The DOI matches its Crossref record; 58 of the 58 references it cites were found in a registry or an index; none of the 8 sources its claims cite is checked for support yet.
Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene
Open accessAbstract
The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure.When the dispersion around the Dirac points is tilted, one can predict the emergence of intricate transport phenomena such as modified Klein tunneling, intrinsic anomalous Hall effects, and ferrimagnetism.However, Dirac materials are rare, particularly with tilted Dirac cones.Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions.Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi-Dirac, tilted, and, most interestingly, type-III Dirac cones that combine flat and linear dispersions.Type-III Dirac cones emerge from the touching of a flat and a parabolic band when synthetic photonic strain is introduced in the lattice, and they possess a nontrivial topological charge.This photonic realization provides a recipe for the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, opens the way to study Dirac superfluids in topological landscapes.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
This paper demonstrates photonic orbital graphene in a honeycomb lattice of polariton micropillars, where strain in the orbital p bands produces semi-Dirac, tilted, and type-III Dirac cones. It reports the first experimental observation of type-III Dirac cones, formed by the touching of a flat band and a linear band, and explains their emergence via topological Lifshitz transitions.
Key findings
- Type-III Dirac cones were observed for synthetic strain β = 1.5, combining a flat band and a linear band; measured velocities were |v0x| = (0.29 ± 0.03) d|tL| and |vx| = (0.35 ± 0.03) d|tL|, in agreement with tight-binding prediction |v0x| = |vx| = 0.37 d|tL|. Along the perpendicular direction, |v0y| = (0.00 ± 0.04) d|tL| and |vy| = (0.46 ± 0.04) d|tL|, matching predictions of 0 and 0.48 d|tL|.
- A semi-Dirac dispersion was directly observed at β = 0.5, where two Dirac cones merge, with parabolic touching along ky and linear dispersion along kx.
- Tilted type-I Dirac cones emerge from the flat-parabolic band touching at Γ for β < 1, with measured tilt v0y agreeing with tight-binding calculations.
- Topological analysis shows the β = 1 flat-parabolic touching has winding W = 2; for β ≠ 1 it evolves into a pair of Dirac cones with W = 1, while the semi-Dirac merging has W = 0. Type-III cones are robust for 1 < β < 2 and merge at β = 2.
Methods
- The platform is a honeycomb lattice of coupled micropillars etched from an AlGaAs semiconductor microcavity with twelve GaAs quantum wells, operating in the strong-coupling regime at 10 K to form exciton-polaritons. Micropillar diameter is 2.75 μm (2.60 μm for type-III samples), with center-to-center distances varied between 2.40 and 2.72 μm, or 2.40 and 2.10 μm for type-III.
- Angle-resolved photoluminescence under nonresonant continuous-wave excitation at 745 nm was used to reconstruct the band dispersion. The p-orbital bands arise from coupling of first excited modes, with longitudinal hopping tL and transverse hopping tT.
- Synthetic uniaxial strain was implemented by changing the center-to-center distance d′ along one link direction, defining β = t′L/tL. Experimental dispersions were fitted with a nearest-neighbor tight-binding model, and effective Dirac velocities were extracted from linear fits near the Dirac points.
Limitations
- The paper states that the β = 2 merging of type-III Dirac cones could not be observed experimentally because engineered hoppings in compressed structures were limited to β = 1.5.
- The paper notes that tT is not strictly zero in the experiment, producing faint emission between horizontal links; simulations reproduce this with tT = −0.1tL on strained links.
- The paper states that the uppermost band deviates from a flat band due to coupling to higher-energy bands from photonic d orbitals, and that polarization-related splitting is neglected because it is much smaller than the bandwidth.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
0 of 8 cited sources checked · 0 supported · 0 flagged
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The orbital bands present a flat band that touches a parabolic band.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > I. INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The result of the compression in the polariton lattice is shown in Fig. 5(c) for β ¼ 1.5:In the direction k x parallel to that along which the center-to-center distance d 0 is reduced, two new Dirac points emerge from the flat-parabolic band touching.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > III. TILTED AND SEMI-DIRAC CONES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The richness of this multiband system allows, in addition, the observation of semi-Dirac cones, which combine massless and massive dispersions.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > I. INTRODUCTION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“they possess a nontrivial topological charge”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Type-III Dirac cones emerge from the touching of a flat and a parabolic band when synthetic photonic strain is introduced in the lattice”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Decreasing β, that is, emulating the stretching of the lattice, brings the Dirac cones closer together in the k y direction [Figs.3(a) and 3(b)] until they merge at β ¼ 0.5 in a single band touching [Fig.3(c)].”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > III. TILTED AND SEMI-DIRAC CONES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“we provide the first experimental observation of type-III Dirac cones”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > I. INTRODUCTION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: Type-III Dirac points have not yet been reported experimentally.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When asymmetry in the hopping is introduced, which simulates uniaxial strain in solid-state graphene, the flat-parabolic band touching evolves into tilted and type-III Dirac cones.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > I. INTRODUCTION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If we account for different hoppings t L and t 0 L for different links, Hamiltonian (B2) is still valid with the same expressions for f 1 and g, and f 2 replaced by f 2 ¼ β þ 1 4 ðe ika 1 þ e ika 2 Þ.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The touching of a flat and a dispersive band with winding W ¼ 2 evolves into two Dirac cones in the presence of strain.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 18
- Probably not a substantial claim. 4
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At the merging point [β ¼ 0.5, Fig. 3(c)], we provide the direct observation of a semi-Dirac dispersion, with the touching of two parabolic bands along the k y direction and a linear dispersion along k x [shown in the left inset of Fig. 3(c)].”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > III. TILTED AND SEMI-DIRAC CONES
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“Four bands are observed: The lowest one is flat, while the two central bands present two type-I Dirac points at the K and K' points and touch the flat band at the Γ point [36].”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > II. PHOTONIC ORBITAL LATTICE
What the sources say
- Not matchedcites [36]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“while for β > 1, they are E D ¼ E 0 - 3 2 jt L j; cosðK x Þ ¼ 2 -β 2 β ; K y ¼ 0:ðB7Þ”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“After converting the slopes to effective Weyl velocities [Eq.( 1)], we obtain jv 0y j ¼ 0.07 Æ 0.03, close to the expected value of 0, and jv y j ¼ 0.72 Æ 0.03 in units of djt L j.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Strength:plain· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“At 10 K, the temperature of the experiments, the excitonic and photonic resonances are in the strong coupling regime, with a Rabi splitting of 15 meV.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Additional information
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For β < 1, the energy E D and momentum-space coordinates of the Dirac points emerging at the bottom bands are, respectively, E D ¼ E 0 - jt L j 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3 þ 6β 2 q ; K x ¼ 0; cosðK y Þ ¼ β;ðB6Þ”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The single band touching at β ¼ 1 is described by a winding W ¼ 2. When β ≷ 1, the band touching evolves into a pair of Dirac cones (tilted type-I or type-III) with winding W ¼ 1.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > V. TOPOLOGICAL INVARIANTS OF TILTED AND TYPE-III DIRAC CONES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From the experimental photoluminescence of Fig. 5(c), we measure jv 0x j ¼ ð0.29 Æ 0.03Þ djt L j and jv x j ¼ ð0.35 Æ 0.03Þ djt L j [with d ¼ ð2d 0 þ dÞ=3], which is in good agreement with the tight-binding prediction for β ¼ 1.5 (jv 0x j ¼ jv x j ¼ 0.37 djt L j, see Appendix C).”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > III. TILTED AND SEMI-DIRAC CONES
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For 1 < β < 2, we have (same units as above) jv 0x j ¼ jv x j ¼ 1 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðβ 2 -1Þð4 -β 2 Þ q; jv 0y j ¼ 0; jv y j ¼ ffiffi ffi 3 p 4 ffiffiffiffiffiffiffiffiffiffiffiffi ffi β 2 -1 q :”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The type-III Dirac cones are thus present for all values of β between 1 and 2, proving their robustness against variations of the strain parameter.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > III. TILTED AND SEMI-DIRAC CONES
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“From the tight-binding Hamiltonian, the effective Dirac velocities can be obtained from the derivative along k x and k y of the eigenvalues of Eqs.(B3)-(B5) at the position of the emergent Dirac cones [Eqs.(B6) and (B7)], resulting in the analytical expressions for β < 1 (normalized to djt L j, where we have assumed that, in the experiment, d ≈ d 0 ):”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: In the experiment, d ≈ d'.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“jv 0x j ¼ 0; jv x j ¼ jv 0y j ¼ 3β 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 -β 2 1 þ 2β 2 s ; jv y j ¼ ffiffi ffi 3 p 4 ffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 -β 2 q :”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At β ¼ 2, actually, the Dirac cones merge at the M point and annihilate, opening a gap for β > 2.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > V. TOPOLOGICAL INVARIANTS OF TILTED AND TYPE-III DIRAC CONES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the etched structures, the lateral defects induced during the microfabrication process reduce the lifetime to about 5-15 ps at the considered photon-exciton detunings.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Additional information
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The polariton lifetime measured in a similar unetched microcavity is of the order of 30 ps.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Additional information
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Remarkably, the orbital p bands show the two possible universal scenarios for the merging of Dirac cones in two dimensions [50]: (i) Two Dirac cones with W ¼ 1 emerge from a point with W ¼ 2, which we have just discussed, and it is reported in the lower part of the spectra of Fig. 3; (ii) two Dirac cones with opposite winding W ¼ Æ1 merge in a semi-Dirac cone with W ¼ 0, reported in the spectra in”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > V. TOPOLOGICAL INVARIANTS OF TILTED AND TYPE-III DIRAC CONES
What the sources say
- Not matchedcites [50]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“they are also sensitive to external magnetic fields, allowing the implementation of quantum Hall phases [54,55]”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
What the sources say
- Not matchedcites [54]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [55]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that for type-I Dirac cones, v 0x ¼ v 0y ¼ 0, and the absolute value of the two slopes should be identical and equal to v y .”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Strength:plain· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
In the paper
“Thanks to their excitonic component, they present significant repulsive interactions in the high-density regime, which can be achieved when using a resonant excitation scheme [53]”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
What the sources say
- Not matchedcites [53]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- Not matched
In the paper
“This behavior has been predicted for other lattice geometries [45]”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > VI. CONCLUSION
What the sources say
- Not matchedcites [45]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that the fact that jv 0x j ¼ jv x j (with opposite sign: v 0x ¼ -v x ) for β > 1 is the signature of the type-III Dirac cone, and it results in a flat band along the k x direction.”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > APPENDIX C: MEASUREMENT AND CALCULATION OF THE EFFECTIVE DIRAC VELOCITIES
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper relies on this without support.
Type-III Dirac points have not yet been reported experimentally.
“Type-III Dirac points have not yet been reported experimentally”
The authors state this as an assumption.
In the nearest-neighbor tight-binding calculation, the coupling t_T is assumed to be zero.
“assuming t T ¼ 0”
The authors state this as an assumption.
The on-site energy for the p_x, p_y orbitals is 0.
“where we have assumed that the on-site energy for the p x , p y orbitals is 0,”
The authors state this as an assumption.
In the experiment, d ≈ d'.
“where we have assumed that, in the experiment, d ≈ d 0”
The authors state this as an assumption.
The hopping of orbitals oriented perpendicular to the links is negligible (t_T = 0).
“If the hopping of orbitals oriented perpendicular to the links is negligible (t T ¼ 0)”
Citations
Cites
The electronic properties of graphene
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S., & Geim, A. K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.109 · Cited by 24,803 · cited 1×
“In two dimensions, Klein tunneling, weak antilocalization, unconventional Landau levels, or bulk pseudoconfinement appear as someof theirmost remarkable features [1,2].”
BackgroundSoluyanov, A. A., Gresch, D., Wang, Z., Wu, Q., Troyer, M., Dai, X., & Bernevig, B. A. (2015) · Nature · doi:10.1038/nature15768 · Cited by 2,526 · cited 3×
“they require materials whose constituent atoms are arranged in lattices with intricate electron hoppings [10,12,16].”
BackgroundCarusotto, I., & Ciuti, C. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.299 · Cited by 1,996 · cited 1×
“Polaritons are particularly well suited to study these scenarios: Thanks to their excitonic component, they present significant repulsive interactions in the high-density regime, which can be achieved when using a resonant excitation scheme [53]; they are also sensitive to external magnetic fields, allowing the implem…”
BackgroundTopological Insulators and Topological Superconductors
Bernevig, B. A. (2013) · doi:10.1515/9781400846733 · Cited by 1,947
Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G., & Esslinger, T. (2012) · Nature · doi:10.1038/nature10871 · Cited by 972
Observation of tunable band gap and anisotropic Dirac semimetal state in black phosphorus
Kim, J., Baik, S. S., Ryu, S. H., Sohn, Y., Park, S., Park, B.-G., Denlinger, J. D., Yi, Y., Choi, H. J., & Kim, K. S. (2015) · Science · doi:10.1126/science.aaa6486 · Cited by 938 · cited 1×
“This case is a topological Lifshitz transition in which two Dirac cones with opposite topological charge merge and annihilate, as predicted for standard s band graphene [4,45] and reported in photonic [7,8] and atomic [5,6] honeycomb lattices and in black phosphorus [9].”
BackgroundLasing in topological edge states of a one-dimensional lattice
St-Jean, P., Goblot, V., Galopin, E., Lemaître, A., Ozawa, T., Le Gratiet, L., Sagnes, I., Bloch, J., & Amo, A. (2017) · Nature Photonics · doi:10.1038/s41566-017-0006-2 · Cited by 892
Self-citationExperimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2
Deng, K., Wan, G., Deng, P., Zhang, K., Ding, S., Wang, E., Yan, M., Huang, H., Zhang, H., Xu, Z., et al. (2016) · Nature Physics · doi:10.1038/nphys3871 · Cited by 794 · cited 1×
“Type-III Dirac points have not yet been reported experimentally, and tilted type-I and type-II Dirac points have been challenging to synthesize [13,18,20] because”
BackgroundArtificial flat band systems: from lattice models to experiments
Leykam, D., Andreanov, A., & Sergej Flach, A. (2018) · Advances in Physics X · doi:10.1080/23746149.2018.1473052 · Cited by 536 · cited 1×
“conducting gap in Weyl semimetals [23], and they provide a new platform for the study of correlated phases with a flat band [24].”
BackgroundExciton-polariton topological insulator
Klembt, S., Harder, T. H., Egorov, O. A., Winkler, K., Ge, R., Bandres, M. A., Emmerling, M., Worschech, L., Liew, T. C. H., Segev, M., et al. (2018) · Nature · doi:10.1038/s41586-018-0601-5 · Cited by 535 · cited 1×
“Polariton orbital bands of the kind reported here open exciting perspectives for the study of topological lasers [56,57] and of Dirac superfluids in the mean-field interacting regime [58].”
Background
Flagged first, then by citations
Cited by
Sorted by citations
Items 101–171 of 171
P T -symmetric photonic lattices with type-II Dirac cones
Tang, Q., Belić, M. R., Zhong, H., Cao, M., Li, Y., & Zhang, Y. (2024) · Optics Letters · doi:10.1364/ol.530600 · Cited by 4
“On the other hand, the type-II diabolic point is quite rare in comparison with its type-I counterpart [30, 31], because the Fermi surface corresponding to the former case is a pair of crossing lines, while for the latter it is a point [32].”
BackgroundMou, D.-S., Zhang, J.-H., Jia, Y.-H., et al. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.115895 · Cited by 4
Complex Dirac-like Electronic Structure in Atomic Site-Ordered Rh3In3.4Ge3.6
Savvidou, A., Clark, J. K., Wang, H., Wei, K., Choi, E. S., Mozaffari, S., Qian, X., Shatruk, M., & Balicas, L. (2021) · Chemistry of Materials · doi:10.1021/acs.chemmater.0c03943 · Cited by 4
Conical diffractions in Kagome lattice
Liu, X., Yang, J., Guo, X., Zhang, J., Li, P., & Liu, Y. (2021) · Results in Physics · doi:10.1016/j.rinp.2021.104007 · Cited by 4
Spin-orbit interactions may relax the rigid conditions leading to flat bands
Kucska, N., & Gulácsi, Z. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.085103 · Cited by 4
Analogous Black Holes in Type-III Dirac Semimetal Ni3In2X2 (X = S, Se)
Sims, C. (2023) · Crystals · doi:10.3390/cryst13050847 · Cited by 4
“Recently, a new type of Dirac semimetal phase, called type-III, has been predicted to exist in some materials [41,42].”
BackgroundOrbital order in a bosonic p -band triangular lattice
Chen, H., & Xie, X. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.205144 · Cited by 4
Multiple Exceptional Rings in One-Dimensional Perovskite Photonic Crystals
Na, Z.-H., Zhang, X., & Feng, J. (2025) · Physical Review Letters · doi:10.1103/clbx-mh6y · Cited by 3
Electronic transport and spin-valley polarization in ferromagnetic 8-Pmmn borophene junctions
Tapia, Y. Y. H., Rodríguez-Vargas, I., Rojas-Briseño, J. G., et al. (2025) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ae0260 · Cited by 3
“In the last years, there has been an increased interest in special 2D materials called tilted Dirac materials [12].”
Polarization charge around impurities in two-dimensional anisotropic Dirac systems
Elsayed, M. M., Kim, S. W., Vanegas, J. M., et al. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.245414 · Cited by 3
Arif, M., Li, Y., Zhang, Q., et al. (2025) · Advanced Theory and Simulations · doi:10.1002/adts.202501346 · Cited by 3
Optical snake states in a photonic graphene
Bahrova, O. M., Koniakhin, S. V., Nalitov, A. V., & Cherotchenko, E. D. (2024) · Optics Letters · doi:10.1364/ol.519717 · Cited by 4
Design of biphenylene-derived tunable dirac materials
Hong, I., Bae, H., Ahn, J., et al. (2024) · FlatChem · doi:10.1016/j.flatc.2024.100760 · Cited by 3
Photonic Type-III Nodal Loop and Topological Phase Transitions at Bilayer Metasurfaces
Li, H., Hu, C., Jiang, J., et al. (2022) · Frontiers in Materials · doi:10.3389/fmats.2022.909381 · Cited by 3
“Newly, the type-III configuration, which is termed for the cross between the flat band and the dispersive band, has been identified for nodal point degeneracy (Milićević et al., 2019).”
BackgroundStabilized Dirac points in one-dimensional non-Hermitian optical lattices
Li, S., Ke, S., Wang, B., & Lu, P. (2022) · Optics Letters · doi:10.1364/ol.471869 · Cited by 3
Third-order orbital corner state and its realization in acoustic crystals
Wang, J., Chen, Y., & Lu, X. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.054115 · Cited by 2
Designer gapped and tilted Dirac cones in lateral graphene superlattices
Wild, A., Hartmann, R., Mariani, E., & Portnoi, M. E. (2025) · APL Quantum · doi:10.1063/5.0251887 · Cited by 2
Olmos, M. G., Baba, Y., López, A., Amado, M., & Molina, R. A. (2025) · 2D Materials · doi:10.1088/2053-1583/ae0f28 · Cited by 2
“In contrast, the present study incorporates spin-flip processes in a type-I model induced by a RSOC that can be controlled by an external electric field.”
Tunable plasmon modes and topological transitions in monolayer and bilayer semi-Dirac materials
Giri, D., Schliemann, J., Molina, R. A., & López, A. (2025) · Physical review. B./Physical review. B · doi:10.1103/vlzv-jpq7 · Cited by 2
“Furthermore, type III Dirac cones that combine flat and linear dispersions were predicted in reference[23] for which Dirac cones emerge from the touching of a flat and a parabolic band when a synthetic photonic strain is introduced into the lattice.”
Type-III Weyl semi-half-metal in an ultralight monolayer Li 2 N
Li, Q., Chen, L., Zhang, R., et al. (2025) · Physical review. B./Physical review. B · doi:10.1103/vqdz-12bz · Cited by 2
Lifshitz transitions and hybrid Weyl points in RbAg5Se3
Fan, X., Lu, Y., Liu, J., Ma, X., Sun, L., Li, Y., & Zhao, M. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac9fea · Cited by 2
Tilt and Anisotropy of the Dirac Spectrum Caused by the Overlapping of Bloch Functions
Алисултанов, З. З., & Демиров, Н. А. (2023) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s002136402360115x · Cited by 2
Sukprasert, N., Rakrong, P., Saipaopan, C., et al. (2024) · Nanomaterials · doi:10.3390/nano14090811 · Cited by 2
Crossover in electronic specific heat near narrow-sense type-III Dirac cones
Kishigi, K., & Hasegawa, Y. (2025) · Physical review. B./Physical review. B · doi:10.1103/15j3-22sr · Cited by 2
“Experimental realizations of this transition and a semi-Dirac point have been reported in artificial systems including ultracold atoms in optical lattices [8], photonic resonator lattices [9], and polariton systems in semiconductor micropillar lattices [10, 11].”
Making an artificial px,y -orbital honeycomb electron lattice on a metal surface
Qiu, W.-X., Ma, L., Lü, J., & Gao, J.-H. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.235404 · Cited by 3
Second harmonic generation in the tilted type-I Dirac metals under terahertz frequency regime
Liang, L.-F., Dai, X., & Chen, Q. (2021) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2020.114604 · Cited by 2
Nonadiabatic transition at a band-touching point
Vaezi, M.-S., & Esfahani, D. N. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013224 · Cited by 2
“On the other hand, there are a variety of physically relevant systems which are gap-less through the presence of a touching point in the energy dispersion, e.g., graphene[23–26], 1D and 2D p-wave superconductors [27–29], and semi-Dirac materials[30–33].”
Topological phenomena demonstrated in photorefractive photonic latticesPreprint
Xia, S., Song, D., Wang, N., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.16147 · Cited by 2
Fano resonances in tilted Weyl semimetals in an oscillating quantum well
Das, S., Maity, A., Sarkar, R., Menon, A., Nag, T., & Basu, B. (2024) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ad5acd · Cited by 1
Quantum criticality of type-I and critically tilted Dirac semimetals
Hu, H., & Krüger, F. (2025) · Physica C Superconductivity · doi:10.1016/j.physc.2025.1354687 · Cited by 1
Topological phases in two-dimensional Rydberg lattices
Svendsen, M. B. M., & Olmos, B. (2025) · Physical Review A · doi:10.1103/lf2c-h1kk · Cited by 2
“Moreover, here we observe that the Dirac cones are not only anisotropic, but also tilted [55–58].”
Espinosa-Champo, A. D. J., Kunold, A., & Naumis, G. G. (2025) · Journal of Physics Materials · doi:10.1088/2515-7639/ae11d3 · Cited by 1
“We are primarily interested in materials that lack a bandgap around the Fermi level [41, 42].”
Topological dual-Wannier cycles in orbital phononic crystals
Xie, W., Wu, J., He, Z., Deng, K., He, H., Ke, M., & Liu, Z. (2025) · Physical review. B./Physical review. B · doi:10.1103/hxs8-qw4r · Cited by 1
Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
Chatterjee, S., Maity, A., Potten, J., Müller, T., Feuerpfeil, A., Thomale, R., Penc, K., Jeschke, H. O., Samajdar, R., & Iqbal, Y. (2026) · Physical Review Research · doi:10.1103/xmtj-4kj9 · Cited by 2
“Upon increasing χ v , a Dirac spin liquid appears but with a tilted cone located along the path between K 2 and K 3 = ( π/ 3 , π/ 2) [124,125].”
Generalized strain-induced pseudomagnetic fields in hexagonal Dirac materials
Xia, J., & Zhu, S. (2025) · Physical review. B./Physical review. B · doi:10.1103/5kgn-84cp · Cited by 1
Synergistic Control of Multi‐Type Polarization Singularities in a Lieb Photonic Crystal Slab
Kang, M., Zhang, T., Geng, Z., et al. (2026) · Laser & Photonics Review · doi:10.1002/lpor.202503105 · Cited by 1
Exploring Stable Long‐Lifetime Plasmon Excitations in the Lieb Lattice
Iurov, A., Zhemchuzhna, L., Gumbs, G. A., & Huang, D. (2026) · Annalen der Physik · doi:10.1002/andp.202600005 · Cited by 1
“In the lowest order for an external perturbation, the dynamical polarization function can be written explicitly as In this notation, 11 ) represents the thermal-equilibrium Fermi–Dirac distribution function.”
InfluentialKishigi, K., Tsukidashi, K., & Hasegawa, Y. (2023) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.92.104601 · Cited by 1
Topological phase transition of photonic Chern insulators by multi-Mie-resonance inversion
Huang, H., Hu, J., Ye, X., Li, S., Li, H., Jiang, Y., Lu, M., & Zhan, P. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.054034 · Cited by 1
Direct Observation of Anisotropic Coulomb Interaction in a Topological Nodal Line Semimetal
Kim, H. W., Jung, J., Lee, G., Park, T., Jang, W., Kim, H., Kim, J. S., Shim, J. H., Yang, B., & Jeon, S. (2025) · Advanced Science · doi:10.1002/advs.202407437 · Cited by 1
Tang, G.-H., Ma, Z.-L., Zhang, R., Hou, B., Dong, Y.-H., Fan, R., Cai, Q., Zhu, Y., Peng, R., & Wang, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.195423 · Cited by 1
Oxidized-driven and strain-tunable anisotropic effects in crystalline graphene oxides
Zhong, C., Ma, J., Li, X., et al. (2025) · New Journal of Physics · doi:10.1088/1367-2630/adfb01 · Cited by 1
Priya, P., Rodriguez, A., Ortiz, O., Lemaître, A., Esmann, M., & Lanzillotti-Kimura, N. D. (2022) · Nanoengineering: Fabrication, Properties, Optics, Thin Films, and Devices · doi:10.1117/12.2633360 · Cited by 1
Self-citationPhotonic p-orbital higher-order topological insulatorsPreprint
Zhang, Y., Bongiovanni, D., Wang, Z., et al. (2022) · Research Square · doi:10.21203/rs.3.rs-2085548/v1 · Cited by 1
Ma, T.-C., Hu, J.-N., Chen, Y.-A., Shao, L., Hu, X.-R., & Deng, J.-B. (2020) · arXiv (Cornell University)
Generation, propagation and control of quantized vortices and dark solitons in polariton superfluidsPreprint
Maître, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.02163
Semi-Dirac transport and localization in polaritonic graphene
Real, B., Jamadi, O., Milićević, M., Pernet, N., St-Jean, P., Ozawa, T., Montambaux, G., Sagnes, I., Lamaitre, A., Gratiet, L. L., et al. (2021) · Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) · doi:10.1109/cleo/europe-eqec52157.2021.9542044
“By measuring the polariton emission, both in momentum and real space, for uncompressed and compressed honeycomb lattices, we evidence a semi-Dirac dispersion [5, 6] [see FIG.”
BackgroundSelf-citationXie, Y., Song, L., Yan, W., Xia, S., Tang, L., Song, D., Rhim, J., & Chen, Z. (2021) · Default Digital Object Group · doi:10.1063/5.0068032.1
Report on scipost_202104_00031v1
Lledó, C., Carusotto, I., & Szymańska, M. H. (2021) · SciPost Physics · doi:10.21468/scipost.report.3164
Report on scipost_202104_00031v2
Lledó, C., Carusotto, I., & Szymańska, M. H. (2021) · SciPost Physics · doi:10.21468/scipost.report.3819
Report on scipost_202104_00031v2
Lledó, C., Carusotto, I., & Szymańska, M. H. (2021) · SciPost Physics · doi:10.21468/scipost.report.4066
Robust and intrinsic type-III nodal points in a diamond-like lattice
Cheng, Q.-Y., Xie, Y., Yan, X., et al. (2022) · Chinese Physics B · doi:10.1088/1674-1056/ac7c00
Tilt and Anisotropy of the Dirac Spectrum Caused by the Overlapping of Bloch Functions
Алисултанов, З. З., & Демиров, Н. А. (2023) · Письма в Журнал экспериментальной и теоретической физики · doi:10.31857/s1234567823100105
Cavity quantum electrodynamics and polaritons
Klembt, S., Betzold, S., & Höfling, S. (2024) · Elsevier eBooks · doi:10.1016/b978-0-323-98378-5.00005-2
Band structures of generalized eigenvalue equations and conic sections
Isobe, T., Yoshida, T., & Hatsugai, Y. (2025) · Physical Review A · doi:10.1103/m6qm-2bll · Cited by 1
Quantum geometry in hexagonal circuit QED lattice with triple leg stripline resonators
Kim, D., Rhim, J., & Moon, K. (2025) · Scientific Reports · doi:10.1038/s41598-025-17586-x
“There exist other 2D Kagome-lattice materials which use this extra degree of freedom to obtain interesting physics (e.g. spin-valley qubits in GaAS) as well as an experiment using a honeycomb lattice made of coupled micropillars with four orbitals per unit cell in the A and B sublattice 48–50 .”
Orbital frontiers: harnessing higher modes in photonic simulators
Noh, J., Schulz, J., Benalcazar, W. A., & Jörg, C. (2025) · Nanophotonics · doi:10.1515/nanoph-2025-0492 · Cited by 2
“Significantly, photonic p -orbital graphene was the platform for the first experimental observation of critically tilted (Type-III) Dirac cones, in addition to semi-Dirac and tilted Type-I Dirac cones [79].”
Orbital magnetic susceptibility of type I, II, and III massless Dirac fermions in two dimensions
Mizoguchi, T., Matsuura, H., & Ogata, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/646v-jjn8 · Cited by 1
Tuning the electronic properties of graphene via embedding diborane molecules
Zhong, C., Li, Z., & Ma, J. (2025) · Applied Physics Letters · doi:10.1063/5.0304052
Realizing type-III acoustic Dirac cones with the staggered Mielke model
Li, Y., Ma, J., & Sun, X. (2025) · Physical review. B./Physical review. B · doi:10.1103/9bsk-2jbt
Tailored Tight‐Binding Couplings in Photonic Crystals
Zheng, J., Ma, J., Tian, Z., & Yi, J. (2026) · Laser & Photonics Review · doi:10.1002/lpor.202502889
“…framework further offers a direct correspondence between structural geometry and Hamiltonian parameters, enabling intuitive design of photonic symmetries, synthetic gauge fields, and topological phases, thereby allowing condensed-matter concepts to be naturally translated into PCs [ 20, 25, 26 ].”
Ding, F., Dai, X., Zou, Y., Jiang, L., & Xiang, Y. (2026) · Laser & Photonics Review · doi:10.1002/lpor.202502802 · Cited by 2
Goblot, V. (2019) · theses.fr (ABES) · doi:10.70675/ad409689zb168z4dc0z9c72z8fc96ce1c6dd
Dynamics of topological defects in exciton-polariton quantum fluids
Koniakhin, S. V. (2020) · theses.fr (ABES) · doi:10.70675/2594e624z1b7cz433ez9d1bz5466ec5e501c
Transport and driven-dissipative localization in exciton-polariton lattices
Real, B. (2022) · theses.fr (ABES) · doi:10.70675/0050a89bze45dz4676z8cbbz920f53ac4338
Self-citationNon-linear physics associated to chiral symmetry in driven dissipative polariton lattices
Pernet, N. (2022) · theses.fr (ABES) · doi:10.70675/7f710a14z7fbbz4e17zb1b0zcf2e0517de77
Bloch Eigenvector structure tomography in polaritonic lattices for multiband topology
Guillot, M. (2024) · theses.fr (ABES) · doi:10.70675/0d57b6c2z4949z4e18za11ezd4f143f9933d
Quadratic Band Touching and Nontrivial Winding Reveal Generalized Angular Momentum Conservation
Wang, Y., Bongiovanni, D., Jukić, D., Lei, S., Hu, Z., Song, D., Xu, J., Morandotti, R., Buljan, H., & Chen, Z. (2026) · Physical Review Letters · doi:10.1103/br8b-n4b4
“…Hall effects [12,22], and anomalous Landau-level quantization [23], all distinct from their counterparts in graphene lattices with LBTPs. Experimental realizations of QBTPs in cold atoms [16] and photonic systems [24–27] now provide effective platforms for exploring physics beyond Dirac cones.”
Anonymous, Faraei, Z., & Moghaddam, A. G. (2026) · Physical review. B./Physical review. B · doi:10.1103/pymr-118x
Antibunching in locally driven dissipative Lieb lattices
Anonymous, Matuszewski, M., Deuar, P., & Szymańska, M. H. (2026) · Physical review. B./Physical review. B · doi:10.1103/g22d-99w7
Metadata
- Authors
- Milićević, M., Montambaux, G., Ozawa, T., Jamadi, O., Real, B., Sagnes, I., Lemaître, A., Le Gratiet, L., Harouri, A., Bloch, J., & Amo, A.
- Affiliations
- Université Paris-Sud (FR)
- RIKEN (JP)
- Centre National de la Recherche Scientifique (FR)
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2019-07-23
- Volume
- 9
- Issue
- 3
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W2884840542
- Semantic Scholar
- 38b2bab9af1d5a17dfd7279a962bf7883f5d587f
- Cited by
- 171
- References
- 55
- Citations by year
- 2026: 8 · 2025: 27 · 2024: 28 · 2023: 22 · 2022: 27 · 2021: 30 · 2020: 25 · 2019: 4
- FWCI
- 9.54
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- HAL (Le Centre pour la Communication Scientifique Directe) (submittedVersion, other-oa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion)
- arXiv (Cornell University)
- Greater South Information System
- Funders
- H2020 European Research Council
- Agence Nationale de la Recherche (ANR-16-CE30-0021, ANR-11-LABX-0007, ANR-10-LABX-0035)
- Japan Society for the Promotion of Science (JP18H05857)
- RIKEN
- French RENATECH network
- CPER Photonics for Society P4S
- I-Site ULNE
- Métropole Européenne de Lille
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Keywords
- tilted Dirac cones, flat bands, photonic lattices, honeycomb lattice, photonic resonators, topological charge, Klein tunneling, anomalous Hall effect, orbital degrees of freedom
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-23, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-23 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
