. (LLM, conf=0.74)

  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
• ?Not checked — no full text of the sourcecites [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.
• ?Not matched

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

  cites [301] 301. Lv Y-Y, Li X, Zhang B-B, Deng WY, Yao S-H, et al. 2017. Experimental observation of anisotropic Adler-Bell-Jackiw anomaly in type-II Weyl semimetal WTe 1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118:096603 304.

In the paper

“Half-Heusler RPtBi is another group of materials that exhibits the magnetic fieldinduced chiral magnetic effect (109, 110).”

What the sources say

• Partly supported

  The Abstract (page not specified) says that magnetic-field-induced Weyl points in GdPtBi and NdPtBi are the source of a chiral anomaly, and the paper reports associated negative magnetoresistance. It does not identify the observed phenomenon as the chiral magnetic effect, so that specific attribution is not established by our copy. (LLM, conf=0.84)

  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. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [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.

In the paper

“With coplanar electric and magnetic fields, the transverse resistance ρ xy of the PHE is (309) ρ xy = (ρ || -ρ ⊥ ) 2 sin 2ϕ, 17.”

What the sources say

• Partly supported

  On p. 3, the paper defines the resistivity difference between directions parallel and perpendicular to the magnetic field and identifies the off-diagonal resistivity in Eq. (15) as the planar Hall effect. The equation itself is not decoded in our copy, so the claimed sin 2φ dependence and factor of one-half cannot be verified from it. (LLM, conf=0.80)

  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. sourceExperimental — accuracy not yet measured

In the paper

“With the above definition of ρ and ρ ⊥ , longitudinal resistivity can be expressed as ( 309) ρ xx = ρ ⊥ + (ρ -ρ ⊥ )cos 2 ϕ. 18.”

What the sources say

• Partly supported

  On p. 3, the paper defines ρ‖ and ρ⊥ as resistivities parallel and perpendicular to the magnetic field and identifies the first equation of Eq. (15) as the anisotropic-magnetoresistance relation. The equation itself is not decoded in our copy, so the specific cos²φ dependence and coefficient cannot be verified. (LLM, conf=0.76)

  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. sourceExperimental — accuracy not yet measured

In the paper

“One possible advantage of using WHMs as a platform for realizing QSHIs is the variable SOC gap with various combinations of W, H, and M (226); such a gap offers the opportunity to design different QSHIs.”

What the sources say

• Partly supported

  The discussion on p. 9 says that changing the W, H, and M elements can fine-tune spin–orbit coupling in WHM compounds and that their symmetry allows an SOC gap. It discusses WHMs as topological semimetals, however, and does not propose using that gap to realize quantum spin Hall insulators. (LLM, conf=0.85)

  cites [226] 226. Hu J, Zhu Y, Gui X, Graf D, Tang Z, et al. 2018. Quantum oscillation evidence of a topological semimetal phase in ZrSnTe. Phys. Rev. B 97:155101 229. sourceExperimental — accuracy not yet measured

In the paper

“and could be ascribed to the large bulk band gap of the 1T -WTe 2 monolayer [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 citing sentence uses this source for the measured gap in MBE-grown monolayer 1T′-WTe₂, not for the authors’ explanation of the conductance plateau temperature. The paper reports MBE growth and estimates a 55 ± 20 meV gap in intrinsic samples (bandgap discussion, Fig. 3). (LLM, conf=0.93)

  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
• Partly supported

  The main text (p. 2) reports that the monolayer conductance develops a plateau below about 100 K as the bulk becomes insulating. It does not ascribe that temperature to a large bulk band gap; instead, the discussion (p. 7) considers either a small band gap or a small band overlap, and SI-5 (p. 15) reports an approximate 5 meV activation energy for bulk conduction. (LLM, conf=0.87)

  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

“The tetragonal layered WHM compounds have also been predicted to become QSHIs in the monolayer form (322).”

What the sources say

• ?Could not verify

  The paper discusses quantum spin Hall behavior in HgTe/(Hg,Cd)Te quantum wells (p. 3) and reports evidence from inverted HgTe wells (p. 8). Searches for WHM, tetragonal layered compounds, and monolayers found no passage addressing the claimed prediction; the HgTe results neither establish nor contradict it. (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

In the paper

“There is transport (74,75) and spectroscopic (73) evidence of the QSHI state in WTe 2 monolayers prepared using mechanical exfoliation or molecular beam epitaxy (MBE) growth.”

What the sources say

• Supported

  This source supports the transport-evidence portion of the sentence: it reports quantum spin Hall transport in monolayer WTe2 (p. 1), and its General Fabrication Scheme says the WTe2 flakes were exfoliated (p. 13). The sentence assigns spectroscopic evidence to a different citation, not to this paper. (LLM, conf=0.92)

  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 source
• ?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
• Supported

  The paper reports transport evidence in monolayer WTe2: an insulating interior with conducting edges, observations it says are consistent with a two-dimensional topological insulator (p. 1). Its devices used exfoliated WTe2 sheets (p. 2). This source supports the transport portion of the citing sentence; the spectroscopic evidence is assigned to a different citation, and the paper does not claim definitive proof of the state. (LLM, conf=0.90)

  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 source

In the paper

“The QSHI state has been proposed in the monolayer form of the layered 1T -transition metal dichalcogenides MX 2 (M = W, Mo; X = S, Se, Te) (72) and WHM (322).”

What the sources say

• Supported

  The paper states that monolayer 1T′ transition-metal dichalcogenides MX₂, with M = W or Mo and X = Te, Se, or S, were theoretically predicted to be QSH insulators. The citation to this paper is attached to that MX₂ proposal; the separate WHM claim carries a different citation. (LLM, conf=0.93)

  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

  The citation (322) is attached to the proposed QSHI state in WHM, not to the preceding claim about monolayer transition-metal dichalcogenides. Our copy discusses a proposed QSH state in HgTe/(Hg,Cd)Te quantum wells (p. 3), but the passages found when searching for WHM do not address a proposal in WHM. (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

In the paper

“In Section 3.2.8,we mention that the QHE in the 3D layered topological semimetal EuMnBi 2 is caused by the formation of 2D electronic states due to restriction of electron motion in the 2D Bi plane (177).”

What the sources say

• ?Could not verify

  The paper’s discussion on p. 1 concerns Weyl fermions and carrier mobility in NbP, not the quantum Hall effect in EuMnBi2. Searches for EuMnBi2, the Bi plane, and restricted electron motion found no passage addressing the claimed mechanism. (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

In the paper

“Because the Fermi level crosses the gapped cones and the band dispersion is extremely linear over a wide energy range, WHMs have been established as topological NLSMs (78,85,154).”

What the sources say

• ?Could not verify

  Section 3.1 discusses the Fermi energy and band dispersion of HgTe and InAs/GaSb quantum wells, not WHMs. Searches for WHMs, gapped cones, and nodal-line semimetals found no passage in our copy addressing the claim; page numbers were not provided. (LLM, conf=0.78)

  cites [78] 78. Liu C-X, Zhang S-C, Qi X-L. 2016. The quantum anomalous Hall effect: theory and experiment. Annu. Rev. Condens. Matter Phys. 7:301-21 sourceExperimental — accuracy not yet measured
• ?Not matched

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

  cites [85] 85. Xu S-Y, Alidoust N, Belopolski I, Yuan Z, Bian G, et al. 2015. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11:748-54
• ?Not checked — no full text of the sourcecites [154] 154. Hu J, Tang Z, Liu J, Liu X, Zhu Y, et al. 2016. Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe. Phys. Rev. Lett. 117:016602 157. source

In the paper

“Furthermore, a QAHI system also provides a promising platform for the creation, manipulation, and utilization of Majorana fermions, the hypothetical particles that are their own antiparticles (328, 329).”

What the sources say

• Partly supported

  The paper proposes a QAH-insulator–superconductor hybrid that generates Majorana edge and vortex modes (p. 1), and discusses detecting vortex modes and their potential use in topological quantum computing (pp. 1, 4). It does not describe how to manipulate the modes, and its proposal requires superconducting proximity rather than a QAH insulator alone. (LLM, conf=0.83)

  cites [328] 328. Chang C-Z, Zhang J, Feng X, Shen J, Zhang Z, et al. 2013. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340:167-70 331. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The discussion on p. 2 describes the quantum anomalous Hall state and possible adjacent topological states, but does not connect them to Majorana fermions. Searches for Majorana fermions and superconducting-proximity platforms found no passage addressing their creation, manipulation, or use. (LLM, conf=0.76)

  cites [329] 329. Checkelsky JG, Yoshimi R, Tsukazaki A, Takahashi KS, Kozuka Y, et al. 2014. Trajectory of the anoma- lous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10:731-36 332. sourceExperimental — accuracy not yet measured

In the paper

“Table 1 shows the mobilities of some representative topological semimetals acquired from two-band model analysis; the mobilities are indeed high, in the range of 10 3 -10 6 cm 2 /(V•s).”

In the paper

“As shown in Section 3.2.2, the cyclotron effective masses derived from quantum oscillations are indeed small for many topological semimetals, reaching as low as 0.02m e (where m e is the free electron mass) for some materials.”

In the paper

“They support exotic, topologically protected boundary modes such as the topological Fermi arcs and drumhead surface states.”

In the paper

“although the Weyl fermion played a crucial rule in the Standard Model (15), it has never been observed as a fundamental particle.”

What the sources say

• ?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

“These surface states have been directly observed in spectroscopic measurements (19,25,27,(38)(39)(40)(41)(42).”

What the sources say

• ?Not matched

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

  cites (19,25,27,(38)(39)(40)(41)(42)

In the paper

“Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect.”

In the paper

“The realization of the topological WSM state (22,23,(25)(26)(27) enables the observation of this elusive particle in physics.”

What the sources say

• ?Not matched

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

  cites (22,23,(25)(26)(27)

In the paper

“The separation of the opposite chiral charges in momentum space leads to surface Fermi arcs, whose constant energy contours are open arcs that connect the Weyl nodes of opposite chiralities on the surface.”

In the paper

“Electron transport in topological semimetals is usually strongly affected by external magnetic field.”

In the paper

“In such a triple-point semimetal, three singly degenerate bands cross at discrete points, the triple points (Figure 1d).”

In the paper

“Furthermore, thinning down a 3D topological semimetal into 2D may give rise to new 2D topology, including the quantum spin Hall insulator (QSHI) and the quantum anomalous Hall insulator (QAHI) (14,20,21,(72)(73)(74)(75)(76).”

What the sources say

• ?Not matched

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

  cites (14,20,21,(72)(73)(74)(75)(76)

In the paper

“Because of the existence of Weyl nodes, WSMs lack a global band gap.”

In the paper

“A power law field dependence (MR ∝ B n ) is usually seen in various topological semimetals, with the exponent n ranging from 1 to 2 (45,46,48,107,(171)(172)(173)(174)(175)(176)(177)(178)(179)(180)(181)(182)(183)(184)(185)(186)(187).”

What the sources say

• ?Not matched

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

  cites (45,46,48,107,(171)(172)(173)(174)(175)(176)(177)(178)(179)(180)(181)(182)(183)(184)(185)(186)(187)

In the paper

“Characterization of relativistic fermions through transport measurements provides a convenient approach for verifying a nontrivial topological state, complementary to the direct observation of nontrivial band topology by ARPES experiments.”

In the paper

“The two-band model, while widely used, provides only an approximate description for the magnetotransport properties of multiple-band materials.”

In the paper

“In the presence of translational symmetry, these Weyl nodes are topologically stable and cannot be removed without pair annihilation.”

In the paper

“Specifically, the Chern number associated with the 2D closed surface directly corresponds to the topological invariant of a Weyl node (i.e., the chiral charge).”

In the paper

“These triple points are not associated with any topological invariant due to the lack of a global band gap on any 2D closed surface that encloses the triple point.”

In the paper

“Under such a circumstance, large MR is expected when mobility is high.”

In the paper

“Such chiral anomaly leads to enhanced conductivity with an increasing magnetic field.”

In the paper

“WSMs are a class of topological semimetals that host Weyl fermions as low-energy quasiparticle excitations (2,(6)(7)(8)(9)(10)(11)(15)(16)(17)(18)(19)(20)(21).”

What the sources say

• ?Not matched

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

  cites (2,(6)(7)(8)(9)(10)(11)(15)(16)(17)(18)(19)(20)(21)

In the paper

“These triple points are protected by the combination of a uniaxial rotational axis, mirror planes, and TRS.”

In the paper

“Their Fermi surface consists of electron and hole pockets that touch at the type II Weyl nodes.”

In the paper

“However, in multiple-band systems, the field dependence of Hall resistivity ρ xy deviates from linearity.”

In the paper

“In NLSMs, conduction and valence bands cross at 1D lines in k space (Figure 1a) (30,40,78,85,133,134,(145)(146)(147)(148)(149)(150)(151)(152)(153)(154)(155)(156)(157)(158)(159)(160)(161).”

What the sources say

• ?Not matched

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

  cites (30,40,78,85,133,134,(145)(146)(147)(148)(149)(150)(151)(152)(153)(154)(155)(156)(157)(158)(159)(160)(161)

In the paper

“The absence of a global band gap prevents the definition of a topological invariant for the entire 3D bulk Brillouin zone (BZ).”

In the paper

“The existence of Weyl nodes does not rely on any additional crystalline point group symmetries.”

In the paper

“For nonrelativistic electrons in 3D, the motion along the magnetic field direction is not quantized, leading to additional energy of ( k z ) 2 /2m (where k z is the momentum along the magnetic field direction) for LLs:”

In the paper

“For the 3D case, due to the additional energy related to unquantized k z as shown in Equations 6 and 7, different LLs overlap in energy space, leading to a mixture of Landau bands for particular energy (Figure 3e,f ) and a continuous energy spectrum.”

In the paper

“Third, according to Equation 3, even approximate electron-hole compensation should be able to lead to a quadratic or nearly-quadratic field dependence for ρ xx .”

In the paper

“Such massless behavior is naturally expected for ideal topological fermions since they are hosted by linearly dispersed bands crossing near the Fermi level, which requires zero mass in the Hamiltonian (11).”

What the sources say

• ?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

“A nonzero Berry phase φ B originates from the band touching point, such as Dirac nodes.”

In the paper

“Under magnetic fields, the cyclotron motion of Dirac fermions, i.e., the closed trajectory in momentum space, induces a Berry phase that changes the phase of quantum oscillations.”

In the paper

“Similarly, an additional energy term due to unquantized k z also occurs for 3D relativistic fermions:”

In the paper

“Therefore, different models have been derived for 3D and 2D quantum oscillations.”

In the paper

“The LL quantization is completely different for the relativistic fermions with linear dispersion (Figure 3c).”

In the paper

“With these considerations, the two-band model appears to be applicable only for a limited field range or at higher temperatures at which quantum effects are not significant.”

In the paper

“As discussed in Section 3.4, the chiral zeroth LL leads to one important effect for Weyl fermions, i.e., the chiral anomaly.”

In the paper

“As illustrated in Figure 3d, LLs are no longer equally spaced for relativistic fermions given ε n ∝ √ |n|.”

In the paper

“Greater relaxation time in topological materials may be associated with symmetry protection in many cases.”

In the paper

“This model successfully explains the extremely large MR arising from high mobility and approximate carrier compensation.”

In the paper

“Although obtaining the precise value of carrier mobility for individual bands might be challenging, the two-band model still provides an effective approach for the approximate description of magnetotransport properties of multiband materials.”