Imaginary part of Hall conductivity in a tilted doped Weyl semimetal with both broken time-reversal and inversion symmetry

Abstract

We consider a Weyl semimetal (WSM) with finite doping and tilt within a continuum model Hamiltonian with both broken time reversal and inversion symmetry. We calculate the absorptive part of the anomalous AC Hall conductivity as a function of photon energy (Ω) for both type I and type II Weyl semimetal. For a given Weyl node, changing the sign of its chirality or of its tilt changes the sign of its contribution to the absorptive Hall conductivity with no change in magnitude. For a noncentrosymmetric system we find that there are ranges of photon energies for which only the positive or only the negative chirality node contributes to the imaginary (absorptive) part of the Hall conductivity. There are also other photon energies where both chirality contribute and there can be other ranges of Ω where there is no absorption associated with the AC Hall conductivity in type I and regions where it is instead constant for type II. We comment on implications for the absorption of circular polarized light.

Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals

“…In addition, the nontrivial topology of the separated Weyl cones results in a surface conductivity (discussed later), which gives rise to an anisotropic surface conductivity tensor. The bulk components have an explicit dependence upon the cone tilting and the cutoff energy c , as found by several other authors [28][29][30][31][32]. The cutoff energy serves as a limit beyond which the Dirac bands are not of linear dispersion anymore [33,34].…”

“…Eqs. (28)(29)(30) can further be re-written as an eigenvalue problem, such that The eigenfunctions of M with k z < 0 eigenvalue correspond to waves propagating to z → −∞ and are the allowed solutions for the transmitted waves. As a result, there are two different solutions (degenerated when is isotropic): v o with k z,o = q o and v e with k z,e = q e .…”

Effect of the chiral anomaly on circular dichroism and Hall angle in doped and tilted Weyl semimetals

“…In panel (b), Re [σxy (Ω)] is shown for the same value of Q0. Note that its dc value is consistent with Eq (26)…”

“…Eq. (26) shows that the tilt makes an important contribution to Re [σ xy (0)]. In the limit of small tilt the leading order in C is linear and consequently this contribution is only non-zero when there is a tilt.…”

“…arXiv:1903.03072v2 [cond-mat.mes-hall] 23 May 2019 pared to non-tilted Weyl case and the undoped background is restored beyond 2µ 0 /(1 − C/v F ). In this same photon energy interval, with tilt and finite doping, the imaginary part of the dynamic transverse Hall conductivity (Im [σ xy (Ω)]) 26 becomes finite. This leads to dichroism in the absorption of circular polarized 27 light, since right and left hand polarizations will have different conductivities (Re [σ ± (Ω)] , see Fig.…”