Giant tunable nonreciprocity of light in Weyl semimetals

O. V. Kotov and Yu. E. Lozovik

Phys. Rev. B 98, 195446 – Published 30 November 2018

Abstract

The propagation of light in Weyl semimetal films is analyzed. The magnetic family of these materials is known by anomalous Hall effect, which, being enhanced by the large Berry curvature, allows one to create strong gyrotropic and nonreciprocity effects without external magnetic field. The existence of nonreciprocal waveguide electromagnetic modes in ferromagnetic Weyl semimetal films in the Voigt configuration is predicted. Thanks to the strong dielectric response caused by the gapless Weyl spectrum and the large Berry curvature, ferromagnetic Weyl semimetals combine the best waveguide properties of magnetic dielectrics or semiconductors with strong anomalous Hall effect in ferromagnets. The magnitude of the nonreciprocity depends both on the internal Weyl semimetal properties, the separation of Weyl nodes, and the external factor, the optical contrast between the media surrounding the film. By tuning the Fermi level in Weyl semimetals, one can vary the operation frequencies of the waveguide modes in THz and mid-IR ranges. Our findings pave the way to the design of compact, tunable, and effective nonreciprocal optical elements.

Received 1 August 2018
Revised 31 October 2018
Corrected 21 February 2019

DOI:https://doi.org/10.1103/PhysRevB.98.195446

Physics Subject Headings (PhySH)

Chirality Magneto-optical effect Surface plasmon polariton Topological phases of matter

Weyl semimetal

Condensed Matter, Materials & Applied Physics

Corrections

21 February 2019

Correction: Grant numbers were missing in the Acknowledgment section and have been inserted.

Authors & Affiliations

O. V. Kotov^1,* and Yu. E. Lozovik^1,2,3,†

¹N. L. Dukhov Research Institute of Automatics (VNIIA), 127055 Moscow, Russia
²Institute for Spectroscopy, Russian Academy of Sciences, 142190 Troitsk, Moscow, Russia
³National Research University Higher School of Economics, 101000 Moscow, Russia

^*oleg.v.kotov@yandex.ru
^†lozovik@isan.troitsk.ru

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Vol. 98, Iss. 19 — 15 November 2018

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Images

Figure 1
(a) The dispersion of BDS dielectric functions in the one-band (Drude) $ɛ_{D}$ Eq. (6) and two-band $ɛ_{2}$ Eq. (7) models. (b) The dispersion of the components of WS dielectric tensor [diagonal component $ɛ_{2}$ , nondiagonal component caused by the AHE $ɛ_{2 b}$ Eq. (5)] and the Voigt dielectric function $ɛ_{V}$ . The parameters of WS are set as $E_{F} = 150 meV, v_{F} = 10^{6} m$ /s, $g = 24, ɛ_{c} = 3, ɛ_{b} = 6.2, ɛ_{\infty} = 13, Ω_{b} = Ω_{p} \approx 0.93$ , (i.e., $2 b \approx 0.4 Å^{- 1}$ and $ɛ_{2 b} (Ω = Ω_{p}) = 12$ ).
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Figure 2
The schematics of the nonreciprocal EM wave propagation in the WS film. In the Voigt configuration, the wave vector $q | | y$ lies in the plane of the film but perpendicular to the AHE vector $2 b | | x$ separating the Weyl nodes in momentum space. ${\hat{ɛ}}_{2}$ is the dielectric tensor of WS, $ɛ_{1}$ is the free space dielectric constant, and $ɛ_{3} \neq ɛ_{1}$ is the dielectric function of a thick substrate.
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Figure 3
The dispersions of light and SPP in BDS ( $ɛ_{2}$ ) film (a) and WS ( ${\hat{ɛ}}_{2}$ ) film in the Voigt configuration (b) with thicknesses $d = 0.5 μ m$ on the semi-infinite dielectric substrate with $ɛ_{3} = 4$ , while the medium above the films with $ɛ_{1} = 1$ . ${SPP}_{>}$ and ${SPP}_{<}$ are the forward and backward nonreciprocal SPP, respectively. SPE denotes the interband Landau damping region. The parameters of BDS and WS are the same as for Fig. 1.
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Figure 4
The dispersions of light and SPP in BDS ( $ɛ_{2}$ ) film with $d = 0.5 μ m$ (a), in WS ( ${\hat{ɛ}}_{2}$ ) film with $d = 0.5 μ m$ and in MD film with $d = 80 nm$ in the Voigt configuration. (a)–(c) the case of the ordinary contrast when all the films on the semi-infinite dielectric substrate ( $ɛ_{3} = 4$ ), (d)-(f) the case of the high contrast when all the films on the semi-infinite silver substrate ( $ɛ_{3} = 3.7 - Ω_{p}^{2} / Ω^{2}$ , where $Ω_{p} = ℏ ω_{p} / E_{F}$ and $ℏ ω_{p} = 9.2 eV$ ). The WG TE (s) modes do not feel the AHE and WG TM (p) modes in (b) and (c); (e) and (f) become nonreciprocal: ( ${SPP}_{>}, p_{>}$ ) and ( ${SPP}_{<}, p_{<}$ ) are the forward and backward nonreciprocal (SPP, WG TM modes), respectively. The MD dielectric tensor ( ${\hat{ɛ}}_{2}$ ) is the same as for the WS but with frequency-independent components ( $ɛ_{\infty} = 13, ɛ_{2 b} = 4$ ). The medium above the films for all cases with $ɛ_{1} = 1$ . The parameters of BDS and WS are the same as for Fig. 1.
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Figure 5
(a) The dispersion of the Voigt dielectric function $ɛ_{V}$ in WS at different Fermi levels $E_{F} = 150 meV$ (solid line) and $E_{F}^{'} = 100 meV$ (dashed line); the WG regions where $ɛ_{V} > 1$ are shaded by color. (b) The slice of the Voigt dielectric function vs frequency and Fermi level at $ɛ_{V} (ω, E_{F}) = 1$ ; weakly damped WG modes regions are shaded by blue and the damping region is gray. (c) The dispersion of the nonreciprocal WG TM modes [forward $p_{>}$ (red) and backward $p_{<}$ (blue)] in WS film with $d = 0.7 μ m$ in the Voigt configuration at different Fermi levels $E_{F} = 150 meV$ (solid lines) and $E_{F}^{'} = 100 meV$ (dashed lines); dotted line denotes the dispersion of light in WS at changed Fermi level $E_{F}^{'}$ . Other parameters of WS are the same as for Fig. 1.
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