Chiral filtration and Faraday rotation in multi-Weyl semimetals

Abstract

The Maxwell equations in Weyl semimetals (WSMs) with broken inversion and time-reversal symmetries are modified by the presence of the axion terms b and b0 where, for a simple two-node model, 2ℏb is the vector that connects the two nodes in momentum space and 2ℏb0 is energy separation between the two Dirac points. As is well known, this modification leads to some unique optical properties such as non-reciprocal propagation, dichroism, birefringence and Faraday rotation. In this paper, we study numerically how these properties depend on the various parameters that characterize the WSM such as doping, axion terms, width, scattering time τ for intraband processes and background dielectric constant. More specifically, we study how the wave propagation, transmission coefficient and Faraday rotation depend on these parameters. For example, the threshold frequency ωthr=2eF/ℏ for interband transitions (with eF the Fermi level) can be split in two when b0 is finite. When intraband transitions are considered and b=0, the left (LCP) and right (RCP) circularly polarized lights are evanescent below the intraband plasmon frequency ωp<ωthr but can propagate with almost no attenuation in the frequency range ω∈ωp,ωth. Attenuation becomes really important when τ<1 ps. A finite b leads to different refractive indices for the RCP and LCP wave and controls the frequency ranges ω∈ω+,ωth (for RCP) and ω∈ω−,ωth (for LCP) where they can propagate without dissipation. Below ω+, both waves are evanescent since ω+<ω−. For light propagating along b, we find that ω+ω− decreases (increases) with b. In the thin-film limit, the Faraday rotation angle due to b is directly proportional to the width d of the WSM and to the Chern number n of the Weyl nodes. This linear behavior breaks down for d≳500μm. When d becomes larger than the wavelength λ+λ− of the RCP(LCP) wave inside the WSM, oscillations in the transmission coefficient appear whose shape and amplitude depends on the frequency range considered. Perfect transmission is possible when the quantization condition d=mλ±/2 is satisfied. One can control these oscillations by inserting the WSM between two dielectrics.