Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
Department of Electronics and Nanoengineering, Aalto University, 02150Espoo, Finland
Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
*Cheng Guoguocheng@stanford.edu
Shanhui Fanshanhui@stanford.edu
纸质出版日期:2023,
网络出版日期:2023-01-04,
收稿日期:2022-08-31,
修回日期:2022-11-07,
录用日期:2022-11-08
Scan QR Code
Light control with Weyl semimetals[J]. 光:快讯(英文), 2023,3(1).
Cheng Guo, Viktar S. Asadchy, Bo Zhao, et al. Light control with Weyl semimetals[J]. eLight, 2023,3(1).
Light control with Weyl semimetals[J]. 光:快讯(英文), 2023,3(1). DOI: 10.1186/s43593-022-00036-w.
Cheng Guo, Viktar S. Asadchy, Bo Zhao, et al. Light control with Weyl semimetals[J]. eLight, 2023,3(1). DOI: 10.1186/s43593-022-00036-w.
Weyl semimetals are topological materials whose electron quasiparticles obey the Weyl equation. They possess many unusual properties that may lead to new applications. This is a tutorial review of the optical properties and applications of Weyl semimetals. We review the basic concepts and optical responses of Weyl semimetals
and survey their applications in optics and thermal photonics. We hope this pedagogical text will motivate further research on this emerging topic.
Weyl semimetalTopological materialsAxion electrodynamicsNanophotonicsThermal photonicsOptical nonreciprocity
C. Herring, Accidental degeneracy in the energy bands of crystals. Phys. Rev.52, 365-373 (1937). https://doi.org/10.1103/PhysRev.52.365https://doi.org/10.1103/PhysRev.52.365
N.P. Armitage, E.J. Mele, A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys.90, 015001 (2018). https://doi.org/10.1103/RevModPhys.90.015001https://doi.org/10.1103/RevModPhys.90.015001
M. Srednicki, Quantum Field Theory (Cambridge University Press, Cambridge, 2007)
E.V. Gorbar, V.A. Miranskij, I.A. Shovkovy, P.O. Sukhachov, Electronic Properties of Dirac and Weyl Semimetals (World Scientific, Singapore, 2021)
N. Nagaosa, T. Morimoto, Y. Tokura, Transport, magnetic and optical properties of Weyl materials. Nat. Rev. Mater.5, 621-636 (2020). https://doi.org/10.1038/s41578-020-0208-yhttps://doi.org/10.1038/s41578-020-0208-y
O.V. Kotov, Y.E. Lozovik, Giant tunable nonreciprocity of light in Weyl semimetals. Phys. Rev. B98(19), 195446 (2018). https://doi.org/10.1103/PhysRevB.98.195446https://doi.org/10.1103/PhysRevB.98.195446
V.S. Asadchy, C. Guo, B. Zhao, S. Fan, Sub-wavelength passive optical isolators using photonic structures based on Weyl semimetals. Adv. Opt. Mater.8, 2000100 (2020). https://doi.org/10.1002/adom.202000100https://doi.org/10.1002/adom.202000100
Y. Park, V.S. Asadchy, B. Zhao, C. Guo, J. Wang, S. Fan, Violating Kirchhoff's law of thermal radiation in semitransparent structures. ACS Photonics8, 2417-2424 (2021). https://doi.org/10.1021/acsphotonics.1c00612https://doi.org/10.1021/acsphotonics.1c00612
Z. Ji, W. Liu, S. Krylyuk, X. Fan, Z. Zhang, A. Pan, L. Feng, A. Davydov, R. Agarwal, Photocurrent detection of the orbital angular momentum of light. Science368(6492), 763-767 (2020). https://doi.org/10.1126/science.aba9192https://doi.org/10.1126/science.aba9192
J. Lai, J. Ma, Z. Fan, X. Song, P. Yu, Z. Liu, P. Zhang, Y. Shi, J. Cheng, D. Sun, Direct light orbital angular momentum detection in mid-infrared based on the type-II Weyl semimetal TalrTe4. Adv. Mater.34(29), 2201229 (2022). https://doi.org/10.1002/adma.202201229https://doi.org/10.1002/adma.202201229
L. Wu, S. Patankar, T. Morimoto, N.L. Nair, E. Thewalt, A. Little, J.G. Analytis, J.E. Moore, J. Orenstein, Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys.13(4), 350-355 (2017). https://doi.org/10.1038/nphys3969https://doi.org/10.1038/nphys3969
S. Almutairi, Q. Chen, M. Tokman, A. Belyanin, Four-wave mixing in Weyl semimetals. Phys. Rev. B101(23), 235156 (2020). https://doi.org/10.1103/PhysRevB.101.235156https://doi.org/10.1103/PhysRevB.101.235156
J.L. Cheng, J.E. Sipe, S.W. Wu, Third-order optical nonlinearity of three-dimensional massless Dirac fermions. ACS Photonics7, 2515-2526 (2020). https://doi.org/10.1021/acsphotonics.0c00836https://doi.org/10.1021/acsphotonics.0c00836
B. Zhao, C. Guo, C.A.C. Garcia, P. Narang, S. Fan, Axion-field-enabled nonreciprocal thermal radiation in Weyl semimetals. Nano Lett.20, 1923-1927 (2020). https://doi.org/10.1021/acs.nanolett.9b05179https://doi.org/10.1021/acs.nanolett.9b05179
Y. Tsurimaki, X. Qian, S. Pajovic, F. Han, M. Li, G. Chen, Large nonreciprocal absorption and emission of radiation in type-I Weyl semimetals with time reversal symmetry breaking. Phys. Rev. B101, 165426 (2020). https://doi.org/10.1103/PhysRevB.101.165426https://doi.org/10.1103/PhysRevB.101.165426
S. Pajovic, Y. Tsurimaki, X. Qian, G. Chen, Intrinsic nonreciprocal reflection and violation of Kirchhoff's law of radiation in planar type-I magnetic Weyl semimetal surfaces. Phys. Rev. B102, 165417 (2020). https://doi.org/10.1103/PhysRevB.102.165417https://doi.org/10.1103/PhysRevB.102.165417
N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976)
G. Burns, Solid State Physics (Academic Press, Boston, 1990)
S. Golin, Band structure of bismuth: Pseudopotential approach. Phys. Rev.166, 643-651 (1968). https://doi.org/10.1103/PhysRev.166.643https://doi.org/10.1103/PhysRev.166.643
Slonczewski J.C., Weiss, P.R.: Band structure of graphite. Phys. Rev.109, 272-279 (1958). https://doi.org/10.1103/PhysRev.109.272https://doi.org/10.1103/PhysRev.109.272
H. Weyl, Elektron und gravitation I. Zeitschrift für Physik56, 330-352 (1929). https://doi.org/10.1007/BF01339504https://doi.org/10.1007/BF01339504
Super-Kamiokande. Collaboration, Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett.81, 1562-1567 (1998). https://doi.org/10.1103/PhysRevLett.81.1562https://doi.org/10.1103/PhysRevLett.81.1562
A. Vishwanath, Where the Weyl things are. Physics8, 84 (2015)
H.B. Nielsen, M. Ninomiya, Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B185, 20-40 (1981). https://doi.org/10.1016/0550-3213(81)90361-8https://doi.org/10.1016/0550-3213(81)90361-8
H.B. Nielsen, M. Ninomiya, Absence of neutrinos on a lattice: (II). Intuitive topological proof. Nucl. Phys. B193, 173-194 (1981). https://doi.org/10.1016/0550-3213(81)90524-1https://doi.org/10.1016/0550-3213(81)90524-1
H.B. Nielsen, M. Ninomiya, A no-go theorem for regularizing chiral fermions. Phys. Lett. B105, 219-223 (1981). https://doi.org/10.1016/0370-2693(81)91026-1https://doi.org/10.1016/0370-2693(81)91026-1
X.-Q. Sun, M. Xiao, T. Bzdušek, S.-C. Zhang, S. Fan, Three-dimensional chiral lattice fermion in floquet systems. Phys. Rev. Lett.121, 196401 (2018). https://doi.org/10.1103/PhysRevLett.121.196401https://doi.org/10.1103/PhysRevLett.121.196401
J. von Neuman, E. Wigner, Uber merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen. Physikalische Zeitschrift30, 467-470 (1929)
D. Vanderbilt, Berry Phases in Electronic Structure Theory (Cambridge University Press, Cambridge, 2018)
I. Belopolski, S.-Y. Xu, D.S. Sanchez, G. Chang, C. Guo, M. Neupane, H. Zheng, C.-C. Lee, S.-M. Huang, G. Bian, N. Alidoust, T.-R. Chang, B. Wang, X. Zhang, A. Bansil, H.-T. Jeng, H. Lin, S. Jia, M.Z. Hasan, Criteria for directly detecting topological Fermi arcs in Weyl semimetals. Phys. Rev. Lett.116, 066802 (2016). https://doi.org/10.1103/PhysRevLett.116.066802https://doi.org/10.1103/PhysRevLett.116.066802
S.-Y. Xu, I. Belopolski, D.S. Sanchez, M. Neupane, G. Chang, K. Yaji, Z. Yuan, C. Zhang, K. Kuroda, G. Bian, C. Guo, H. Lu, T.-R. Chang, N. Alidoust, H. Zheng, C.-C. Lee, S.-M. Huang, C.-H. Hsu, H.-T. Jeng, A. Bansil, T. Neupert, F. Komori, T. Kondo, S. Shin, H. Lin, S. Jia, M.Z. Hasan, Spin polarization and texture of the Fermi arcs in the Weyl fermion semimetal TaAs. Phys. Rev. Lett.116, 096801 (2016). https://doi.org/10.1103/PhysRevLett.116.096801https://doi.org/10.1103/PhysRevLett.116.096801
B. Yan, C. Felser, Topological materials: Weyl semimetals. Ann. Rev. Condens. Matter Phys.8(1), 337-354 (2017). https://doi.org/10.1146/annurev-conmatphys-031016-025458https://doi.org/10.1146/annurev-conmatphys-031016-025458
H.A. Kramers, Théorie générale de la rotation paramagnétique dans les cristaux. Proceedings Koninklijke Akademie van Wetenschappen 33, 959-972 (1930)
A.A. Burkov, L. Balents, Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett.107, 127205 (2011). https://doi.org/10.1103/PhysRevLett.107.127205https://doi.org/10.1103/PhysRevLett.107.127205
S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D.S. Sanchez, B. Wang, A. Bansil, F. Chou, P.P. Shibayev, H. Lin, S. Jia, M.Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science349, 613-617 (2015). https://doi.org/10.1126/science.aaa9297https://doi.org/10.1126/science.aaa9297
B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X5, 031013 (2015). https://doi.org/10.1103/PhysRevX.5.031013https://doi.org/10.1103/PhysRevX.5.031013
L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J.D. Joannopoulos, M. Soljačić, Experimental observation of Weyl points. Science349, 622-624 (2015). https://doi.org/10.1126/science.aaa9273https://doi.org/10.1126/science.aaa9273
Xu S.-Y., Belopolski, I., Sanchez, D.S., Zhang, C., Chang, G., Guo, C., Bian, G., Yuan, Z., Lu, H., Chang, T.-R., Shibayev, P.P., Prokopovych, M.L., Alidoust, N., Zheng, H., Lee, C.-C., Huang, S.-M., Sankar, R., Chou, F., Hsu, C.-H., Jeng, H.-T., Bansil, A., Neupert, T., Strocov, V.N., Lin, H., Jia, S., Hasan, M.Z.: Experimental discovery of a topological Weyl semimetal state in TaP. Science Advances1, 1501092 (2015). Chap. Research Article. https://doi.org/10.1126/sciadv.1501092https://doi.org/10.1126/sciadv.1501092
C.-L. Zhang, S.-Y. Xu, C.M. Wang, Z. Lin, Z.Z. Du, C. Guo, C.-C. Lee, H. Lu, Y. Feng, S.-M. Huang, G. Chang, C.-H. Hsu, H. Liu, H. Lin, L. Li, C. Zhang, J. Zhang, X.-C. Xie, T. Neupert, M.Z. Hasan, H.-Z. Lu, J. Wang, S. Jia, Magnetic-tunnelling-induced Weyl node annihilation in TaP. Nat. Phys.13, 979-986 (2017). https://doi.org/10.1038/nphys4183https://doi.org/10.1038/nphys4183
S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V.N. Strocov, D.S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C.-C. Lee, S.-M. Huang, B. Wang, A. Bansil, H.-T. Jeng, T. Neupert, A. Kaminski, H. Lin, S. Jia, M. Zahid Hasan, Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys.11, 748-754 (2015). https://doi.org/10.1038/nphys3437https://doi.org/10.1038/nphys3437
H. Zheng, S.-Y. Xu, G. Bian, C. Guo, G. Chang, D.S. Sanchez, I. Belopolski, C.-C. Lee, S.-M. Huang, X. Zhang, R. Sankar, N. Alidoust, T.-R. Chang, F. Wu, T. Neupert, F. Chou, H.-T. Jeng, N. Yao, A. Bansil, S. Jia, H. Lin, M.Z. Hasan, Atomic-scale visualization of quantum interference on a Weyl semimetal surface by scanning tunneling microscopy. ACS Nano10, 1378-1385 (2016). https://doi.org/10.1021/acsnano.5b06807https://doi.org/10.1021/acsnano.5b06807
H. Zheng, G. Chang, S.-M. Huang, C. Guo, X. Zhang, S. Zhang, J. Yin, S.-Y. Xu, I. Belopolski, N. Alidoust, D.S. Sanchez, G. Bian, T.-R. Chang, T. Neupert, H.-T. Jeng, S. Jia, H. Lin, M.Z. Hasan, Mirror protected Dirac fermions on a Weyl semimetal NbP surface. Phys. Rev. Lett.119, 196403 (2017). https://doi.org/10.1103/PhysRevLett.119.196403https://doi.org/10.1103/PhysRevLett.119.196403
J. Gooth, A.C. Niemann, T. Meng, A.G. Grushin, K. Landsteiner, B. Gotsmann, F. Menges, M. Schmidt, C. Shekhar, V. Süß, R. Hühne, B. Rellinghaus, C. Felser, B. Yan, K. Nielsch, Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP. Nature547, 324-327 (2017). https://doi.org/10.1038/nature23005https://doi.org/10.1038/nature23005
N. Morali, R. Batabyal, P.K. Nag, E. Liu, Q. Xu, Y. Sun, B. Yan, C. Felser, N. Avraham, H. Beidenkopf, Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science365(6459), 1286-1291 (2019). https://doi.org/10.1126/science.aav2334https://doi.org/10.1126/science.aav2334
I. Belopolski, K. Manna, D.S. Sanchez, G. Chang, B. Ernst, J. Yin, S.S. Zhang, T. Cochran, N. Shumiya, H. Zheng, B. Singh, G. Bian, D. Multer, M. Litskevich, X. Zhou, S.-M. Huang, B. Wang, T.-R. Chang, S.-Y. Xu, A. Bansil, C. Felser, H. Lin, M.Z. Hasan, Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science365(6459), 1278-1281 (2019). https://doi.org/10.1126/science.aav2327https://doi.org/10.1126/science.aav2327
D.F. Liu, A.J. Liang, E.K. Liu, Q.N. Xu, Y.W. Li, C. Chen, D. Pei, W.J. Shi, S.K. Mo, P. Dudin, T. Kim, C. Cacho, G. Li, Y. Sun, L.X. Yang, Z.K. Liu, S.S.P. Parkin, C. Felser, Y.L. Chen, Magnetic Weyl semimetal phase in a Kagomé crystal. Science365(6459), 1282-1285 (2019). https://doi.org/10.1126/science.aav2873https://doi.org/10.1126/science.aav2873
D.J. Fisher, Topological Semimetals (Materials Research Forum LLC, Millersville, 2019)
J. Xiong, S.K. Kushwaha, T. Liang, J.W. Krizan, M. Hirschberger, W. Wang, R.J. Cava, N.P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science350, 413-416 (2015). https://doi.org/10.1126/science.aac6089https://doi.org/10.1126/science.aac6089
C.-L. Zhang, S.-Y. Xu, I. Belopolski, Z. Yuan, Z. Lin, B. Tong, G. Bian, N. Alidoust, C.-C. Lee, S.-M. Huang, T.-R. Chang, G. Chang, C.-H. Hsu, H.-T. Jeng, M. Neupane, D.S. Sanchez, H. Zheng, J. Wang, H. Lin, C. Zhang, H.-Z. Lu, S.-Q. Shen, T. Neupert, M. Zahid Hasan, S. Jia, Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal. Nat. Commun.7, 10735 (2016). https://doi.org/10.1038/ncomms10735https://doi.org/10.1038/ncomms10735
N.P. Ong, S. Liang, Experimental signatures of the chiral anomaly in Dirac-Weyl semimetals. Nat. Rev. Phys.3, 394-404 (2021). https://doi.org/10.1038/s42254-021-00310-9https://doi.org/10.1038/s42254-021-00310-9
C. Zhang, C. Guo, H. Lu, X. Zhang, Z. Yuan, Z. Lin, J. Wang, S. Jia, Large magnetoresistance over an extended temperature regime in monophosphides of tantalum and niobium. Phys. Rev. B92, 041203 (2015). https://doi.org/10.1103/PhysRevB.92.041203https://doi.org/10.1103/PhysRevB.92.041203
A. Westström, T. Ojanen, Designer curved-space geometry for relativistic fermions in Weyl metamaterials. Phys. Rev. X7, 041026 (2017). https://doi.org/10.1103/PhysRevX.7.041026https://doi.org/10.1103/PhysRevX.7.041026
A. Cortijo, Y. Ferreirós, K. Landsteiner, M.A.H. Vozmediano, Elastic gauge fields in Weyl semimetals. Phys. Rev. Lett.115, 177202 (2015). https://doi.org/10.1103/PhysRevLett.115.177202https://doi.org/10.1103/PhysRevLett.115.177202
D.I. Pikulin, A. Chen, M. Franz, Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals. Phys. Rev. X6, 041021 (2016). https://doi.org/10.1103/PhysRevX.6.041021https://doi.org/10.1103/PhysRevX.6.041021
Z. Song, X. Dai, Hear the sound of Weyl fermions. Phys. Rev. X9, 021053 (2019). https://doi.org/10.1103/PhysRevX.9.021053https://doi.org/10.1103/PhysRevX.9.021053
P.E.C. Ashby, J.P. Carbotte, Magneto-optical conductivity of Weyl semimetals. Phys. Rev. B87, 245131 (2013). https://doi.org/10.1103/PhysRevB.87.245131https://doi.org/10.1103/PhysRevB.87.245131
M. Stålhammar, J. Larana-Aragon, J. Knolle, E.J. Bergholtz, Magneto-optical conductivity in generic Weyl semimetals. Phys. Rev. B102, 235134 (2020). https://doi.org/10.1103/PhysRevB.102.235134https://doi.org/10.1103/PhysRevB.102.235134
S. Polatkan, M.O. Goerbig, J. Wyzula, R. Kemmler, L.Z. Maulana, B.A. Piot, I. Crassee, A. Akrap, C. Shekhar, C. Felser, M. Dressel, A.V. Pronin, M. Orlita, Magneto-optics of a Weyl semimetal beyond the conical band approximation: case study of TaP. Phys. Rev. Lett.124, 176402 (2020). https://doi.org/10.1103/PhysRevLett.124.176402https://doi.org/10.1103/PhysRevLett.124.176402
O. Vafek, A. Vishwanath, Dirac fermions in solids: from high-Tc cuprates and graphene to topological insulators and Weyl semimetals. Ann. Rev. Condens. Matter Phys.5, 83-112 (2014). https://doi.org/10.1146/annurev-conmatphys-031113-133841https://doi.org/10.1146/annurev-conmatphys-031113-133841
A.A. Burkov, Weyl metals. Ann. Rev. Condens. Matter Phys.9, 359-378 (2018). https://doi.org/10.1146/annurev-conmatphys-033117-054129https://doi.org/10.1146/annurev-conmatphys-033117-054129
W. Witczak-Krempa, G. Chen, Y.B. Kim, L. Balents, Correlated quantum phenomena in the strong spin-orbit regime. Ann. Rev. Condens. Matter Phys.5, 57-82 (2014). https://doi.org/10.1146/annurev-conmatphys-020911-125138https://doi.org/10.1146/annurev-conmatphys-020911-125138
L. Šmejkal, T. Jungwirth, J. Sinova, Route towards Dirac and Weyl antifer-romagnetic spintronics. Physica Status Solidi (RRL) Rapid Res Lett11, 1700044 (2017). https://doi.org/10.1002/pssr.201700044https://doi.org/10.1002/pssr.201700044
G.P. Mikitik, Y.V. Sharlai, Magnetic susceptibility of topological semimetals. J. Low Temp. Phys.197, 272-309 (2019). https://doi.org/10.1007/s10909-019-02225-3https://doi.org/10.1007/s10909-019-02225-3
P. Hosur, X. Qi, Recent developments in transport phenomena in Weyl semimetals. C R Phys.14, 857-870 (2013). https://doi.org/10.1016/j.crhy.2013.10.010https://doi.org/10.1016/j.crhy.2013.10.010
A.A. Burkov, Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter27, 113201 (2015). https://doi.org/10.1088/0953-8984/27/11/113201https://doi.org/10.1088/0953-8984/27/11/113201
S. Wang, B.-C. Lin, A.-Q. Wang, D.-P. Yu, Z.-M. Liao, Quantum transport in Dirac and Weyl semimetals: a review. Adv. Phys. X2, 518-544 (2017). https://doi.org/10.1080/23746149.2017.1327329https://doi.org/10.1080/23746149.2017.1327329
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy, P.O. Sukhachov, Anomalous transport properties of Dirac and Weyl semimetals (Review Article). Low Temp. Phys.44, 487-505 (2018). https://doi.org/10.1063/1.5037551https://doi.org/10.1063/1.5037551
H. Wang, J. Wang, Electron transport in Dirac and Weyl semimetals. Chin. Phys. B27(107402), 2020030514010695 (2018)
J. Hu, S.-Y. Xu, N. Ni, Z. Mao, Transport of topological semimetals. Annu. Rev. Mater. Res.49, 207-252 (2019). https://doi.org/10.1146/annurev-matsci-070218-010023https://doi.org/10.1146/annurev-matsci-070218-010023
C.-K. Chiu, J.C.Y. Teo, A.P. Schnyder, S. Ryu, Classification of topological quantum matter with symmetries. Rev. Mod. Phys.88, 035005 (2016). https://doi.org/10.1103/RevModPhys.88.035005https://doi.org/10.1103/RevModPhys.88.035005
E. Witten, Three lectures on topological phases of matter. La Rivista del Nuovo Cimento39, 313-370 (2016). https://doi.org/10.1393/ncr/i2016-10125-3https://doi.org/10.1393/ncr/i2016-10125-3
H. Weng, X. Dai, Z. Fang, Topological semimetals predicted from first-principles calculations. J. Phys. Condens. Matter28, 303001 (2016). https://doi.org/10.1088/0953-8984/28/30/303001https://doi.org/10.1088/0953-8984/28/30/303001
M.Z. Hasan, S.-Y. Xu, G. Bian, Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks. Phys. Scr.T164, 014001 (2015). https://doi.org/10.1088/0031-8949/2015/T164/014001https://doi.org/10.1088/0031-8949/2015/T164/014001
M.Z. Hasan, S.-Y. Xu, I. Belopolski, S.-M. Huang, Discovery of Weyl fermion semimetals and topological Fermi arc states. Ann. Rev. Condens. Matter Phys.8, 289-309 (2017). https://doi.org/10.1146/annurev-conmatphys-031016-025225https://doi.org/10.1146/annurev-conmatphys-031016-025225
B. Yan, C. Felser, Topological materials: Weyl semimetals. Ann. Rev. Condens. Matter Phys.8, 337-354 (2017). https://doi.org/10.1146/annurev-conmatphys-031016-025458https://doi.org/10.1146/annurev-conmatphys-031016-025458
H. Zheng, M. Zahid Hasan, Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: a review. Adv. Phys. X3, 1466661 (2018). https://doi.org/10.1080/23746149.2018.1466661https://doi.org/10.1080/23746149.2018.1466661
N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong, Anomalous Hall effect. Rev. Mod. Phys.82, 1539-1592 (2010). https://doi.org/10.1103/RevModPhys.82.1539https://doi.org/10.1103/RevModPhys.82.1539
E.V. Gorbar, V.A. Miransky, I.A. Shovkovy, Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field. Phys. Rev. C (2009). https://doi.org/10.1103/PhysRevC.80.032801https://doi.org/10.1103/PhysRevC.80.032801
A.A. Zyuzin, A.A. Burkov, Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B86(11), 115133 (2012). https://doi.org/10.1103/PhysRevB.86.115133https://doi.org/10.1103/PhysRevB.86.115133
S. Nie, T. Hashimoto, F.B. Prinz, Magnetic Weyl semimetal in K2Mn3 (AsO4)3 with the minimum number of Weyl points. Phys. Rev. Lett.128, 176401 (2022). https://doi.org/10.1103/PhysRevLett.128.176401https://doi.org/10.1103/PhysRevLett.128.176401
J.-R. Soh, F. de Juan, M.G. Vergniory, N.B.M. Schröter, M.C. Rahn, D.Y. Yan, J. Jiang, M. Bristow, P.A. Reiss, J.N. Blandy, Y.F. Guo, Y.G. Shi, T.K. Kim, A. McCollam, S.H. Simon, Y. Chen, A.I. Coldea, A.T. Boothroyd, Ideal Weyl semimetal induced by magnetic exchange. Phys. Rev. B100, 201102 (2019). https://doi.org/10.1103/PhysRevB.100.201102https://doi.org/10.1103/PhysRevB.100.201102
A. Zangwill, Modern Electrodynamics (Cambridge University Press, Cambridge, 2013)
F. Wilczek, Two applications of axion electrodynamics. Phys. Rev. Lett.58, 1799-1802 (1987). https://doi.org/10.1103/PhysRevLett.58.1799https://doi.org/10.1103/PhysRevLett.58.1799
T.-P. Cheng, L.-F. Li, Gauge Theory of Elementary Particle Physics (Oxford University Press, Oxford, 1984)
G.E. Volovik, The Universe in a Helium Droplet (Oxford University Press, Oxford, 2009)
X.-L. Qi, T.L. Hughes, S.-C. Zhang, Topological field theory of time-reversal invariant insulators. Phys. Rev. B78, 195424 (2008). https://doi.org/10.1103/PhysRevB.78.195424https://doi.org/10.1103/PhysRevB.78.195424
X.-L. Qi, S.-C. Zhang, Topological insulators and superconductors. Rev. Mod. Phys.83, 1057-1110 (2011). https://doi.org/10.1103/RevModPhys.83.1057https://doi.org/10.1103/RevModPhys.83.1057
B.A. Bernevig, T.L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, Princeton, 2013)
A.G. Grushin, Consequences of a condensed matter realization of Lorentz-violating QED in Weyl semi-metals. Phys. Rev. D86, 045001 (2012). https://doi.org/10.1103/PhysRevD.86.045001https://doi.org/10.1103/PhysRevD.86.045001
P. Goswami, S. Tewari, Axionic field theory of (3+1)-dimensional Weyl semimetals. Phys. Rev. B88, 245107 (2013). https://doi.org/10.1103/PhysRevB.88.245107https://doi.org/10.1103/PhysRevB.88.245107
M.M. Vazifeh, M. Franz, Electromagnetic response of Weyl semimetals. Phys. Rev. Lett.111, 027201 (2013). https://doi.org/10.1103/PhysRevLett.111.027201https://doi.org/10.1103/PhysRevLett.111.027201
K. Deng, J.S. Van Dyke, D. Minic, J.J. Heremans, E. Barnes, Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals. Phys. Rev. B104, 075202 (2021). https://doi.org/10.1103/PhysRevB.104.075202https://doi.org/10.1103/PhysRevB.104.075202
Armitage N.P., Wu, L.: On the matter of topological insulators as magne-toelectrics. SciPost Phys.6, 046 (2019). https://doi.org/10.21468/SciPostPhys.6.4.046https://doi.org/10.21468/SciPostPhys.6.4.046
D. Tong, Gauge Theory. Lecture Notes (DAMTP Cambridge, Cambridge, 2018)
A. Karch, Electric-magnetic duality and topological insulators. Phys. Rev. Lett.103, 171601 (2009). https://doi.org/10.1103/PhysRevLett.103.171601https://doi.org/10.1103/PhysRevLett.103.171601
J. Hofmann, S. Das Sarma, Surface plasmon polaritons in topological Weyl semimetals. Phys. Rev. B93(24), 241402 (2016). https://doi.org/10.1103/PhysRevB.93.241402https://doi.org/10.1103/PhysRevB.93.241402
E. Witten, Fermion path integrals and topological phases. Rev. Mod. Phys.88, 035001 (2016). https://doi.org/10.1103/RevModPhys.88.035001https://doi.org/10.1103/RevModPhys.88.035001
K. Fujikawa, H. Suzuki, Path Integrals and Quantum Anomalies (Clarendon Press, Oxford, 2013)
C. Rylands, A. Parhizkar, A.A. Burkov, V. Galitski, Chiral anomaly in interacting condensed matter systems. Phys. Rev. Lett.126, 185303 (2021). https://doi.org/10.1103/PhysRevLett.126.185303https://doi.org/10.1103/PhysRevLett.126.185303
R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn.12, 570-586 (1957). https://doi.org/10.1143/JPSJ.12.570https://doi.org/10.1143/JPSJ.12.570
D.A. Greenwood, The Boltzmann equation in the theory of electrical conduction in metals. Proc. Phys. Soc.71, 585-596 (1958). https://doi.org/10.1088/0370-1328/71/4/306https://doi.org/10.1088/0370-1328/71/4/306
L.L. Moseley, T. Lukes, A simplified derivation of the Kubo-Greenwood formula. Am. J. Phys.46, 676-677 (1978). https://doi.org/10.1119/1.11229https://doi.org/10.1119/1.11229
H.A. Lorentz, The theorem of Poynting concerning the energy in the electromagnetic field and two general propositions concerning the propagation of light. Amsterdammer Akademie der Wetenschappen4, 176 (1896)
R.J. Potton, Reciprocity in optics. Rep. Prog. Phys.67(5), 717-754 (2004). https://doi.org/10.1088/0034-4885/67/5/R03https://doi.org/10.1088/0034-4885/67/5/R03
C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, Z.-L. Deck-Léger, Electromagnetic nonreciprocity. Phys. Rev. Appl.10(4), 047001 (2018). https://doi.org/10.1103/PhysRevApplied.10.047001https://doi.org/10.1103/PhysRevApplied.10.047001
V.S. Asadchy, M.S. Mirmoosa, A. Díaz-Rubio, S. Fan, S.A. Tretyakov, Tutorial on electromagnetic nonreciprocity and its origins. Proc. IEEE108, 1684-1727 (2020). https://doi.org/10.1109/JPROC.2020.3012381https://doi.org/10.1109/JPROC.2020.3012381
C. Guo, Z. Zhao, S. Fan, Internal transformations and internal symmetries in linear photonic systems. Phys. Rev. A105, 023509 (2022). https://doi.org/10.1103/PhysRevA.105.023509https://doi.org/10.1103/PhysRevA.105.023509
H.A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, New Jersey, 1984)
C. Guo, S. Fan, Reciprocity constraints on reflection. Phys. Rev. Lett.128, 256101 (2022). https://doi.org/10.1103/PhysRevLett.128.256101https://doi.org/10.1103/PhysRevLett.128.256101
G. Kirchhoff, Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Ann. Phys.185(2), 275-301 (1860). https://doi.org/10.1002/andp.18601850205https://doi.org/10.1002/andp.18601850205
J.-J. Greffet, P. Bouchon, G. Brucoli, F. Marquier, Light emission by non-equilibrium bodies: local Kirchhoff law. Phys. Rev. X8, 021008 (2018). https://doi.org/10.1103/PhysRevX.8.021008https://doi.org/10.1103/PhysRevX.8.021008
Z. Yu, S. Fan, Complete optical isolation created by indirect interband photonic transitions. Nat. Photonics3(2), 91-94 (2009). https://doi.org/10.1038/nphoton.2008.273https://doi.org/10.1038/nphoton.2008.273
D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J.D. Joannopoulos, M. Vanwolleghem, C.R. Doerr, H. Renner, What is--and what is not——an optical isolator. Nat. Photonics7, 579-582 (2013). https://doi.org/10.1038/nphoton.2013.185https://doi.org/10.1038/nphoton.2013.185
Z. Wang, S. Fan, Optical circulators in two-dimensional magneto-optical photonic crystals. Opt. Lett.30, 1989-1991 (2005). https://doi.org/10.1364/OL.30.001989https://doi.org/10.1364/OL.30.001989
Z. Wang, Y. Chong, J.D. Joannopoulos, M. Soljačić, Observation of unidirectional backscattering-immune topological electromagnetic states. Nature461, 772-775 (2009). https://doi.org/10.1038/nature08293https://doi.org/10.1038/nature08293
K. Fang, Z. Yu, S. Fan, Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photonics6(11), 782-787 (2012). https://doi.org/10.1038/nphoton.2012.236https://doi.org/10.1038/nphoton.2012.236
L. Zhu, S. Fan, Near-complete violation of detailed balance in thermal radiation. Phys. Rev. B90(22), 220301 (2014). https://doi.org/10.1103/PhysRevB.90.220301https://doi.org/10.1103/PhysRevB.90.220301
C. Guo, B. Zhao, S. Fan, Adjoint Kirchhoff's law and general symmetry implications for all thermal emitters. Phys. Rev. X12, 021023 (2022). https://doi.org/10.1103/PhysRevX.12.021023https://doi.org/10.1103/PhysRevX.12.021023
A.K. Zvezdin, V.A. Kotov, Modern Magnetooptics and Magnetooptical Materials (CRC Press, New York, 1997)
X. Han, A. Markou, J. Stensberg, Y. Sun, C. Felser, L. Wu, Giant intrinsic anomalous terahertz Faraday rotation in the magnetic Weyl semimetal Co2MnGa at room temperature. Phys. Rev. B105, 174406 (2022). https://doi.org/10.1103/PhysRevB.105.174406https://doi.org/10.1103/PhysRevB.105.174406
H. Huang, Y. Fan, B.-I. Wu, A.J. Kong, Tunable TE/TM wave splitter using a gyrotropic slab. Prog. Electromagn. Res.85, 367-380 (2008). https://doi.org/10.2528/PIER08080303https://doi.org/10.2528/PIER08080303
S.O. Abdol, B. Abdollahipour, A.S. Vala, Surface plasmon polaritons in a waveguide composed of Weyl semimetals with different symmetries. J. Phys. D Appl. Phys.53(4), 045105 (2019). https://doi.org/10.1088/1361-6463/ab52eehttps://doi.org/10.1088/1361-6463/ab52ee
P.E.C. Ashby, J.P. Carbotte, Chiral anomaly and optical absorption in Weyl semimetals. Phys. Rev. B89, 245121 (2014). https://doi.org/10.1103/PhysRevB.89.245121https://doi.org/10.1103/PhysRevB.89.245121
J. Huang, L. Wang, D.-X. Yao, A semiclassical approach to surface Fermi arcs in Weyl semimetals. Sci. China Phys. Mech. Astron.65, 266811 (2022). https://doi.org/10.1007/s11433-021-1884-xhttps://doi.org/10.1007/s11433-021-1884-x
Q. Chen, A.R. Kutayiah, I. Oladyshkin, M. Tokman, A. Belyanin, Optical properties and electromagnetic modes of Weyl semimetals. Phys. Rev. B99(7), 075137 (2019). https://doi.org/10.1103/PhysRevB.99.075137https://doi.org/10.1103/PhysRevB.99.075137
J.C.W. Song, M.S. Rudner, Fermi arc plasmons in Weyl semimetals. Phys. Rev. B96, 205443 (2017). https://doi.org/10.1103/PhysRevB.96.205443https://doi.org/10.1103/PhysRevB.96.205443
ŽB. Lošić, The coupling effects of surface plasmons and Fermi arc plasmons in Weyl semimetals. J. Phys.: Condens. Matter31, 285001 (2019). https://doi.org/10.1088/1361-648X/ab1734https://doi.org/10.1088/1361-648X/ab1734
J.S. Gomez-Diaz, M. Tymchenko, A. Alù, Hyperbolic plasmons and topological transitions over uniaxial metasurfaces. Phys. Rev. Lett.114, 233901 (2015). https://doi.org/10.1103/PhysRevLett.114.233901https://doi.org/10.1103/PhysRevLett.114.233901
F. Zhang, Y. Gao, W. Zhang, Three-dimensional topological plasmons in Weyl semimetals. Phys. Rev. B104, 205141 (2021). https://doi.org/10.1103/PhysRevB.104.205141https://doi.org/10.1103/PhysRevB.104.205141
A.A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, B.A. Bernevig, Type-II Weyl semimetals. Nature527, 495-498 (2015). https://doi.org/10.1038/nature15768https://doi.org/10.1038/nature15768
I. Lifshitz, Anomalies of electron characteristics of a metal in the high pressure region. Soviet Phys. JETP11, 1130-1135 (1960)
G.E. Volovik, Topological Lifshitz transitions. Low Temp. Phys.43, 47-55 (2017). https://doi.org/10.1063/1.4974185https://doi.org/10.1063/1.4974185
G.E. Volovik, Exotic Lifshitz transitions in topological materials. Phys. Usp.61, 89 (2018). https://doi.org/10.3367/UFNe.2017.01.038218https://doi.org/10.3367/UFNe.2017.01.038218
P.K. Das, D.D. Sante, F. Cilento, C. Bigi, D. Kopic, D. Soranzio, A. Sterzi, J.A. Krieger, I. Vobornik, J. Fujii, T. Okuda, V.N. Strocov, M.B.H. Breese, F. Parmigiani, G. Rossi, S. Picozzi, R. Thomale, G. Sangiovanni, R.J. Cava, G. Panaccione, Electronic properties of candidate type-II Weyl semimetal WTe2. A review perspective. Electron. Struct.1, 014003 (2019). https://doi.org/10.1088/2516-1075/ab0835https://doi.org/10.1088/2516-1075/ab0835
Y. Wang, E. Liu, H. Liu, Y. Pan, L. Zhang, J. Zeng, Y. Fu, M. Wang, K. Xu, Z. Huang, Z. Wang, H.-Z. Lu, D. Xing, B. Wang, X. Wan, F. Miao, Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2. Nat. Commun.7, 13142 (2016). https://doi.org/10.1038/ncomms13142https://doi.org/10.1038/ncomms13142
Y. Wu, D. Mou, N.H. Jo, K. Sun, L. Huang, S.L. Bud'ko, P.C. Canfield, A. Kaminski, Observation of Fermi arcs in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B94, 121113 (2016). https://doi.org/10.1103/PhysRevB.94.121113https://doi.org/10.1103/PhysRevB.94.121113
P. Li, Y. Wen, X. He, Q. Zhang, C. Xia, Z.-M. Yu, S.A. Yang, Z. Zhu, H.N. Alshareef, X.-X. Zhang, Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun.8, 2150 (2017). https://doi.org/10.1038/s41467-017-02237-1https://doi.org/10.1038/s41467-017-02237-1
Y. Sun, S.-C. Wu, M.N. Ali, C. Felser, B. Yan, Prediction of Weyl semimetal in orthorhombic MoTe2. Phys. Rev. B92, 161107 (2015). https://doi.org/10.1103/PhysRevB.92.161107https://doi.org/10.1103/PhysRevB.92.161107
T.-R. Chang, S.-Y. Xu, G. Chang, C.-C. Lee, S.-M. Huang, B. Wang, G. Bian, H. Zheng, D.S. Sanchez, I. Belopolski, N. Alidoust, M. Neupane, A. Bansil, H.-T. Jeng, H. Lin, M. Zahid Hasan, Prediction of an arc-tunable Weyl Fermion metallic state in MoxW1-xTe2. Nat. Commun.7, 10639 (2016). https://doi.org/10.1038/ncomms10639https://doi.org/10.1038/ncomms10639
K. Deng, G. Wan, P. Deng, K. Zhang, S. Ding, E. Wang, M. Yan, H. Huang, H. Zhang, Z. Xu, J. Denlinger, A. Fedorov, H. Yang, W. Duan, H. Yao, Y. Wu, S. Fan, H. Zhang, X. Chen, S. Zhou, Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys.12, 1105-1110 (2016). https://doi.org/10.1038/nphys3871https://doi.org/10.1038/nphys3871
L. Huang, T.M. McCormick, M. Ochi, Z. Zhao, M.-T. Suzuki, R. Arita, Y. Wu, D. Mou, H. Cao, J. Yan, N. Trivedi, A. Kaminski, Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater.15, 1155-1160 (2016). https://doi.org/10.1038/nmat4685https://doi.org/10.1038/nmat4685
Z. Wang, D. Gresch, A.A. Soluyanov, W. Xie, S. Kushwaha, X. Dai, M. Troyer, R.J. Cava, B.A. Bernevig, MoTe2: a type-II Weyl topological metal. Phys. Rev. Lett.117, 056805 (2016). https://doi.org/10.1103/PhysRevLett.117.056805https://doi.org/10.1103/PhysRevLett.117.056805
M.N. Ali, J. Xiong, S. Flynn, J. Tao, Q.D. Gibson, L.M. Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N.P. Ong, R.J. Cava, Large, non-saturating magnetoresistance in WTe2. Nature514, 205-208 (2014). https://doi.org/10.1038/nature13763https://doi.org/10.1038/nature13763
C. Wang, Y. Zhang, J. Huang, S. Nie, G. Liu, A. Liang, Y. Zhang, B. Shen, J. Liu, C. Hu, Y. Ding, D. Liu, Y. Hu, S. He, L. Zhao, L. Yu, J. Hu, J. Wei, Z. Mao, Y. Shi, X. Jia, F. Zhang, S. Zhang, F. Yang, Z. Wang, Q. Peng, H. Weng, X. Dai, Z. Fang, Z. Xu, C. Chen, X.J. Zhou, Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal WTe2. Phys. Rev. B94, 241119 (2016). https://doi.org/10.1103/PhysRevB.94.241119https://doi.org/10.1103/PhysRevB.94.241119
C. Wang, S. Huang, Q. Xing, Y. Xie, C. Song, F. Wang, H. Yan, Van der Waals thin films of WTe2 for natural hyperbolic plasmonic surfaces. Nat. Commun.11, 1158 (2020). https://doi.org/10.1038/s41467-020-15001-9https://doi.org/10.1038/s41467-020-15001-9
A. Poddubny, I. Iorsh, P. Belov, Y. Kivshar, Hyperbolic metamaterials. Nat. Photonics7, 948-957 (2013). https://doi.org/10.1038/nphoton.2013.243https://doi.org/10.1038/nphoton.2013.243
Y. Guo, Z. Jacob, Thermal hyperbolic metamaterials. Opt. Express21, 15014-15019 (2013). https://doi.org/10.1364/OE.21.015014https://doi.org/10.1364/OE.21.015014
P. Shekhar, J. Atkinson, Z. Jacob, Hyperbolic metamaterials: fundamentals and applications. Nano Conver.1, 14 (2014). https://doi.org/10.1186/s40580-014-0014-6https://doi.org/10.1186/s40580-014-0014-6
L. Ferrari, C. Wu, D. Lepage, X. Zhang, Z. Liu, Hyperbolic metamaterials and their applications. Prog. Quantum Electron.40, 1-40 (2015). https://doi.org/10.1016/j.pquantelec.2014.10.001https://doi.org/10.1016/j.pquantelec.2014.10.001
F. Peragut, L. Cerutti, A. Baranov, J.P. Hugonin, T. Taliercio, Y.D. Wilde, J.J. Greffet, Hyperbolic metamaterials and surface plasmon polaritons. Optica4, 1409-1415 (2017). https://doi.org/10.1364/OPTICA.4.001409https://doi.org/10.1364/OPTICA.4.001409
A. Nemilentsau, T. Low, G. Hanson, Anisotropic 2D materials for tunable hyperbolic plasmonics. Phys. Rev. Lett.116, 066804 (2016). https://doi.org/10.1103/PhysRevLett.116.066804https://doi.org/10.1103/PhysRevLett.116.066804
K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969)
H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, A.F. Popkov, Applications of magneto-optical waveguides in integrated optics: review. J. Opt. Soc. Am. B22, 240-253 (2005). https://doi.org/10.1364/JOSAB.22.000240https://doi.org/10.1364/JOSAB.22.000240
Y. Shoji, T. Mizumoto, Magneto-optical non-reciprocal devices in silicon photonics. Sci. Technol. Adv. Mater.15, 014602 (2014). https://doi.org/10.1088/1468-6996/15/1/014602https://doi.org/10.1088/1468-6996/15/1/014602
N.V. Kravtsov, N.N. Kravtsov, Nonreciprocal effects in ring lasers. Quantum Electron.29, 378 (1999). https://doi.org/10.1070/QE1999v029n05ABEH001495https://doi.org/10.1070/QE1999v029n05ABEH001495
E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu, J. Kroder, V. Süß, H. Borrmann, C. Shekhar, Z. Wang, C. Xi, W. Wang, W. Schnelle, S. Wirth, Y. Chen, S.T.B. Goennenwein, C. Felser, Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys.14, 1125-1131 (2018). https://doi.org/10.1038/s41567-018-0234-5https://doi.org/10.1038/s41567-018-0234-5
K. Halterman, M. Alidoust, Waveguide modes in Weyl semimetals with tilted Dirac cones. Opt. Express27(25), 36164-36182 (2019). https://doi.org/10.1364/OE.27.036164https://doi.org/10.1364/OE.27.036164
A. Figotin, I. Vitebsky, Nonreciprocal magnetic photonic crystals. Phys. Rev. E63(6), 066609 (2001). https://doi.org/10.1103/PhysRevE.63.066609https://doi.org/10.1103/PhysRevE.63.066609
T. Li, C. Yin, F. Wu, Strong optical non-reciprocity in one-dimensional photonic crystal containing a Weyl semimetal-based defect. Opt. Mater.121, 111583 (2021). https://doi.org/10.1016/j.optmat.2021.111583https://doi.org/10.1016/j.optmat.2021.111583
S. Fan, J.D. Joannopoulos, Analysis of guided resonances in photonic crystal slabs. Phys. Rev. B65, 235112 (2002). https://doi.org/10.1103/PhysRevB.65.235112https://doi.org/10.1103/PhysRevB.65.235112
M. Kargarian, M. Randeria, N. Trivedi, Theory of Kerr and Faraday rotations and linear dichroism in topological Weyl semimetals. Sci. Rep.5, 12683 (2015). https://doi.org/10.1038/srep12683https://doi.org/10.1038/srep12683
N.M. Chtchelkatchev, O.L. Berman, R.Y. Kezerashvili, Y.E. Lozovik, Chiral filtration of light by Weyl-semimetal medium. Phys. Lett. A399, 127294 (2021). https://doi.org/10.1016/j.physleta.2021.127294https://doi.org/10.1016/j.physleta.2021.127294
C. Yang, B. Zhao, W. Cai, Z.M. Zhang, Mid-infrared broadband circular polarizer based on Weyl semimetals. Opt. Express30(2), 3035-3046 (2022). https://doi.org/10.1364/OE.445803https://doi.org/10.1364/OE.445803
S.P. Mukherjee, J.P. Carbotte, Absorption of circular polarized light in tilted type-I and type-II Weyl semimetals. Phys. Rev. B96, 085114 (2017). https://doi.org/10.1103/PhysRevB.96.085114https://doi.org/10.1103/PhysRevB.96.085114
V.G. Veselago, The electrodynamics of substances with simultaneously negative values of є and μ. Soviet Phys. Uspekhi10(4), 509 (1968). https://doi.org/10.1070/PU1968v010n04ABEH003699https://doi.org/10.1070/PU1968v010n04ABEH003699
J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett.85(18), 3966-3969 (2000). https://doi.org/10.1103/PhysRevLett.85.3966https://doi.org/10.1103/PhysRevLett.85.3966
R.A. Shelby, D.R. Smith, S. Schultz, Experimental verification of a negative index of refraction. Science292(5514), 77-79 (2001). https://doi.org/10.1126/science.1058847https://doi.org/10.1126/science.1058847
M. Notomi, Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap. Phys. Rev. B62, 10696-10705 (2000). https://doi.org/10.1103/PhysRevB.62.10696https://doi.org/10.1103/PhysRevB.62.10696
C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, All-angle negative refraction without negative effective index. Phys. Rev. B65, 201104 (2002). https://doi.org/10.1103/PhysRevB.65.201104https://doi.org/10.1103/PhysRevB.65.201104
E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, C.M. Soukoulis, Negative refraction by photonic crystals. Nature423, 604-605 (2003). https://doi.org/10.1038/423604bhttps://doi.org/10.1038/423604b
S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, C. Simovski, Waves and energy in chiral nihility. J. Electromagn. Waves Appl.17(5), 695-706 (2003). https://doi.org/10.1163/156939303322226356https://doi.org/10.1163/156939303322226356
J.B. Pendry, A chiral route to negative refraction. Science306, 1353-1355 (2004). https://doi.org/10.1126/science.1104467https://doi.org/10.1126/science.1104467
C. Monzon, D.W. Forester, Negative refraction and focusing of circularly polarized waves in optically active media. Phys. Rev. Lett.95, 123904 (2005). https://doi.org/10.1103/PhysRevLett.95.123904https://doi.org/10.1103/PhysRevLett.95.123904
S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, X. Zhang, Negative refractive index in chiral metamaterials. Phys. Rev. Lett.102, 023901 (2009). https://doi.org/10.1103/PhysRevLett.102.023901https://doi.org/10.1103/PhysRevLett.102.023901
M.S. Ukhtary, A.R.T. Nugraha, R. Saito, Negative refraction in Weyl semimetals. J. Phys. Soc. Jpn.86(10), 104703 (2017). https://doi.org/10.7566/JPSJ.86.104703https://doi.org/10.7566/JPSJ.86.104703
T. Hayata, A new route to negative refractive index from topological metals. Prog. Theor. Exp. Phys.2018, 083-101 (2018). https://doi.org/10.1093/ptep/pty082https://doi.org/10.1093/ptep/pty082
R.D.Y. Hills, A. Kusmartseva, F.V. Kusmartsev, Current-voltage characteristics of Weyl semimetal semiconducting devices, Veselago lenses, and hyperbolic Dirac phase. Phys. Rev. B95, 214103 (2017). https://doi.org/10.1103/PhysRevB.95.214103https://doi.org/10.1103/PhysRevB.95.214103
S. Tchoumakov, J. Cayssol, A.G. Grushin, Three-dimensional chiral Veselago lensing. Phys. Rev. B105(7), 075309 (2022). https://doi.org/10.1103/PhysRevB.105.075309https://doi.org/10.1103/PhysRevB.105.075309
G. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005)
J.E. Moore, Optical properties of Weyl semimetals. Natl. Sci. Rev.6, 206-208 (2019). https://doi.org/10.1093/nsr/nwy164https://doi.org/10.1093/nsr/nwy164
R.L. Peterson, Formal theory of nonlinear response. Rev. Mod. Phys.39, 69-77 (1967). https://doi.org/10.1103/RevModPhys.39.69https://doi.org/10.1103/RevModPhys.39.69
I. Sodemann, L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett.115, 216806 (2015). https://doi.org/10.1103/PhysRevLett.115.216806https://doi.org/10.1103/PhysRevLett.115.216806
A. Cortijo, Magnetic-field-induced nonlinear optical responses in inversion symmetric Dirac semimetals. Phys. Rev. B94, 235123 (2016). https://doi.org/10.1103/PhysRevB.94.235123https://doi.org/10.1103/PhysRevB.94.235123
T. Morimoto, N. Nagaosa, Topological nature of nonlinear optical effects in solids. Sci. Adv.2, 1501524 (2016). https://doi.org/10.1126/sciadv.1501524https://doi.org/10.1126/sciadv.1501524
T. Morimoto, S. Zhong, J. Orenstein, J.E. Moore, Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals. Phys. Rev. B94(24), 245121 (2016). https://doi.org/10.1103/PhysRevB.94.245121https://doi.org/10.1103/PhysRevB.94.245121
Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin, W. Xie, T. Palacios, H. Lin, S. Jia, P.A. Lee, P. Jarillo-Herrero, N. Gedik, Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys.13, 842-847 (2017). https://doi.org/10.1038/nphys4146https://doi.org/10.1038/nphys4146
F. de Juan, A.G. Grushin, T. Morimoto, J.E. Moore, Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun.8, 15995 (2017). https://doi.org/10.1038/ncomms15995https://doi.org/10.1038/ncomms15995
C.-K. Chan, N.H. Lindner, G. Refael, P.A. Lee, Photocurrents in Weyl semimetals. Phys. Rev. B95, 041104 (2017). https://doi.org/10.1103/PhysRevB.95.041104https://doi.org/10.1103/PhysRevB.95.041104
E.J. König, H.-Y. Xie, D.A. Pesin, A. Levchenko, Photogalvanic effect in Weyl semimetals. Phys. Rev. B96, 075123 (2017). https://doi.org/10.1103/PhysRevB.96.075123https://doi.org/10.1103/PhysRevB.96.075123
L.E. Golub, E.L. Ivchenko, B.Z. Spivak, Photocurrent in gyrotropic Weyl semimetals. JETP Lett.105(12), 782-785 (2017). https://doi.org/10.1134/S0021364017120062https://doi.org/10.1134/S0021364017120062
R.W. Boyd, Nonlinear Optics, 4th edn. (Academic Press, San Diego, 2020). https://doi.org/10.1016/C2015-0-05510-1https://doi.org/10.1016/C2015-0-05510-1
B.I. Sturman, V.M. Fridkin, The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials (Gordon and Breach Science Publishers, Philadelphia, 1992)
J.E. Sipe, A.I. Shkrebtii, Second-order optical response in semiconductors. Phys. Rev. B61(8), 5337-5352 (2000). https://doi.org/10.1103/PhysRevB.61.5337https://doi.org/10.1103/PhysRevB.61.5337
H. Rostami, M. Polini, Nonlinear anomalous photocurrents in Weyl semimetals. Phys. Rev. B97, 195151 (2018). https://doi.org/10.1103/PhysRevB.97.195151https://doi.org/10.1103/PhysRevB.97.195151
W. Shockley, H.J. Queisser, Detailed balance limit of efficiency of p-n junction solar cells. J. Appl. Phys.32, 510-519 (1961). https://doi.org/10.1063/1.1736034https://doi.org/10.1063/1.1736034
J.E. Spanier, V.M. Fridkin, A.M. Rappe, A.R. Akbashev, A. Polemi, Y. Qi, Z. Gu, S.M. Young, C.J. Hawley, D. Imbrenda, G. Xiao, A.L. Bennett-Jackson, C.L. Johnson, Power conversion efficiency exceeding the Shockley-Queisser limit in a ferroelectric insulator. Nat. Photonics10, 611-616 (2016). https://doi.org/10.1038/nphoton.2016.143https://doi.org/10.1038/nphoton.2016.143
G.B. Osterhoudt, L.K. Diebel, M.J. Gray, X. Yang, J. Stanco, X. Huang, B. Shen, N. Ni, P.J.W. Moll, Y. Ran, K.S. Burch, Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater.18, 471-475 (2019). https://doi.org/10.1038/s41563-019-0297-4https://doi.org/10.1038/s41563-019-0297-4
L. Zhang, Z. Chen, K. Zhang, L. Wang, H. Xu, L. Han, W. Guo, Y. Yang, C.-N. Kuo, C.S. Lue, D. Mondal, J. Fuji, I. Vobornik, B. Ghosh, A. Agarwal, H. Xing, X. Chen, A. Politano, W. Lu, High-frequency rectifiers based on type-II Dirac fermions. Nat. Commun.12(1), 1584 (2021). https://doi.org/10.1038/s41467-021-21906-whttps://doi.org/10.1038/s41467-021-21906-w
L. Wang, L. Han, W. Guo, L. Zhang, C. Yao, Z. Chen, Y. Chen, C. Guo, K. Zhang, C.-N. Kuo, C.S. Lue, A. Politano, H. Xing, M. Jiang, X. Yu, X. Chen, W. Lu, Hybrid Dirac semimetal-based photodetector with efficient low-energy photon harvesting. Light Sci. Appl.11(1), 53 (2022). https://doi.org/10.1038/s41377-022-00741-8https://doi.org/10.1038/s41377-022-00741-8
H. Weng, Lighting up Weyl semimetals. Nat. Mater.18, 428-429 (2019). https://doi.org/10.1038/s41563-019-0330-7https://doi.org/10.1038/s41563-019-0330-7
A.M. Glass, D. von der Linde, T.J. Negran, High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3. Appl. Phys. Lett.25, 233-235 (1974). https://doi.org/10.1063/1.1655453https://doi.org/10.1063/1.1655453
F. Nastos, J.E. Sipe, Optical rectification and shift currents in GaAs and GaP response: below and above the band gap. Phys. Rev. B74, 035201 (2006). https://doi.org/10.1103/PhysRevB.74.035201https://doi.org/10.1103/PhysRevB.74.035201
N. Laman, A.I. Shkrebtii, J.E. Sipe, H.M. van Driel, Quantum interference control of currents in CdSe with a single optical beam. Appl. Phys. Lett.75, 2581-2583 (1999). https://doi.org/10.1063/1.125084https://doi.org/10.1063/1.125084
Y. Zhang, H. Ishizuka, J. van den Brink, C. Felser, B. Yan, N. Nagaosa, Photogalvanic effect in Weyl semimetals from first principles. Phys. Rev. B97, 241118 (2018). https://doi.org/10.1103/PhysRevB.97.241118https://doi.org/10.1103/PhysRevB.97.241118
B. Sadhukhan, T. Nag, Electronic structure and unconventional nonlinear response in double Weyl semimetal SrSi2. Phys. Rev. B104, 245122 (2021). https://doi.org/10.1103/PhysRevB.104.245122https://doi.org/10.1103/PhysRevB.104.245122
B. Sadhukhan, T. Nag, Role of time reversal symmetry and tilting in circular photogalvanic responses. Phys. Rev. B103, 144308 (2021). https://doi.org/10.1103/PhysRevB.103.144308https://doi.org/10.1103/PhysRevB.103.144308
T. Nag, D.M. Kennes, Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals. Phys. Rev. B105, 214307 (2022). https://doi.org/10.1103/PhysRevB.105.214307https://doi.org/10.1103/PhysRevB.105.214307
K. Sun, S.-S. Sun, L.-L. Wei, C. Guo, H.-F. Tian, G.-F. Chen, H.-X. Yang, J.-Q. Li, Circular photogalvanic effect in the Weyl semimetal TaAs. Chin. Phys. Lett.34, 117203 (2017). https://doi.org/10.1088/0256-307X/34/11/117203https://doi.org/10.1088/0256-307X/34/11/117203
Z. Ji, G. Liu, Z. Addison, W. Liu, P. Yu, H. Gao, Z. Liu, A.M. Rappe, C.L. Kane, E.J. Mele, R. Agarwal, Spatially dispersive circular photogalvanic effect in a Weyl semimetal. Nat. Mater.18, 955-962 (2019). https://doi.org/10.1038/s41563-019-0421-5https://doi.org/10.1038/s41563-019-0421-5
N.M. Gabor, J.C.W. Song, Q. Ma, N.L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L.S. Levitov, P. Jarillo-Herrero, Hot carrier-assisted intrinsic photoresponse in graphene. Science334, 648-652 (2011). https://doi.org/10.1126/science.1211384https://doi.org/10.1126/science.1211384
J.W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, N. Gedik, Control over topological insulator photocurrents with light polarization. Nat. Nanotechnol.7, 96-100 (2012). https://doi.org/10.1038/nnano.2011.214https://doi.org/10.1038/nnano.2011.214
H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen, G. Xu, Y. Xu, S.-C. Zhang, H.Y. Hwang, Y. Cui, Generation and electric control of spin-valley-coupled circular photogalvanic current in WSe2. Nat. Nanotechnol.9, 851-857 (2014). https://doi.org/10.1038/nnano.2014.183https://doi.org/10.1038/nnano.2014.183
L.Z. Tan, F. Zheng, S.M. Young, F. Wang, S. Liu, A.M. Rappe, Shift current bulk photovoltaic effect in polar materials-hybrid and oxide perovs-kites and beyond. NPJ Comput. Mater.2, 1-12 (2016). https://doi.org/10.1038/npjcompumats.2016.26https://doi.org/10.1038/npjcompumats.2016.26
J. Ibañez-Azpiroz, S.S. Tsirkin, I. Souza, Ab initio calculation of the shift photocurrent by Wannier interpolation. Phys. Rev. B97, 245143 (2018). https://doi.org/10.1103/PhysRevB.97.245143https://doi.org/10.1103/PhysRevB.97.245143
J.-M. Lihm, Comment on Ab initio calculation of the shift photocurrent by Wannier interpolation. Phys. Rev. B103, 247101 (2021). https://doi.org/10.1103/PhysRevB.103.247101https://doi.org/10.1103/PhysRevB.103.247101. (arXiv 2105.14302)
D. Côté, N. Laman, H.M. van Driel, Rectification and shift currents in GaAs. Appl. Phys. Lett.80, 905-907 (2002). https://doi.org/10.1063/1.1436530https://doi.org/10.1063/1.1436530
J. Ma, Q. Gu, Y. Liu, J. Lai, P. Yu, X. Zhuo, Z. Liu, J.-H. Chen, J. Feng, D. Sun, Nonlinear photoresponse of type-II Weyl semimetals. Nat. Mater.18, 476-481 (2019). https://doi.org/10.1038/s41563-019-0296-5https://doi.org/10.1038/s41563-019-0296-5
R. Karplus, J.M. Luttinger, Hall effect in ferromagnetics. Phys. Rev.95, 1154-1160 (1954). https://doi.org/10.1103/PhysRev.95.1154https://doi.org/10.1103/PhysRev.95.1154
G. Sundaram, Q. Niu, Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects. Phys. Rev. B59, 14915-14925 (1999). https://doi.org/10.1103/PhysRevB.59.14915https://doi.org/10.1103/PhysRevB.59.14915
Y. Zhang, Y. Sun, B. Yan, Berry curvature dipole in Weyl semimetal materials: an ab initio study. Phys. Rev. B97, 041101 (2018). https://doi.org/10.1103/PhysRevB.97.041101https://doi.org/10.1103/PhysRevB.97.041101
Y. Gao, F. Zhang, W. Zhang, Second-order nonlinear Hall effect in Weyl semimetals. Phys. Rev. B102(24), 245116 (2020). https://doi.org/10.1103/PhysRevB.102.245116https://doi.org/10.1103/PhysRevB.102.245116
G. Chang, J.-X. Yin, T. Neupert, D.S. Sanchez, I. Belopolski, S.S. Zhang, T.A. Cochran, Z. Chéng, M.-C. Hsu, S.-M. Huang, B. Lian, S.-Y. Xu, H. Lin, M.Z. Hasan, Unconventional photocurrents from surface Fermi arcs in topological chiral semimetals. Phys. Rev. Lett.124(16), 166404 (2020). https://doi.org/10.1103/PhysRevLett.124.166404https://doi.org/10.1103/PhysRevLett.124.166404
J.F. Steiner, A.V. Andreev, M. Breitkreiz, Surface photogalvanic effect in Weyl semimetals. Phys. Rev. Res.4(2), 023021 (2022). https://doi.org/10.1103/PhysRevResearch.4.023021https://doi.org/10.1103/PhysRevResearch.4.023021
L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A45(11), 8185-8189 (1992). https://doi.org/10.1103/PhysRevA.45.8185https://doi.org/10.1103/PhysRevA.45.8185
G.F. Quinteiro, P.I. Tamborenea, Theory of the optical absorption of light carrying orbital angular momentum by semiconductors. EPL Europhys. Lett.85, 47001 (2009). https://doi.org/10.1209/0295-5075/85/47001https://doi.org/10.1209/0295-5075/85/47001
P. Lebedew, Untersuchungen über die Druckkräfte des Lichtes. Ann. Phys.311, 433-458 (1901). https://doi.org/10.1002/andp.19013111102https://doi.org/10.1002/andp.19013111102
S. Patankar, L. Wu, B. Lu, M. Rai, J.D. Tran, T. Morimoto, D.E. Parker, A.G. Grushin, N.L. Nair, J.G. Analytis, J.E. Moore, J. Orenstein, D.H. Torchinsky, Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs. Phys. Rev. B98(16), 165113 (2018). https://doi.org/10.1103/PhysRevB.98.165113https://doi.org/10.1103/PhysRevB.98.165113
Y. Gao, S. Kaushik, E.J. Philip, Z. Li, Y. Qin, Y.P. Liu, W.L. Zhang, Y.L. Su, X. Chen, H. Weng, D.E. Kharzeev, M.K. Liu, J. Qi, Chiral terahertz wave emission from the Weyl semimetal TaAs. Nat. Commun.11, 720 (2020). https://doi.org/10.1038/s41467-020-14463-1https://doi.org/10.1038/s41467-020-14463-1
J.P. van der Ziel, P.S. Pershan, L.D. Malmstrom, Optically-induced magnetization resulting from the inverse Faraday effect. Phys. Rev. Lett.15(5), 190-193 (1965). https://doi.org/10.1103/PhysRevLett.15.190https://doi.org/10.1103/PhysRevLett.15.190
R. Hertel, Theory of the inverse Faraday effect in metals. J. Magn. Magn. Mater.303(1), 1-4 (2006). https://doi.org/10.1016/j.jmmm.2005.10.225https://doi.org/10.1016/j.jmmm.2005.10.225
P.S. Pershan, Nonlinear optical properties of solids: energy considerations. Phys. Rev.130(3), 919-929 (1963). https://doi.org/10.1103/PhysRev.130.919https://doi.org/10.1103/PhysRev.130.919
A.V. Kimel, A. Kirilyuk, P.A. Usachev, R.V. Pisarev, A.M. Balbashov, T. Rasing, Ultrafast non-thermal control of magnetization by instantaneous photomagnetic pulses. Nature435(7042), 655-657 (2005). https://doi.org/10.1038/nature03564https://doi.org/10.1038/nature03564
A.V. Kimel, A. Kirilyuk, T. Rasing, Femtosecond opto-magnetism: ultrafast laser manipulation of magnetic materials. Laser Photonics Rev.1(3), 275-287 (2007). https://doi.org/10.1002/lpor.200710022https://doi.org/10.1002/lpor.200710022
A.A. Zyuzin, M. Silaev, V.A. Zyuzin, Nonlinear chiral transport in Dirac semimetals. Phys. Rev. B98, 205149 (2018). https://doi.org/10.1103/PhysRevB.98.205149https://doi.org/10.1103/PhysRevB.98.205149
Kawaguchi M., Hirose, H., Chi, Z., Lau, Y.-C., Freimuth, F., Hayashi, M.: Giant Inverse Faraday Effect in Dirac Semimetals. arXiv (2020). arXiv2009.01388
I.D. Tokman, Q. Chen, I.A. Shereshevsky, V.I. Pozdnyakova, I. Oladyshkin, M. Tokman, A. Belyanin, Inverse Faraday effect in graphene and Weyl semimetals. Phys. Rev. B101, 174429 (2020). https://doi.org/10.1103/PhysRevB.101.174429https://doi.org/10.1103/PhysRevB.101.174429
Gao Y., Wang, C., Xiao, D.: Topological inverse Faraday effect in Weyl semimetals. arXiv (2020). arXiv2009.13392
Cao J., Zeng, C., Li, X.-P., Wang, M., Yang, S.A., Yu, Z.-M., Yao, Y.: Low-Frequency Divergence of Circular Photomagnetic Effect in Topological Semimetals. arXiv (2022). arXiv2201.06243
L. Liang, P.O. Sukhachov, A.V. Balatsky, Axial magnetoelectric effect in Dirac semimetals. Phys. Rev. Lett.126, 247202 (2021). https://doi.org/10.1103/PhysRevLett.126.247202https://doi.org/10.1103/PhysRevLett.126.247202
Y.-Y. Lv, J. Xu, S. Han, C. Zhang, Y. Han, J. Zhou, S.-H. Yao, X.-P. Liu, M.-H. Lu, H. Weng, Z. Xie, Y.B. Chen, J. Hu, Y.-F. Chen, S. Zhu, High-harmonic generation in Weyl semimetal β-WP2 crystals. Nat. Commun.12(1), 6437 (2021). https://doi.org/10.1038/s41467-021-26766-yhttps://doi.org/10.1038/s41467-021-26766-y
S. Ghimire, A.D. DiChiara, E. Sistrunk, P. Agostini, L.F. DiMauro, D.A. Reis, Observation of high-order harmonic generation in a bulk crystal. Nat. Phys.7, 138-141 (2011). https://doi.org/10.1038/nphys1847https://doi.org/10.1038/nphys1847
H. Liu, Y. Li, Y.S. You, S. Ghimire, T.F. Heinz, D.A. Reis, High-harmonic generation from an atomically thin semiconductor. Nat. Phys.13, 262-265 (2017). https://doi.org/10.1038/nphys3946https://doi.org/10.1038/nphys3946
H. Liu, C. Guo, G. Vampa, J.L. Zhang, T. Sarmiento, M. Xiao, P.H. Bucksbaum, J. Vučković, S. Fan, D.A. Reis, Enhanced high-harmonic generation from an all-dielectric metasurface. Nat. Phys.14, 1006-1010 (2018). https://doi.org/10.1038/s41567-018-0233-6https://doi.org/10.1038/s41567-018-0233-6
E. Goulielmakis, T. Brabec, High harmonic generation in condensed matter. Nat. Photonics16, 411-421 (2022). https://doi.org/10.1038/s41566-022-00988-yhttps://doi.org/10.1038/s41566-022-00988-y
Y. Bai, F. Fei, S. Wang, N. Li, X. Li, F. Song, R. Li, Z. Xu, P. Liu, High-harmonic generation from topological surface states. Nat. Phys.17, 311-315 (2021). https://doi.org/10.1038/s41567-020-01052-8https://doi.org/10.1038/s41567-020-01052-8
C. Heide, Y. Kobayashi, D.R. Baykusheva, D. Jain, J.A. Sobota, M. Hashimoto, P.S. Kirchmann, S. Oh, T.F. Heinz, D.A. Reis, S. Ghimire, Probing topological phase transitions using high-harmonic generation. Nat. Photonics (2022). https://doi.org/10.1038/s41566-022-01050-7https://doi.org/10.1038/s41566-022-01050-7
T.T. Luu, H.J. Wörner, Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat. Commun.9, 916 (2018). https://doi.org/10.1038/s41467-018-03397-4https://doi.org/10.1038/s41467-018-03397-4
A. Bharti, M.S. Mrudul, G. Dixit, High-harmonic spectroscopy of light-driven nonlinear anisotropic anomalous Hall effect in a Weyl semimetal. Phys. Rev. B105, 155140 (2022). https://doi.org/10.1103/PhysRevB.105.155140https://doi.org/10.1103/PhysRevB.105.155140
S. Zhong, J.E. Moore, I. Souza, Gyrotropic magnetic effect and the magnetic moment on the Fermi surface. Phys. Rev. Lett.116(7), 077201 (2016). https://doi.org/10.1103/PhysRevLett.116.077201https://doi.org/10.1103/PhysRevLett.116.077201
C.-K. Chan, P.A. Lee, K.S. Burch, J.H. Han, Y. Ran, When chiral photons meet chiral fermions: Photoinduced anomalous Hall effects in Weyl semimetals. Phys. Rev. Lett.116(2), 026805 (2016). https://doi.org/10.1103/PhysRevLett.116.026805https://doi.org/10.1103/PhysRevLett.116.026805
Nathan F., Martin, I., Refael, G.: Topological Frequency Conversion in Weyl Semimetals. arXiv (2022). arXiv2201.07804
H. Ishizuka, T. Hayata, M. Ueda, N. Nagaosa, Emergent electromagnetic induction and adiabatic charge pumping in noncentrosymmetric Weyl semimetals. Phys. Rev. Lett.117(21), 216601 (2016). https://doi.org/10.1103/PhysRevLett.117.216601https://doi.org/10.1103/PhysRevLett.117.216601
H. Ishizuka, T. Hayata, M. Ueda, N. Nagaosa, Momentum-space electromagnetic induction in Weyl semimetals. Phys. Rev. B95(24), 245211 (2017). https://doi.org/10.1103/PhysRevB.95.245211https://doi.org/10.1103/PhysRevB.95.245211
K. Halterman, M. Alidoust, A. Zyuzin, Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals. Phys. Rev. B98(8), 085109 (2018). https://doi.org/10.1103/PhysRevB.98.085109https://doi.org/10.1103/PhysRevB.98.085109
C. Zhao, C. Zhao, G. Hu, Y. Chen, Q. Zhang, Y. Zhang, Y. Zhang, C.-W. Qiu, C.-W. Qiu, Unidirectional bound states in the continuum in Weyl semimetal nanostructures. Photonics Res.10(8), 1828-1838 (2022). https://doi.org/10.1364/PRJ.459383https://doi.org/10.1364/PRJ.459383
M.Q. Liu, C.Y. Zhao, H. Bao, Transverse Kerker scattering governed by two nondegenerate electric dipoles and its application in arbitrary beam steering. J. Quant. Spectrosc. Radiat. Transfer262, 107514 (2021). https://doi.org/10.1016/j.jqsrt.2021.107514https://doi.org/10.1016/j.jqsrt.2021.107514
G. Oktay, M. Sarısaman, M. Tas, Lasing with topological Weyl semimetal. Sci. Rep.10, 3127 (2020). https://doi.org/10.1038/s41598-020-59423-3https://doi.org/10.1038/s41598-020-59423-3
G. Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Oxford University Press, Oxford, 2005)
Z.M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, New York, 2007)
T.L. Bergman, T.L. Bergman, F.P. Incropera, D.P. Dewitt, A.S. Lavine, Fundamentals of Heat and Mass Transfer (Wiley, Hoboken, 2011)
M.F. Modest, S. Mazumder, Radiative Heat Transfer (Academic Press, London, 2021)
J.R. Howell, M.P. Mengüç, K. Daun, R. Siegel, Thermal Radiation Heat Transfer (CRC Press, London, 2020)
W.C. Snyder, Z. Wan, X. Li, Thermodynamic constraints on reflectance reciprocity and Kirchhoff's law. Appl. Opt.37, 3464-3470 (1998). https://doi.org/10.1364/AO.37.003464https://doi.org/10.1364/AO.37.003464
B. Zhao, Y. Shi, J. Wang, Z. Zhao, N. Zhao, S. Fan, Near-complete violation of Kirchhoff's law of thermal radiation with a 0.3 T magnetic field. Opt. Lett.44, 4203-4206 (2019). https://doi.org/10.1364/OL.44.004203https://doi.org/10.1364/OL.44.004203
L. Onsager, Reciprocal relations in irreversible processes. I. Phys. Rev.37(4), 405-426 (1931). https://doi.org/10.1103/PhysRev.37.405https://doi.org/10.1103/PhysRev.37.405
L. Onsager, Reciprocal relations in irreversible processes. II. Phys. Rev.38(12), 2265-2279 (1931). https://doi.org/10.1103/PhysRev.38.2265https://doi.org/10.1103/PhysRev.38.2265
O. Madelung, Semiconductors: Data Handbook (Springer, Berlin, 2004)
D.B. Tanner, Optical Effects in Solids (Cambridge University Press, Cambridge, 2019)
L. Zhu, S. Fan, Near-complete violation of detailed balance in thermal radiation. Phys. Rev. B90, 220301 (2014). https://doi.org/10.1103/PhysRevB.90.220301https://doi.org/10.1103/PhysRevB.90.220301
J.M.D. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, 2010)
W. Feng, X. Fu, C. Wan, Z. Yuan, X. Han, N.V. Quang, S. Cho, Spin gapless semiconductor like Ti2MnAl film as a new candidate for spintronics application. Phys. Status solidi (RRL) Rapid Res. Lett.9, 641-645 (2015). https://doi.org/10.1002/pssr.201510340https://doi.org/10.1002/pssr.201510340
W. Shi, L. Muechler, K. Manna, Y. Zhang, K. Koepernik, R. Car, J. van den Brink, C. Felser, Y. Sun, Prediction of a magnetic Weyl semimetal without spin-orbit coupling and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl. Phys. Rev. B97, 060406 (2018). https://doi.org/10.1103/PhysRevB.97.060406https://doi.org/10.1103/PhysRevB.97.060406
J. Wu, Z. Wang, H. Zhai, Z. Shi, X. Wu, X. Wu, F. Wu, F. Wu, Near-complete violation of Kirchhoff's law of thermal radiation in ultrathin magnetic Weyl semimetal films. Opt. Mater. Express11, 4058-4066 (2021). https://doi.org/10.1364/OME.444308https://doi.org/10.1364/OME.444308
X. Wu, H. Yu, F. Wu, B. Wu, Enhanced nonreciprocal radiation in Weyl semimetals by attenuated total reflection. AIP Adv.11, 075106 (2021). https://doi.org/10.1063/5.0055418https://doi.org/10.1063/5.0055418
J. Wu, B. Wu, Z. Wang, X. Wu, Strong nonreciprocal thermal radiation in Weyl semimetal-dielectric multilayer structure. Int. J. Therm. Sci.181, 107788 (2022). https://doi.org/10.1016/j.ijthermalsci.2022.107788https://doi.org/10.1016/j.ijthermalsci.2022.107788
B. Zhao, J. Wang, Z. Zhao, C. Guo, Z. Yu, S. Fan, Nonreciprocal thermal emitters using metasurfaces with multiple diffraction channels. Phys. Rev. Appl.16, 064001 (2021). https://doi.org/10.1103/PhysRevApplied.16.064001https://doi.org/10.1103/PhysRevApplied.16.064001
M.F. Maghrebi, A.V. Gorshkov, J.D. Sau, Fluctuation-induced torque on a topological insulator out of thermal equilibrium. Phys. Rev. Lett.123, 055901 (2019). https://doi.org/10.1103/PhysRevLett.123.055901https://doi.org/10.1103/PhysRevLett.123.055901
E. Khan, E.E. Narimanov, Spinning radiation from a topological insulator. Phys. Rev. B100, 081408 (2019). https://doi.org/10.1103/PhysRevB.100.081408https://doi.org/10.1103/PhysRevB.100.081408
Y. Wang, C. Khandekar, X. Gao, T. Li, D. Jiao, Z. Jacob, Broadband circularly polarized thermal radiation from magnetic Weyl semimetals. Opt. Mater. Express11(11), 3880-3895 (2021). https://doi.org/10.1364/OME.437838https://doi.org/10.1364/OME.437838
C. Khandekar, F. Khosravi, Z. Li, Z. Jacob, New spin-resolved thermal radiation laws for nonreciprocal bianisotropic media. New J. Phys.22(12), 123005 (2020). https://doi.org/10.1088/1367-2630/abc988https://doi.org/10.1088/1367-2630/abc988
A. Ott, P. Ben-Abdallah, S.-A. Biehs, Circular heat and momentum flux radiated by magneto-optical nanoparticles. Phys. Rev. B97, 205414 (2018). https://doi.org/10.1103/PhysRevB.97.205414https://doi.org/10.1103/PhysRevB.97.205414
Y. Guo, S. Fan, Single gyrotropic particle as a heat engine. ACS Photonics8, 1623-1629 (2021). https://doi.org/10.1021/acsphotonics.0c01920https://doi.org/10.1021/acsphotonics.0c01920
S. Fan, Thermal photonics and energy applications. Joule1, 264-273 (2017). https://doi.org/10.1016/j.joule.2017.07.012https://doi.org/10.1016/j.joule.2017.07.012
L. Zhu, S. Fan, Persistent directional current at equilibrium in nonreciprocal many-body near field electromagnetic heat transfer. Phys. Rev. Lett.117, 134303 (2016). https://doi.org/10.1103/PhysRevLett.117.134303https://doi.org/10.1103/PhysRevLett.117.134303
M.G. Silveirinha, Topological angular momentum and radiative heat transport in closed orbits. Phys. Rev. B95, 115103 (2017). https://doi.org/10.1103/PhysRevB.95.115103https://doi.org/10.1103/PhysRevB.95.115103
C. Khandekar, Z. Jacob, Thermal spin photonics in the near-field of non-reciprocal media. New J. Phys.21(10), 103030 (2019). https://doi.org/10.1088/1367-2630/ab494dhttps://doi.org/10.1088/1367-2630/ab494d
C. Guo, Y. Guo, S. Fan, Relation between photon thermal Hall effect and persistent heat current in nonreciprocal radiative heat transfer. Phys. Rev. B100, 205416 (2019). https://doi.org/10.1103/PhysRevB.100.205416https://doi.org/10.1103/PhysRevB.100.205416
C. Guo, S. Fan, Theoretical constraints on reciprocal and non-reciprocal many-body radiative heat transfer. Phys. Rev. B102, 085401 (2020). https://doi.org/10.1103/PhysRevB.102.085401https://doi.org/10.1103/PhysRevB.102.085401
P. Ben-Abdallah, Photon thermal Hall effect. Phys. Rev. Lett.116, 084301 (2016). https://doi.org/10.1103/PhysRevLett.116.084301https://doi.org/10.1103/PhysRevLett.116.084301
A. Ott, S.-A. Biehs, P. Ben-Abdallah, Anomalous photon thermal Hall effect. Phys. Rev. B101, 241411 (2020). https://doi.org/10.1103/PhysRevB.101.241411https://doi.org/10.1103/PhysRevB.101.241411
C.R. Otey, W.T. Lau, S. Fan, Thermal rectification through vacuum. Phys. Rev. Lett.104, 154301 (2010). https://doi.org/10.1103/PhysRevLett.104.154301https://doi.org/10.1103/PhysRevLett.104.154301
A. Ott, R. Messina, P. Ben-Abdallah, S.-A. Biehs, Radiative thermal diode driven by nonreciprocal surface waves. Appl. Phys. Lett.114(16), 163105 (2019). https://doi.org/10.1063/1.5093626https://doi.org/10.1063/1.5093626
Wang K., Gao, L.: High-Efficient Photonic Thermal Rectification with Magnetocontrollability. ES Energy Environ7, 12-16 (2020). https://doi.org/10.30919/esee8c350https://doi.org/10.30919/esee8c350
A. Ott, S.-A. Biehs, Thermal rectification and spin-spin coupling of non-reciprocal localized and surface modes. Phys. Rev. B101, 155428 (2020). https://doi.org/10.1103/PhysRevB.101.155428https://doi.org/10.1103/PhysRevB.101.155428
G. Tang, J. Chen, L. Zhang, Twist-induced control of near-field heat radiation between magnetic Weyl semimetals. ACS Photonics8(2), 443-448 (2021). https://doi.org/10.1021/acsphotonics.0c01945https://doi.org/10.1021/acsphotonics.0c01945
G. Xu, J. Sun, H. Mao, Near-field radiative thermal modulation between Weyl semimetal slabs. J. Quant. Spectrosc. Radiat. Transfer253, 107173 (2020). https://doi.org/10.1016/j.jqsrt.2020.107173https://doi.org/10.1016/j.jqsrt.2020.107173
R.M. Abraham Ekeroth, P. Ben-Abdallah, J.C. Cuevas, A. García-Martín, Anisotropic thermal magnetoresistance for an active control of radiative heat transfer. ACS Photonics5(3), 705-710 (2018). https://doi.org/10.1021/acsphotonics.7b01223https://doi.org/10.1021/acsphotonics.7b01223
C. Guo, B. Zhao, D. Huang, S. Fan, Radiative thermal router based on tunable magnetic Weyl semimetals. ACS Photonics7(11), 3257-3263 (2020). https://doi.org/10.1021/acsphotonics.0c01376https://doi.org/10.1021/acsphotonics.0c01376
L. Zhu, Y. Guo, S. Fan, Theory of many-body radiative heat transfer without the constraint of reciprocity. Phys. Rev. B97, 094302 (2018). https://doi.org/10.1103/PhysRevB.97.094302https://doi.org/10.1103/PhysRevB.97.094302
L. Fan, Y. Guo, G.T. Papadakis, B. Zhao, Z. Zhao, S. Buddhiraju, M. Oren-stein, S. Fan, Nonreciprocal radiative heat transfer between two planar bodies. Phys. Rev. B101, 085407 (2020). https://doi.org/10.1103/PhysRevB.101.085407https://doi.org/10.1103/PhysRevB.101.085407
Y. Tsurimaki, X. Qian, S. Pajovic, S. Boriskina, G. Chen, Casimir Force among Spheres Made of Weyl Semimetals Breaking Lorentz Reciprocity. arXiv (2021). arXiv2109.03809
J.H. Wilson, A.A. Allocca, V. Galitski, Repulsive Casimir force between Weyl semimetals. Phys. Rev. B91, 235115 (2015). https://doi.org/10.1103/PhysRevB.91.235115https://doi.org/10.1103/PhysRevB.91.235115
M.B. Farias, A.A. Zyuzin, T.L. Schmidt, Casimir force between Weyl semimetals in a chiral medium. Phys. Rev. B101, 235446 (2020). https://doi.org/10.1103/PhysRevB.101.235446https://doi.org/10.1103/PhysRevB.101.235446
L. Chen, K. Chang, Chiral-anomaly-driven Casimir-Lifshitz torque between Weyl semimetals. Phys. Rev. Lett.125, 047402 (2020). https://doi.org/10.1103/PhysRevLett.125.047402https://doi.org/10.1103/PhysRevLett.125.047402
P. Rodriguez-Lopez, A. Popescu, I. Fialkovsky, N. Khusnutdinov, L.M. Woods, Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals. Commun. Mater.1, 1-9 (2020). https://doi.org/10.1038/s43246-020-0015-4https://doi.org/10.1038/s43246-020-0015-4
T.H. Boyer, Van der Waals forces and zero-point energy for dielectric and permeable materials. Phys. Rev. A9, 2078-2084 (1974). https://doi.org/10.1103/PhysRevA.9.2078https://doi.org/10.1103/PhysRevA.9.2078
W.-K. Tse, A.H. MacDonald, Quantized Casimir force. Phys. Rev. Lett.109, 236806 (2012). https://doi.org/10.1103/PhysRevLett.109.236806https://doi.org/10.1103/PhysRevLett.109.236806
A.G. Grushin, A. Cortijo, Tunable Casimir repulsion with three-dimensional topological insulators. Phys. Rev. Lett.106, 020403 (2011). https://doi.org/10.1103/PhysRevLett.106.020403https://doi.org/10.1103/PhysRevLett.106.020403
D. Gelbwaser-Klimovsky, N. Graham, M. Kardar, M. Krüger, Near field propulsion forces from nonreciprocal media. Phys. Rev. Lett.126, 170401 (2021). https://doi.org/10.1103/PhysRevLett.126.170401https://doi.org/10.1103/PhysRevLett.126.170401
0
浏览量
0
Downloads
0
CSCD
关联资源
相关文章
相关作者
相关机构
京公网安备11010802024621