Abstract

We theoretically study unattenuated electromagnetic guided wave modes in centrosymmetric Weyl semimetal layered systems. By solving Maxwell’s equations for the electromagnetic fields and using the appropriate boundary conditions, we derive dispersion relations for propagating modes in a finite-sized Weyl semimetal. Our findings reveal that for ultrathin structures and proper Weyl cones tilts, extremely localized guided waves can propagate along the semimetal interface over a certain range of frequencies. This follows from the anisotropic nature of the semimetal where the diagonal components of the permittivity can exhibit a tunable epsilon-near-zero response. From the dispersion diagrams, we determine experimentally accessible regimes that lead to high energy-density confinement in the Weyl semimetal layer. Furthermore, we show that the net system power can vanish all together, depending on the Weyl cone tilt and frequency of the electromagnetic wave. These effects are seen in the energy transport velocity, which demonstrates a substantial slowdown in the propagation of electromagnetic energy near critical points of the dispersion diagrams. Our results can provide guidelines in designing Weyl semimetal waveguides that can offer efficient control in the velocity and direction of energy flow.

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2019 (2)

Q. Chen, A. R. Kutayiah, I. Oladyshkin, M. Tokman, and A. Belyanin, “Optical properties and electromagnetic modes of Weyl semimetals,” Phys. Rev. B 99(7), 075137 (2019).
[Crossref]

V. Caligiuri, M. Palei, G. Biffi, S. Artyukhin, and R. Krahne, “A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities,” Nano Lett. 19(5), 3151–3160 (2019).
[Crossref]

2018 (3)

K. Halterman, M. Alidoust, and A. Zyuzin, “Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals,” Phys. Rev. B 98(8), 085109 (2018).
[Crossref]

S. P. Mukherjee and J. P. Carbotte, “Imaginary part of Hall conductivity in a tilted doped Weyl semimetal with both broken time-reversal and inversion symmetry,” Phys. Rev. B 97(3), 035144 (2018).
[Crossref]

O. V. Kotov and Yu. E. Lozovik, “Giant tunable nonreciprocity of light in Weyl semimetals,” Phys. Rev. B 98(19), 195446 (2018).
[Crossref]

2017 (8)

S. P. Mukherjee and J. P. Carbotte, “Absorption of circular polarized light in tilted type-I and type-II Weyl semimetals,” Phys. Rev. B 96(8), 085114 (2017).
[Crossref]

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. J.-Herrero, and N. Gedik, “Direct optical detection of Weyl fermion chirality in a topological semimetal,” Nat. Phys. 13(9), 842–847 (2017).
[Crossref]

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. P. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points and Fermi arc-like surface states,” Nat. Phys. 13(6), 611–617 (2017).
[Crossref]

F. Detassis, L. Fritz, and S. Grubinskas, “Collective effects in tilted Weyl cones: Optical conductivity, polarization, and Coulomb interactions reshaping the cone,” Phys. Rev. B 96(19), 195157 (2017).
[Crossref]

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

E. Haubold, K. Koepernik, D. Efremov, S. Khim, A. Fedorov, Y. Kushnirenko, J. van den Brink, S. Wurmehl, B. Buchner, T. K. Kim, M. Hoesch, K. Sumida, K. Taguchi, T. Yoshikawa, A. Kimura, T. Okuda, and S. V. Borisenko, “Experimental realization of type-II Weyl state in noncentrosymmetric Ta IrTe4,” Phys. Rev. B 95(24), 241108 (2017).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

H. Galinski, G. Favraud, H. Dong, J. S. Totero Gongora, G. Favaro, M. Döbeli, R. Spolenak, A. Fratalocchi, and F. Capasso, “Scalable, ultra-resistant structural colors based on network metamaterials,” Light: Sci. Appl. 6(5), e16233 (2017).
[Crossref]

2016 (6)

M. Mattheakis, C. A. Valagiannopoulos, and E. Kaxiras, “Epsilon-near-zero behavior from plasmonic Dirac point: Theory and realization using two-dimensional materials,” Phys. Rev. B 94(20), 201404 (2016).
[Crossref]

Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla, “Chiral magnetic effect in ZrTe5,” Nat. Phys. 12(6), 550–554 (2016).
[Crossref]

G. Autès, D. Gresch, M. Troyer, A. A. Soluyanov, and O. V. Yazyev, “Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W),” Phys. Rev. Lett. 117(6), 066402 (2016).
[Crossref]

Y. Wu, N. Hyun Jo, D. Mou, L. Huang, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, “Observation of Fermi arcs in the type-II Weyl semimetal candidate WTe2,” Phys. Rev. B 94(12), 121113 (2016).
[Crossref]

O. V. Kotov and Yu. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016).
[Crossref]

B. Xu, Y. M. Dai, L. X. Zhao, K. Wang, R. Yang, W. Zhang, J. Y. Liu, H. Xiao, G. F. Chen, A. J. Taylor, D. A. Yarotski, R. P. Prasankumar, and X. G. Qiu, “Optical spectroscopy of the Weyl semimetal TaAs,” Phys. Rev. B 93(12), 121110 (2016).
[Crossref]

2015 (16)

M. Kargarian, M. Randeria, and N. Trivedi, “Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals,” Sci. Rep. 5(1), 12683 (2015).
[Crossref]

A. A. Zyuzin and V. A. Zyuzin, “Chiral electromagnetic waves in Weyl semimetals,” Phys. Rev. B 92(11), 115310 (2015).
[Crossref]

R. Y. Chen, S. J. Zhang, J. A. Schneeloch, C. Zhang, Q. Li, G. D. Gu, and N. L. Wang, “Optical spectroscopy study of the three-dimensional Dirac semimetal,” Phys. Rev. B 92(7), 075107 (2015).
[Crossref]

A. B. Sushkov, J. B. Hofmann, G. S. Jenkins, J. Ishikawa, S. Nakatsuji, S. Das Sarma, and H. D. Drew, “Optical evidence for a Weyl semimetal state in pyrochlore Eu2Ir2O7,” Phys. Rev. B 92(24), 241108 (2015).
[Crossref]

S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, “A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class,” Nat. Commun. 6(1), 7373 (2015).
[Crossref]

H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, “Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides,” Phys. Rev. X 5(1), 011029 (2015).
[Crossref]

C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, Y. Skourski, J. Wosnitza, Z. Liu, Y. Chen, W. Schnelle, H. Borrmann, Y. Grin, C. Felser, and B. Yan, “Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP,” Nat. Phys. 11(8), 645–649 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
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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, and M. Z. Hasan, “Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide,” Nat. Phys. 11(9), 748–754 (2015).
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2014 (2)

K. Halterman and J. M. Elson, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22(6), 7337 (2014).
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P. E. C. Ashby and J. P. Carbotte, “Chiral anomaly and optical absorption in Weyl semimetals,” Phys. Rev. B 89(24), 245121 (2014).
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2013 (5)

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
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A. Ciattoni, A. Marini, C. Rizza, M. Scalora, and F. Biancalana, “Polariton excitation in epsilon-near-zero slabs: Transient trapping of slow light,” Phys. Rev. A 87(5), 053853 (2013).
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A. N. Poddubny, I. Iorsh, P. A. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
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2012 (4)

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86(16), 165103 (2012).
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Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907 (2012).
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2011 (5)

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D. Slocum, S. Inampudi, D. C. Adams, S. Vangala, N. A. Kuhta, W. D. Goodhue, V. A. Podolskiy, and D. Wasserman, “Funneling light through a subwavelength aperture with epsilon-near-zero materials,” Phys. Rev. Lett. 107(13), 133901 (2011).
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2010 (2)

2009 (1)

A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009).
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2008 (3)

G.-D. Xu, T. Pan, T.-C. Zang, and J. Sun, “Characteristics of guided waves in indefinite-medium waveguides,” Opt. Commun. 281(10), 2819–2825 (2008).
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B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
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R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903 (2008).
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2007 (2)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
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K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
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2006 (1)

M. Silveirinha and N. Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using epsilon-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
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2002 (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2-3), 309–312 (2002).
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1998 (1)

D. J. Bergman and Y. M. Strelniker, “Anisotropic ac electrical permittivity of a periodic metal-dielectric composite film in a strong magnetic field,” Phys. Rev. Lett. 80(4), 857–860 (1998).
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1970 (1)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A: Gen. Phys. 3(3), 233–245 (1970).
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1929 (1)

H. Z. Weyl, “Elektron und Gravitation. I,” Z. Physik 56(5-6), 330–352 (1929).
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Adams, D. C.

D. Slocum, S. Inampudi, D. C. Adams, S. Vangala, N. A. Kuhta, W. D. Goodhue, V. A. Podolskiy, and D. Wasserman, “Funneling light through a subwavelength aperture with epsilon-near-zero materials,” Phys. Rev. Lett. 107(13), 133901 (2011).
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Ali, M. N.

Y. Sun, S.-C. Wu, M. N. Ali, C. Felser, and B. Yan, “Prediction of Weyl semimetal in orthorhombic MoTe2,” Phys. Rev. B 92(16), 161107 (2015).
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Alidoust, M.

K. Halterman, M. Alidoust, and A. Zyuzin, “Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals,” Phys. Rev. B 98(8), 085109 (2018).
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Alidoust, N.

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, “A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class,” Nat. Commun. 6(1), 7373 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide,” Nat. Phys. 11(9), 748–754 (2015).
[Crossref]

I. Belopolski, S.-Y. Xu, Y. Ishida, X. Pan, P. Yu, D. S. Sanchez, M. Neupane, N. Alidoust, G. Chang, T.-R. Chang, Y. Wu, G. Bian, H. Zheng, S.-M. Huang, C.-C. Lee, D. Mou, L. Huang, Y. Song, B. Wang, G. Wang, Y.-W. Yeh, N. Yao, J. Rault, P. Lefevre, F. Bertran, H.-T. Jeng, T. Kondo, A. Kaminski, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Unoccupied electronic structure and signatures of topological Fermi arcs in the Weyl semimetal candidate MoxW1−x Te2, arXiv:1512.09099 (2015).

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[Crossref]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Artyukhin, S.

V. Caligiuri, M. Palei, G. Biffi, S. Artyukhin, and R. Krahne, “A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities,” Nano Lett. 19(5), 3151–3160 (2019).
[Crossref]

Ashby, P. E. C.

P. E. C. Ashby and J. P. Carbotte, “Chiral anomaly and optical absorption in Weyl semimetals,” Phys. Rev. B 89(24), 245121 (2014).
[Crossref]

P. E. C. Ashby and J. P. Carbotte, “Magneto-optical conductivity of Weyl semimetals,” Phys. Rev. B 87(24), 245131 (2013).
[Crossref]

Autès, G.

G. Autès, D. Gresch, M. Troyer, A. A. Soluyanov, and O. V. Yazyev, “Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W),” Phys. Rev. Lett. 117(6), 066402 (2016).
[Crossref]

Ba nuls, M. J.

Balents, L.

A. A. Burkov and L. Balents, “Weyl semimetal in a topological insulator multilayer,” Phys. Rev. Lett. 107(12), 127205 (2011).
[Crossref]

Bansil, A.

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, “A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class,” Nat. Commun. 6(1), 7373 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide,” Nat. Phys. 11(9), 748–754 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref]

Basov, D. N.

T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B 87(23), 235121 (2013).
[Crossref]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Imaginary part of Hall conductivity in a tilted doped Weyl semimetal with both broken time-reversal and inversion symmetry,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

Belopolski, I.

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide,” Nat. Phys. 11(9), 748–754 (2015).
[Crossref]

S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, “A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class,” Nat. Commun. 6(1), 7373 (2015).
[Crossref]

I. Belopolski, S.-Y. Xu, Y. Ishida, X. Pan, P. Yu, D. S. Sanchez, M. Neupane, N. Alidoust, G. Chang, T.-R. Chang, Y. Wu, G. Bian, H. Zheng, S.-M. Huang, C.-C. Lee, D. Mou, L. Huang, Y. Song, B. Wang, G. Wang, Y.-W. Yeh, N. Yao, J. Rault, P. Lefevre, F. Bertran, H.-T. Jeng, T. Kondo, A. Kaminski, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Unoccupied electronic structure and signatures of topological Fermi arcs in the Weyl semimetal candidate MoxW1−x Te2, arXiv:1512.09099 (2015).

Belov, P. A.

A. N. Poddubny, I. Iorsh, P. A. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Belyanin, A.

Q. Chen, A. R. Kutayiah, I. Oladyshkin, M. Tokman, and A. Belyanin, “Optical properties and electromagnetic modes of Weyl semimetals,” Phys. Rev. B 99(7), 075137 (2019).
[Crossref]

Bergman, D. J.

D. J. Bergman and Y. M. Strelniker, “Anisotropic ac electrical permittivity of a periodic metal-dielectric composite film in a strong magnetic field,” Phys. Rev. Lett. 80(4), 857–860 (1998).
[Crossref]

Bernevig, B. A.

H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, “Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides,” Phys. Rev. X 5(1), 011029 (2015).
[Crossref]

Bertran, F.

I. Belopolski, S.-Y. Xu, Y. Ishida, X. Pan, P. Yu, D. S. Sanchez, M. Neupane, N. Alidoust, G. Chang, T.-R. Chang, Y. Wu, G. Bian, H. Zheng, S.-M. Huang, C.-C. Lee, D. Mou, L. Huang, Y. Song, B. Wang, G. Wang, Y.-W. Yeh, N. Yao, J. Rault, P. Lefevre, F. Bertran, H.-T. Jeng, T. Kondo, A. Kaminski, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Unoccupied electronic structure and signatures of topological Fermi arcs in the Weyl semimetal candidate MoxW1−x Te2, arXiv:1512.09099 (2015).

Bian, G.

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref]

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, and M. Z. Hasan, “Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide,” Nat. Phys. 11(9), 748–754 (2015).
[Crossref]

S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, “A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class,” Nat. Commun. 6(1), 7373 (2015).
[Crossref]

I. Belopolski, S.-Y. Xu, Y. Ishida, X. Pan, P. Yu, D. S. Sanchez, M. Neupane, N. Alidoust, G. Chang, T.-R. Chang, Y. Wu, G. Bian, H. Zheng, S.-M. Huang, C.-C. Lee, D. Mou, L. Huang, Y. Song, B. Wang, G. Wang, Y.-W. Yeh, N. Yao, J. Rault, P. Lefevre, F. Bertran, H.-T. Jeng, T. Kondo, A. Kaminski, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Unoccupied electronic structure and signatures of topological Fermi arcs in the Weyl semimetal candidate MoxW1−x Te2, arXiv:1512.09099 (2015).

Bian, Y.

S.-Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, M.-A. Husanu, Y. Bian, S.-M. Huang, C.-H. Hsu, T.-R. Chang, H.-T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of Lorentz-violating type II Weyl fermions in LaAlGe,” Sci. Adv. 3(6), e1603266 (2017).
[Crossref]

Biancalana, F.

A. Ciattoni, A. Marini, C. Rizza, M. Scalora, and F. Biancalana, “Polariton excitation in epsilon-near-zero slabs: Transient trapping of slow light,” Phys. Rev. A 87(5), 053853 (2013).
[Crossref]

Biffi, G.

V. Caligiuri, M. Palei, G. Biffi, S. Artyukhin, and R. Krahne, “A Semi-Classical View on Epsilon-Near-Zero Resonant Tunneling Modes in Metal/Insulator/Metal Nanocavities,” Nano Lett. 19(5), 3151–3160 (2019).
[Crossref]

Blanchard, R.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Imaginary part of Hall conductivity in a tilted doped Weyl semimetal with both broken time-reversal and inversion symmetry,” Appl. Phys. Lett. 101(22), 221101 (2012).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref]

Borisenko, S. V.

E. Haubold, K. Koepernik, D. Efremov, S. Khim, A. Fedorov, Y. Kushnirenko, J. van den Brink, S. Wurmehl, B. Buchner, T. K. Kim, M. Hoesch, K. Sumida, K. Taguchi, T. Yoshikawa, A. Kimura, T. Okuda, and S. V. Borisenko, “Experimental realization of type-II Weyl state in noncentrosymmetric Ta IrTe4,” Phys. Rev. B 95(24), 241108 (2017).
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Borrmann, H.

C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, Y. Skourski, J. Wosnitza, Z. Liu, Y. Chen, W. Schnelle, H. Borrmann, Y. Grin, C. Felser, and B. Yan, “Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP,” Nat. Phys. 11(8), 645–649 (2015).
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Figures (7)

Fig. 1.
Fig. 1. Schematic of the waveguide configuration involving a Weyl semimetal (in region $1$) with width $d$ on top of a perfectly conducting substrate. In this configuration, the wavevector ${\boldsymbol k}$ resides in the plane of the WS (along $x$), while the separation of Weyl nodes is perpendicular to the layers (along $z$). The surrounding medium (region $0$) is taken to be vacuum.
Fig. 2.
Fig. 2. Diagrams depicting the scaled frequency dependence to the relevant physical quantities for the Weyl semimetal waveguide shown in Fig. 1. (a) The mode diagram showing the dimensionless propagation constant $\kappa _x$. The numbers $1\rightarrow 5$ identify regions of the diagram discussed below. (b) The normalized wavevector in the WS region $\kappa _{1z}$ for the labeled band in (a). (c) The frequency dependence of the diagonal permittivity components $\epsilon _{\parallel }$ and $\epsilon _{zz}$ are shown in the main plot while the off-diagonal component $\gamma$ is shown in the inset. (d) The energy confinement factor $\eta$ for the modes calculated in (a). Note that $\kappa _x$ and $\kappa _{1z}$ are shown on a logarithmic scale. The modes to the left of the vertical line in panel (a) correspond to the frequency range in which $\epsilon _{\parallel }$ and $\epsilon _{zz}$ are both negative [see panel (c)]. The dimensionless WS material parameters are set to $\beta =0.9$ and $\widetilde {\mu }=0.2$.
Fig. 3.
Fig. 3. (a) The energy transport velocity (normalized by the speed of light $c$) as a function of dimensionless frequency. The inset is a magnification of $v_T$ for the lower curve along the points $3\rightarrow 5$. (b) The total normalized power of the system. Both $v_T$ and $P_\textrm {tot}$ are calculated for the modes described by the first dispersion curve in Fig. 2(a), and correlated with the number labels. The WS has its conical tilting parameter set to $\beta =0.9$.
Fig. 4.
Fig. 4. (a) Representative snapshot of the instantaneous Poynting vector ${\boldsymbol E} \times {\boldsymbol H}$. (b) The time-averaged Poynting vector, averaged over one cycle. The frequency in both cases corresponds to the point on the dispersion diagram in Fig. 3(a) where the energy velocity vanishes (labeled 3). The interface between the vacuum region and the WS is located at $z=0$.
Fig. 5.
Fig. 5. Spatial behavior of the electromagnetic field profiles. (a) The $x$-component of the electric field $E_x$ is plotted as a function of the normalized coordinate $z/d$. In (b) the electromagnetic energy density $U$ is shown. The legends in (a) and (b) identify the four frequencies considered along the dispersion curve shown in the inset. As the frequency increases, the overall field amplitudes are shown to decline. The vertical line at $z=0$ locates the vacuum/WS interface. Panels (c) and (d) are maps depicting $E_{x}$ and $E_{z}$, respectively. Bright regions correspond to high field intensities. The frequency corresponds to the mode labeled 1 in panel (a), and the tilt parameter is set to $\beta =0.9$.
Fig. 6.
Fig. 6. The effects of the conical tilt $\beta$ on the waveguide characteristics. In (a) the propagation constant $\kappa _x$ is shown vs $\beta$. The wavevector in the WS, $\kappa _{1z}$, is shown in (b). The electromagnetic response of the WS waveguide is shown in (c), where the diagonal components of the permittivity tensor $\epsilon _{\parallel }$ and $\epsilon _{zz}$ are presented in the main plot, while the inset reveals the off-diagonal component $\gamma$. The fraction of EM energy $\eta$ that is confined to the semimetal for the modes calculated in (a) is shown in (d). The normalized frequency corresponds to $\widetilde {\omega }=0.117$, which is the point labeled 5 of the dispersion curve shown in Fig. 2(a). Note that $\kappa _x$ and $\kappa _{1z}$ are shown on a logarithmic scale.
Fig. 7.
Fig. 7. Panels (a) and (b) display the electric field profiles as a function of the normalized position $z/d$. The legends depict the range of conical tilts considered, which correspond to the upper branch of the mode diagram in Fig. 6(a) (with the labels $3\rightarrow 5$). The frequency is identical to that used in Fig. 6.

Equations (52)

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H s ( p ) = v F [ β s ( p z s Q ) + s σ ( p s Q e z ) ] .
ϵ ¯ ¯ ( ω ) = ( ϵ ( ω ) i γ ( ω ) 0 i γ ( ω ) ϵ ( ω ) 0 0 0 ϵ z z ( ω ) ) ,
ϵ ( ω ) = 1 + α 3 π [ ln | 4 Γ 2 4 μ 2 ω 2 | 4 μ 2 ω 2 + i π Θ ( ω 2 μ ) ] ,
2 μ α 3 π + 2 α ln | Γ / μ | < ω < 2 μ .
ω < 2 μ ( 1 + | β | ) ,
ϵ z z = 1 + α μ 2 π ω 2 s = ± 1 β s 3 { 8 3 β s 4 arctanh β s + ln | 4 μ 2 ω 2 ( 1 + β s ) 2 4 μ 2 ω 2 ( 1 β s ) 2 | + ω 2 12 μ 2 t = ± 1 [ t ( 1 + 2 t β s ) ( 1 t β s ) 2 ln | 4 Γ 2 ( 1 t β s ) 2 4 μ 2 ω 2 ( 1 t β s ) 2 | 2 μ ω ( 4 μ 2 ω 2 + 3 3 β s 2 ) ln | 2 μ t ω ( 1 + t β s ) 2 μ + t ω ( 1 + t β s ) | ] } ,
γ = α π ω [ 2 v F Q s = ± s μ 2 β s ( 1 β s ln | 1 + β s 1 β s | 2 ) ] , | β s | 1.
× E i = i ω μ 0 H i ,
× H i = i ω D i ,
k 1 × ( k 1 × E 1 ) = k 0 2 ϵ ¯ ¯ E 1 .
( k 0 2 ϵ x x k 1 z 2 i k 0 2 γ k 1 z k x i k 0 2 γ k 2 k 0 2 ϵ y y 0 k x k 1 z 0 k 0 2 ϵ z z k x 2 ) ( E x 1 E y 1 E z 1 ) = 0 ,
( ϵ x x k 0 2 k 2 ) ( ϵ x x ϵ z z k 0 2 ϵ x x k x 2 ϵ z z k 1 z 2 ) + k 0 2 ( k x 2 ϵ z z k 0 2 ) γ 2 = 0.
k ± = ± k 0 2 2 ϵ z z ( 2 ϵ z z ϵ ( ϵ + ϵ z z ) κ x 2 ± ( ϵ ϵ z z ) 2 κ x 4 + 4 ϵ z z γ 2 ( ϵ z z κ x 2 ) ) ,
ϵ z z ( κ 1 z 2 κ + 2 ) ( κ 1 z 2 κ 2 ) = 0 ,
H x 0 = r 3 e k 0 z z e i k x x ,
H y 0 = r 1 e k 0 z z e i k x x ,
H z 0 = r 2 e k 0 z z e i k x x ,
E x 0 = Z 0 r 1 i k 0 z k 0 e k 0 z z e i k x x ,
E y 0 = Z 0 r 2 k 0 k x e k 0 z z e i k x x ,
E z 0 = Z 0 r 1 k x k 0 e k 0 z z e i k x x ,
E y 1 = ( a 1 e i k + z + a 2 e i k + z + a 3 e i k z + a 4 e i k z ) e i k x x .
H y 1 z = i ω ϵ 0 ( ϵ E x 1 + i γ E y 1 ) ,
H x 1 z i k x H z 1 = i ω ϵ 0 ( i γ E x 1 ϵ E y 1 ) ,
k x H y 1 = ω ϵ 0 ϵ z z E z 1 .
E y 1 z = i ω μ 0 H x 1 ,
E x 1 z i k x E z 1 = i ω μ 0 H y 1 ,
k x E y 1 = ω μ 0 H z 1 .
κ + cos q + sin q { κ x 2 ( ϵ z z 1 ) ( κ x 2 ϵ ) + ϵ z z ( κ 2 κ + 2 ) + κ x 2 ( ϵ z z κ + 2 κ 2 ) } + κ cos q sin q + { κ x 2 ( ϵ z z 1 ) ( κ x 2 ϵ ) + ϵ z z ( κ + 2 κ 2 ) + κ x 2 ( ϵ z z κ 2 κ + 2 ) } + ϵ z z κ + κ κ 0 z cos q cos q + ( κ 2 κ + 2 ) + κ 0 z sin q + sin q ( κ x 2 ϵ z z ) ( κ 2 κ + 2 ) = 0.
tan ( k 0 d ϵ κ x 2 ) = ϵ κ x 2 κ x 2 1 ,
tan ( k 0 d ϵ ( 1 κ x 2 / ϵ z z ) ) = ϵ ( κ x 2 1 ) 1 κ x 2 / ϵ z z .
η = 1 1 + U 0 / U 1 ,
U i ( z ) = 1 4 [ E i ( ω ϵ ¯ ¯ i ) ω E i + H i ( ω μ i ) ω H i ] ,
S x i ( z ) = 1 2 ( E y i H z i E z i H y i ) , for  i = 0 , 1.
v T S U ,
U 1 μ ( κ x 2 1 ) 4 ( ϵ z z κ x 2 ) 2 sin 2 ( k + d ) { ( ϵ z z 2 + ( ω ϵ z z ) ω κ x 2 ) κ + 2 cos 2 ( k + d [ 1 + z d ] ) + ( ω ϵ ) ω ( ϵ z z κ x 2 ) 2 sin 2 ( k + d [ 1 + z d ] ) } ,
U 0 = μ κ x 2 2 e 2 k 0 z κ x 2 1 .
S x 1 c μ ϵ z z κ x ( κ x 2 1 ) κ + 2 cos 2 ( k + d [ 1 + z / d ] ) 2 ( ϵ z z κ x 2 ) 2 sin 2 ( k + d ) ,
S x 0 = c μ κ x 2 e 2 k 0 z κ x 2 1 .
P tot = P x 0 + P x 1 | P x 0 | + | P x 1 | .
E x 1 i Z 0 κ x 2 1 ( 1 + z d ) ,
E z 1 Z 0 κ x κ x 2 1 k 0 d ( κ x 2 ϵ z z ) ,
H y 1 ϵ z z κ x 2 1 k 0 d ( ϵ z z κ x 2 ) ,
S x 1 Z 0 2 ϵ z z κ x ( κ x 2 1 ) ( k 0 d ) 2 ( ϵ z z κ x 2 ) 2 ,
U 1 μ ( κ x 2 1 ) ω ω ( ϵ ) ( k 0 d ) 2 ( ϵ z z κ x 2 ) 2 + 3 ( ϵ z z 2 + κ x 2 ω ( ω ϵ z z ) ) 12 ( k 0 d ) 2 ( ϵ z z κ x 2 ) 2 .
κ x ϵ z z [ ϵ z z + 2 ( k 0 d ) 2 ± ϵ z z 2 + ( 2 k 0 d ) 2 ( ϵ z z 1 ) ] 2 k 0 d ,
γ F S ( s ) ( ω ) = s α ω 2 0 p d p 2 π Γ s v F Q Γ s v F Q d p z p z p i ω k p 2 + ω k 2 / 4 [ Θ ( μ ζ s , + ) Θ ( μ ζ s , ) 1 ] ,
γ 0 ( s ) ( ω ) = s α ω 2 0 p d p 2 π Γ 0 s v F Q Γ 0 s v F Q d p z p z p i ω k p 2 + ω k 2 / 4 ,
r 2 = κ x γ [ ϵ z z κ 0 z κ κ + ( cos q cos q + ) + ( κ x 2 ϵ z z ) ( κ + sin q κ sin q + ) ] ϵ z z [ κ + ( κ x 2 + κ + 2 ϵ ) ( κ cos q + κ 0 z sin q ) κ ( κ x 2 + κ 2 ϵ ) ( κ + cos q + + κ 0 z sin q + ) ] ,
a 1 = Z 0 r 2 ϵ z z ( ϵ κ x 2 κ 2 ) ( i κ 0 z + κ + ) + κ x γ ( i ( κ x 2 ϵ z z ) + ϵ z z κ 0 z κ + ) 2 ϵ z z κ x κ + ( κ + 2 κ 2 ) ,
b 1 = Z 0 r 2 ϵ z z ( ϵ κ x 2 κ 2 ) ( κ + i κ 0 z ) + κ x γ ( i ( ϵ z z κ x 2 ) + ϵ z z κ 0 z κ + ) 2 ϵ z z κ x κ + ( κ + 2 κ 2 ) ,
c 1 = Z 0 r 2 ϵ z z ( ϵ κ x 2 κ + 2 ) ( i κ 0 z + κ ) + κ x γ ( i ( κ x 2 ϵ z z ) + ϵ z z κ 0 z κ ) 2 ϵ z z κ x κ ( κ 2 κ + 2 ) ,
d 1 = Z 0 r 2 ϵ z z ( ϵ κ x 2 κ + 2 ) ( κ i κ 0 z ) + κ x γ ( i ( ϵ z z κ x 2 ) + ϵ z z κ 0 z κ ) 2 ϵ z z κ x κ ( κ 2 κ + 2 ) .