Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals

Abstract

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.

Vector optical activity in the Weyl semimetal TaAs

“…Interestingly, the I4 1 md space group for TaAs and its relatives (TaP, NbAs, NbP) also has this property [20]. This is of particular relevance since similar optical effects have been discussed by Kargarian et al [3] that are connected with the Fermi surface arc states which are known to be present in TaAs. In one of their geometries where the surface contains Fermi arcs, they predict the generation of a longitudinal electric field.…”

“…This has been treated most definitively by Kargarian et al [3]. To make connection to this work, let us summarize what would be expected for optical activity due to crystallographic effects (Table 1).…”

“…Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed. Weyl semimetals are predicted to have a variety of novel optical effects due to their topological electronic structure [1][2][3][4]. But in the case of Weyl semimetals which exist because of inversion symmetry breaking, unusual optical effects can also arise depending on the space group of the lattice.…”

“…These and related materials also show novel magnetoresistance phenomena, including evidence for the axial anomaly [9,10] predicted long ago by Nielsen and Ninomiya [11]. This axial anomaly can also cause circular dichroism and related chiral optical effects [1][2][3][4].…”

Chiral magnetic plasmons in anomalous relativistic matter

“…(C2) in Appendix C, the coefficient A 1 in front of this term is proportional to a magnetic or pseudomagnetic field. Also, the last term in polarization vector (63) captures the anomalous Faraday effect of Weyl materials, i.e., the rotation of polarization in the absence of a background magnetic field [66]. In terms of the electric susceptibility tensor, we obtain…”