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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.
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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.
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“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
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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
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“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
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“they possess a nontrivial topological charge”
§ Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene > Abstract
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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
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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
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“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.
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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
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“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
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“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
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- Probably not a substantial claim. 4
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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
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“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
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- Not matchedcites [36]
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“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
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“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
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“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
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“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
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“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
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“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
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“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
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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
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“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
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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
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“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
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“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
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“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.
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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.
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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
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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
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BackgroundLasing in topological edge states of a one-dimensional lattice
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Background
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Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
“Interestingly, homogeneous strain has been employed to synthesize critically tilted Dirac cones in the orbital p bands of lattices of coupled micropillars (Milićević et al., 2018).”
MethodSelf-citationNi, X., Yves, S., Krasnok, A., & Alù, A. (2023) · Chemical Reviews · doi:10.1021/acs.chemrev.2c00800 · Cited by 166
Photonic flat‐band lattices and unconventional light localization
Tang, L., Song, D., Xia, S., Xia, S., Ma, J., Yan, W., Hu, Y., Xu, J., Leykam, D., & Chen, Z. (2020) · Nanophotonics · doi:10.1515/nanoph-2020-0043 · Cited by 126
Li, J., Yang, X., Ma, C., et al. (2021) · Applied Catalysis B: Environmental · doi:10.1016/j.apcatb.2021.120053 · Cited by 96
Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices
Jamadi, O., Rozas, E., Salerno, G., Milićević, M., Ozawa, T., Sagnes, I., Lemaître, A., Gratiet, L. L., Harouri, A., Carusotto, I., et al. (2020) · Light Science & Applications · doi:10.1038/s41377-020-00377-6 · Cited by 97
“[33] M.”
Self-citationOptical analogue of Dresselhaus spin–orbit interaction in photonic graphene
Whittaker, C. E., Dowling, T., Nalitov, A. V., Yulin, A. V., Royall, B., Clarke, E., Skolnick, M. S., Shelykh, I. A., & Krizhanovskii, D. N. (2021) · Nature Photonics · doi:10.1038/s41566-020-00729-z · Cited by 83
Direct observation of photonic Landau levels and helical edge states in strained honeycomb lattices
Jamadi, O., Rozas, E., Salerno, G. (., Milićević, M., Ozawa, T., Sagnes, I., Lemaître, A., Gratiet, L. L., Harouri, A., Carusotto, I., et al. (2020) · LillOA (Université de Lille (University Of Lille)) · Cited by 75
Self-citationNonlinear topological valley Hall edge states arising from type-II Dirac cones
Zhong, H., Xia, S., Zhang, Y., Li, Y., Song, D., Liu, C., & Chen, Z. (2021) · Advanced Photonics · doi:10.1117/1.ap.3.5.056001 · Cited by 71
“1(f)]—the characteristic feature of the type-II Dirac cone.(61)”
BackgroundRealization of photonic p-orbital higher-order topological insulators
Zhang, Y., Bongiovanni, D., Wang, Z., Wang, X., Xia, S., Hu, Z., Song, D., Jukić, D., Xu, J., Morandotti, R., et al. (2023) · eLight · doi:10.1186/s43593-022-00039-7 · Cited by 82
“In particular, by employing the p-orbital bands of polariton micropillars arranged in a honeycomb lattice, both orbital edge states and exotic Dirac dispersions were observed [13, 14].”
MethodPhotonic quadrupole topological insulator using orbital-induced synthetic flux
Schulz, J., Noh, J., Benalcazar, W. A., Bahl, G., & von Freymann, G. (2022) · Nature Communications · doi:10.1038/s41467-022-33894-6 · Cited by 72
Topological transition in stratified fluids
Perrot, M., Delplace, P., & Venaille, A. (2019) · Nature Physics · doi:10.1038/s41567-019-0561-1 · Cited by 64
Moiré Fringe Induced Gauge Field in Photonics
Wang, W., Gao, W., Chen, X., Shi, F., Li, G., Dong, J., Xiang, Y., & Zhang, S. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.203901 · Cited by 61
Semi-Dirac Transport and Anisotropic Localization in Polariton Honeycomb Lattices
Real, B., Jamadi, O., Milićević, M., Pernet, N., St-Jean, P., Ozawa, T., Montambaux, G., Sagnes, I., Lemaître, A., Gratiet, L. L., et al. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.186601 · Cited by 57
Self-citationDirac points emerging from flat bands in Lieb-kagome lattices
Lim, L.-K., Fuchs, J.-N., Piéchon, F., et al. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.045131 · Cited by 54
“In these artificial systems, direct imaging of localized states [4, 7, 8] or the study of tunable interaction-induced effects [9] are few examples which show approaches hitherto not easily realizable in conventional condensed matter systems.”
BackgroundSelf-citationAnnihilation of exceptional points from different Dirac valleys in a 2D photonic system
Król, M., Septembre, I., Oliwa, P., Kędziora, M., Łempicka-Mirek, K., Muszyński, M., Mazur, R., Morawiak, P., Piecek, W., Kula, P., et al. (2022) · Nature Communications · doi:10.1038/s41467-022-33001-9 · Cited by 54
“(6) The winding numbers of the eight EPs alternate in sign along the ellipse.”
BackgroundTwo-dimensional Dirac materials: Tight-binding lattice models and material candidates
Fan, R., Sun, L., Shao, X., Li, Y., & Zhao, M. (2022) · ChemPhysMater · doi:10.1016/j.chphma.2022.04.009 · Cited by 57
Jia, H., Wang, M., Ma, S., Zhang, R.-Y., Hu, J., Wang, D., & Chan, C. T. (2023) · Light Science & Applications · doi:10.1038/s41377-023-01209-z · Cited by 51
Hybrid exceptional point created from type-III Dirac point
Jin, L., Wu, H., Wei, B.-B., & Song, Z. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.045130 · Cited by 48
Orbital topological edge states and phase transitions in one-dimensional acoustic resonator chains
Gao, F., Xiao, X., Peng, Y., Ni, X., Sun, Q., Yves, S., Zhu, X., & Alù, A. (2023) · Nature Communications · doi:10.1038/s41467-023-44042-z · Cited by 45
“Within the tight-binding approximation 34,35 , the orbital-dependent lattice can be characterized by the real-space Hamiltonian where a y n , i ( a n , i ) is the creation (annihilation) operator for the resonant modes associated with p orbitals of indices i ð j Þ = σ , π , representing the…”
BackgroundMethodUniversal momentum-to-real-space mapping of topological singularities
Liu, X., Xia, S., Jajtić, E., Song, D., Li, D., Tang, L., Leykam, D., Xu, J., Buljan, H., & Chen, Z. (2020) · Nature Communications · doi:10.1038/s41467-020-15374-x · Cited by 45
Wu, X., Li, X., Zhang, R.-Y., Xiao, X. H., Tian, J., Huang, Y., Wang, S., Hou, B., Chan, C. T., & Wen, W. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.075501 · Cited by 37
Topological optical and phononic interface mode by simultaneous band inversion
Ortiz, O., Priya, P., Rodriguez, A., Lemaître, A., Esmann, M., & Lanzillotti-Kimura, N. D. (2021) · Optica · doi:10.1364/optica.411945 · Cited by 39
Self-citationFully Quantum Scalable Description of Driven-Dissipative Lattice Models
Deuar, P., Ferrier, A., Matuszewski, M., Orso, G., & Szymańska, M. H. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010319 · Cited by 42
Reconfigurable quantum fluid molecules of bound states in the continuum
Gianfrate, A., Sigurðsson, H., Ardizzone, V., Nguyen, H. S., Riminucci, F., Efthymiou-Tsironi, M., Baldwin, K. W., Pfeiffer, L. N., Trypogeorgos, D., Giorgi, M. D., et al. (2024) · Nature Physics · doi:10.1038/s41567-023-02281-3 · Cited by 37
Measuring Topological Invariants in a Polaritonic Analog of Graphene
St-Jean, P., Dauphin, A., Massignan, P., Real, B., Jamadi, O., Milićević, M., Lemaître, A., Harouri, A., Gratiet, L. L., Sagnes, I., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.127403 · Cited by 42
“Using polaritonic lattices emulating regular [24] and critically compressed [25] graphene (i.e., where Dirac cones have merged), we measure these 1D topological invariants and thus provide a direct evidence of the bulk-edge correspondence in these systems.”
Self-citationExperimental Observation of Flat Bands in One-Dimensional Chiral Magnonic Crystals
Tacchi, S., Flores-Farías, J., Petti, D., et al. (2023) · Nano Letters · doi:10.1021/acs.nanolett.2c04215 · Cited by 35
Orbital corner states on breathing kagome lattices
Lu, X., Chen, Y., & Chen, H. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.195143 · Cited by 35
Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands
Xie, Y., Song, L., Yan, W., Xia, S., Tang, L., Song, D., Rhim, J., & Chen, Z. (2021) · APL Photonics · doi:10.1063/5.0068032 · Cited by 36
Recent advances in density functional theory approach for optoelectronics properties of graphene
Agbolade, L. O., Adam, T., Edet, C.-A., Adewale, A. A., Chik, A., Mohammed, M., Gopinath, S. C. B., & Hashim, U. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e14279 · Cited by 34
Zangeneh‐Nejad, F., & Fleury, R. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.054301 · Cited by 29
Optically modulated tunneling current of dressed electrons in graphene and a dice lattice
Iurov, A., Zhemchuzhna, L., Gumbs, G. A., Huang, D., & Fekete, P. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.115309 · Cited by 29
Chen, R., Wang, Y., Qian, G., et al. (2023) · ACS Applied Nano Materials · doi:10.1021/acsanm.2c05240 · Cited by 29
Photoinduced Floquet mixed-Weyl semimetallic phase in a carbon allotrope
Deng, T., Zheng, B., Zhan, F., Fan, J., Wu, X., & Wang, R. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.201105 · Cited by 27
Fully Quantum Scalable Description of Driven-Dissipative Lattice Models
Deuar, P., Ferrier, A., Matuszewski, M., Orso, G., & Szymańska, M. H. (2021) · UCL Discovery (University College London) · Cited by 26
Photonic Flatband Resonances in Multiple Light Scattering
Hoang, T. X., Leykam, D., & Kivshar, Y. S. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.043803 · Cited by 27
Topological phenomena demonstrated in photorefractive photonic lattices [Invited]
Xia, S., Song, D., Wang, N., Liu, X., Ma, J., Tang, L., Buljan, H., & Chen, Z. (2021) · Optical Materials Express · doi:10.1364/ome.417392 · Cited by 28
Liu, H., Cao, H., & Meng, S. (2023) · Progress in Surface Science · doi:10.1016/j.progsurf.2023.100705 · Cited by 26
Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice
Könye, V., Morice, C., Chernyavsky, D., Moghaddam, A. G., van den Brink, J., & van Wezel, J. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033237 · Cited by 25
Symmetry-Induced Error Filtering in a Photonic Lieb Lattice
Chang, Y.-J., Lu, Y., Wang, Y., Xu, X.-Y., Zhou, W.-H., Cui, W.-H., Wang, X., Gao, J., Qiao, L., & Jin, X. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.110501 · Cited by 22
Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices
Lang, J.-P., Hanafi, H., Imbrock, J., & Denz, C. (2023) · Physical Review A · doi:10.1103/physreva.107.023509 · Cited by 20
Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices
Pyrialakos, G. G., Schmitt, N., Nye, N. S., Heinrich, M., Kantartzis, N. V., Szameit, A., & Christodoulides, D. N. (2020) · Nature Communications · doi:10.1038/s41467-020-15952-z · Cited by 20
Strain-induced topological transitions and tilted Dirac cones in kagome lattices
Mojarro, M. A., & Ulloa, S. E. (2023) · 2D Materials · doi:10.1088/2053-1583/acfe88 · Cited by 19
“Here, the tilting is along the qx axis and characterized by vt/vx < 1, describing tilted type-I Dirac cones [29, 30].”
BackgroundType-III Dirac fermions in HfxZr1−xTe2 topological semimetal candidate
Fragkos, S., Tsipas, P., Xenogiannopoulou, E., Panayiotatos, Y., & Dimoulas, A. (2021) · Journal of Applied Physics · doi:10.1063/5.0038799 · Cited by 19
Observation of Copropagating Chiral Zero Modes in Magnetic Photonic Crystals
Li, Z., Ma, S., Li, S., You, O., Liu, Y., Yang, Q., Xiang, Y., Zhou, P., & Zhang, S. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.033802 · Cited by 19
Effects of uniaxial and shear strains on the electronic spectrum of Lieb and kagome lattices
Lima, W. P., da Costa, D. R., Sena, S. H. R., & Pereira, J. M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.125433 · Cited by 19
Multi-orbital tight binding model for cavity-polariton lattices
Mangussi, F., Milićević, M., Sagnes, I., Gratiet, L. L., Harouri, A., Lemaître, A., Bloch, J., Amo, A., & Usaj, G. (2020) · LillOA (Université de Lille (University Of Lille)) · Cited by 18
Self-citationPhotonic Dirac nodal-line semimetals realized by a hypercrystal
Hu, S., Guo, Z., Jiang, H., & Chen, H. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.023047 · Cited by 17
Universal Design Platform for an Extended Class of Photonic Dirac Cones
Kim, J., Yu, S., & Park, N. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.13.044015 · Cited by 17
Self-Assembly of Isostatic Self-Dual Colloidal Crystals
Lei, Q., Wei, Z., Tang, F., et al. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.018001 · Cited by 16
Wang, S., & Yang, B. (2024) · ACS Applied Electronic Materials · doi:10.1021/acsaelm.3c01402 · Cited by 15
Tuneable Schottky contact of MoSi2N4/TaS2 van der Waals heterostructure
Xia, J., Gu, Y., Mai, J., et al. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e20619 · Cited by 14
“After the discovery of graphene as a two-dimensional material [1], its exceptional physical properties, such as high electron mobility [2], the quantum Hall effect [3] and the Dirac cone [4] have garnered significant attention [5–8].”
BackgroundMizoguchi, T., & Hatsugai, Y. (2020) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.89.103704 · Cited by 14
Dirac points and topological phases in correlated altermagnets
Re, L. D. (2025) · Physical Review Research · doi:10.1103/7nvm-s225 · Cited by 13
Tabanelli, H., Castelnovo, C., & Štrkalj, A. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.184208 · Cited by 16
Shao, X., Sun, L., Ma, X., Feng, X., Gao, H., Ding, C., & Zhao, M. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ac0dd4 · Cited by 13
“Dirac cone in a two-dimensional (2D) system can be described by an effective Hamiltonian ( = 1) [14]:”
PT -symmetric non-Hermitian zigzag-edged ribbon of bilayer photonic graphene
Zhang, L.-L., Li, J., Zhang, D., Xu, T., Cui, W., & Gong, W. (2022) · Results in Physics · doi:10.1016/j.rinp.2022.105274 · Cited by 13
Topologically Protected Wormholes in Type-III Weyl Semimetal Co3In2X2 (X = S, Se)
Sims, C. (2021) · Condensed Matter · doi:10.3390/condmat6020018 · Cited by 13
Chu, H., Zhang, Y., Luo, J., Xu, C., Xiong, X., Peng, R., Wang, M., & Lai, Y. (2021) · Optics Express · doi:10.1364/oe.427389 · Cited by 14
Dirac fermions collimation in heterostructures based on tilted Dirac cone materials
Choubabi, E. B., Lemaalem, B., Raggui, M., Belouad, A., Houça, R., Kamal, A., & Monkade, M. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad6109 · Cited by 12
Reconfiguring graphene to achieve intrinsic negative Poisson’s ratio and strain-tunable bandgap
Wang, S., Yao, Y., Peng, Z., et al. (2021) · Nanotechnology · doi:10.1088/1361-6528/ac1220 · Cited by 12
“which will greatly improve its application in superconductivity [42, 43].”
Quantum electrodynamics in anisotropic and tilted Dirac photonic lattices
Redondo–Yuste, J., de Paz, M. B., Huidobro, P. A., & González-Tudela, A. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac27e0 · Cited by 10
Topological band crossings in epitaxial strained SnTe
Fragkos, S., Sant, R., Alvarez, C., Golias, E., Marquez‐Velasco, J., Tsipas, P., Tsoutsou, D., Aminalragia‐Giamini, S., Xenogiannopoulou, E., Okuno, H., et al. (2019) · Physical Review Materials · doi:10.1103/physrevmaterials.3.104201 · Cited by 12
Dirac exciton–polariton condensates in photonic crystal gratings
Sigurðsson, H., Nguyen, H. S., & Nguyen, H. S. (2024) · Nanophotonics · doi:10.1515/nanoph-2023-0834 · Cited by 11
Mizoguchi, T., Matsuura, H., & Ogata, M. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.205203 · Cited by 11
Domain-Wall Topology Induced by Spontaneous Symmetry Breaking in Polariton Graphene
Solnyshkov, D. D., Leblanc, C., Septembre, I., & Malpuech, G. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.066802 · Cited by 11
“The Dirac cones, both ”straight” [37] and ”tilted” [41], have been observed in polariton graphene, and the topological edge states based on the quantum anomalous Hall effect were evidenced experi-”
Circularly polarized light irradiated ferromagnetic MnBi 2 Te 4 : A possible ideal Weyl semimetal
Fan, S., Huang, S., Chen, Z., Zhan, F., Ding, X., Ma, D., & Wang, R. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.125204 · Cited by 13
Subspace-induced Dirac point and nondissipative wave dynamics in a non-Hermitian optical lattice
Li, S., Wang, S., Chen, S., Wu, Y., Ke, S., Wang, B., & Lu, P. (2022) · Physical Review A · doi:10.1103/physreva.105.033512 · Cited by 10
Moving Dirac nodes by chemical substitution
Nilforoushan, N., Casula, M., Amaricci, A., Caputo, M., Caillaux, J., Khalil, L., Papalazarou, E., Simon, P., Perfetti, L., Vobornik, I., et al. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2108617118 · Cited by 14
“Such movable Dirac nodes in the k-space have recently attracted a great deal of interest from theory (15, 28, 57), as well as in the context of optical lattices (25) and photonic crystals (26).”
BackgroundZheng, L., Theocharis, G., Fleury, R., Tournat, V., & Gusev, V. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abb862 · Cited by 9
Visualization of orbital twig edge states in phononic graphene lattices
Gao, F., Peng, Y., Xiao, X., Sun, Q., Chen, Z., Li, B., & Zhu, X. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.044005 · Cited by 9
Topological states in the noncentrosymmetric superconductors LaPtSi and LaPtGe
Shi, X., Liu, Q., He, P., Yuan, Y., Kong, X., Li, K., & Zhao, W. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.245129 · Cited by 9
Effective medium model for graphene superlattices with electrostatic and magnetic vector potentials
Fernandes, D. E. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.085119 · Cited by 8
“Such dispersion characteristic corresponds to a type-III Dirac cone [45, 50, 51], where one of the bands is flat and the other has a linear dispersion.”
BackgroundOptical conductivity of tilted higher pseudospin Dirac-Weyl cones
Wareham, W. C., & Nicol, E. J. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.085424 · Cited by 8
PT-symmetric non-Hermitian AB-stacked bilayer honeycomb photonic lattice
Zhang, D., Li, X., Zhang, L.-L., Fan, D.-Z., Jin, Z., & Gong, W. (2020) · Journal of the Optical Society of America B · doi:10.1364/josab.398686 · Cited by 7
Gupta, N., Srinivasu, S., Kumar, M., et al. (2024) · Applied Physics Letters · doi:10.1063/5.0175495 · Cited by 7
Tuning electronic pairing by uniaxial strain in kagome lattices
Mojarro, M. A., & Ulloa, S. E. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.235129 · Cited by 7
“The quadratic band-crossing point at the Γ point of the Bril-louin zone carries a Berry flux of 2 π [33, 53] without strain, which splits into two Dirac points with Berry flux π each when a strain is applied, reducing the C 6 symmetry of the lattice down to C 2 [54].”
MethodXiong, W., Zhang, T., Zhang, Z., Zhu, Y., Wang, S., Zhang, H., Cheng, Y., Liu, X., & Christensen, J. (2025) · Physical Review Letters · doi:10.1103/wkwd-cbn2 · Cited by 7
Smart holes: analogue black holes with the right temperature and entropy
Yang, J., Afshordi, N., Torabian, M., Jafari, S. A., & Baskaran, G. (2025) · Journal of High Energy Physics · doi:10.1007/jhep07(2025)226 · Cited by 10
Monoatomic orbital-based one-dimensional topological crystalline insulator
Liu, G., Workman, V., Noh, J., Ma, Y., Hughes, T. L., Benalcazar, W. A., & Bahl, G. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.214110 · Cited by 7
“…investigations of orbital physics have leveraged more flexible synthetic materials produced through a variety of approaches, such as with ultracold atoms trapped in optical lattices [27, 30–36], polariton lattices [37–40], photonic waveguide arrays [41–45], and nanomechanical resonators [46].”
BackgroundMethodWeyl points and exceptional rings with polaritons in bulk semiconductors
Guinness, R. L. M., & Eastham, P. R. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043268 · Cited by 7
Topological phonons in arrays of ultracold dipolar particles
Liberto, M. F. D., Kruckenhauser, A., Zoller, P., & Baranov, M. A. (2022) · Quantum · doi:10.22331/q-2022-06-07-731 · Cited by 7
Propagation of Dirac waves through various temporal interfaces, slabs, and crystals
Kim, S., & Kim, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023162 · Cited by 7
Analogies for Dirac fermions physics in graphene
Dragoman, D., & Dragoman, M. (2023) · Solid-State Electronics · doi:10.1016/j.sse.2023.108818 · Cited by 8
Engineering Two-Dimensional Nodal Semimetals in Functionalized Biphenylene by Fluorine Adatoms
Mo, S., Seo, J., Son, S., Kim, S., Rhim, J., & Lee, H. (2024) · Nano Letters · doi:10.1021/acs.nanolett.4c00314 · Cited by 7
Nonlinear current response of Weyl semimetals in the ultraquantum regime
Wang, Z., Fu, Z., Zhang, P., Zhao, X.-G., & Zhang, W. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.245313 · Cited by 7
Band evolution and Landau-Zener Bloch oscillations in strained photonic rhombic lattices
Xia, S., Zhang, Y., Li, Z., Qin, L., Yang, C.-J., Lu, H., Zhang, J., Zhao, X.-D., & Zhu, Z. (2021) · Optics Express · doi:10.1364/oe.441554 · Cited by 7
Manipulating generalized Dirac cones in subwavelength dipolar arrays
de Paz, M. B., González-Tudela, A., & Huidobro, P. A. (2022) · Physical Review A · doi:10.1103/physreva.106.033505 · Cited by 6
González-Tudela, A. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac58b7 · Cited by 8
Yu, Q., Liu, Z., Dawei, G., Liang, S. K., Zhang, Y., & Zhang, Z. (2022) · Nanomaterials · doi:10.3390/nano12183222 · Cited by 6
“All the three types of Dirac cones have been realized by the aforementioned methods [25,35,36].”
BackgroundMethodInfluentialBipolar electron waveguides in two-dimensional materials with tilted Dirac cones
Hartmann, R., & Portnoi, M. E. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad2b34 · Cited by 6
Lledó, C., Carusotto, I., & Szymańska, M. H. (2022) · SciPost Physics · doi:10.21468/scipostphys.12.2.068 · Cited by 9
Wu, B.-Q., Lin, Z., Wang, L.-W., & Jiang, J. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.205136 · Cited by 5
Quasi-localization and Wannier obstruction in partially flat bands
Park, J.-H., & Rhim, J. (2024) · Communications Physics · doi:10.1038/s42005-024-01679-6 · Cited by 6
Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems
Yu, G., Xie, J., Gao, S., Wang, W., Lai, L., Jiang, C., & Li, Y. (2024) · Materials & Design · doi:10.1016/j.matdes.2024.113262 · Cited by 5
Tailoring higher-order topological phases via orbital hybridization
Mazanov, M., & Gorlach, M. A. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.205117 · Cited by 5
Montage Operation of Plaquette States in Acoustic Orbital Lattices with Type-III Dirac Points
Sun, Q., Peng, Y., Gao, F., Li, B., & Zhu, X. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.20.024025 · Cited by 5
Unconventional Dirac-Weyl semimetal with ultralong surface arc in phononic crystals
Wu, P., Gao, F., Xiao, X., Chen, Z., Peng, Y., & Zhu, X. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.094104 · Cited by 5
Novel phenomena in flatband photonic structures: from localized states to real-space topology
Xia, S., Tang, L., Xia, S., Ma, J., Yan, W., Song, D., Hu, Y., Xu, J., & Chen, Z. (2020) · Acta Physica Sinica · doi:10.7498/aps.69.20200384 · Cited by 4
All-optical triangular and honeycomb lattices of exciton–polaritons
Alyatkin, S., Sigurðsson, H., Kartashov, Y. V., et al. (2024) · Applied Physics Letters · doi:10.1063/5.0180272 · Cited by 4
Bound-in-continuum-like corner states in the type-II Dirac photonic lattice
Feng, S., Zhong, H., Belić, M. R., MIHALACHE, D. B., Li, Y., & Zhang, Y. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114719 · Cited by 4
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).
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