Trigonal warping effects on optical properties of anomalous Hall materials

TL;DR

This paper investigates how trigonal warping alters the optical and topological properties of anomalous Hall materials, revealing new phases, additional Dirac cones, and higher order Hall responses through semi-analytical calculations.

Contribution

It introduces the effects of trigonal warping on Dirac cones in AHE materials, showing topological phase changes and activation of higher order Hall responses.

Findings

Trigonal warping creates additional Dirac cones with combined Chern number of d7 1.

Breaking rotational symmetry leads to topologically distinct phases.

Higher order Hall responses, including a non-zero second order Hall current, are activated.

Abstract

The topological nature of topological insulators are related to the symmetries present in the material, for example, quantum spin Hall effect can be observed in topological insulators with time reversal symmetry, while broken time reversal symmetry may give rise to the presence of anomalous quantum Hall effect (AHE). Here we consider the effects of broken rotational symmetry on the Dirac cone of an AHE material by adding trigonal warping terms to the Dirac Hamiltonian. We calculate the linear optical conductivity semi-analytically to show how by breaking the rotational symmetry we can obtain a topologically distinct phase. The addition of trigonal warping terms causes the emergence of additional Dirac cones, which when combined has a total Chern number of $\mp 1$ instead of $\pm 1/2$. This results in drastic changes in the anomalous Hall and longitudinal conductivity. The trigonal warping terms also activates the higher order Hall responses which does not exist in a $\mathcal{R}$ symmetric conventional Dirac material. We found the presence of a non-zero second order Hall current even in the absence of Berry curvature dipole. This shift current is also unaffected by the chirality of the Dirac cone, which should lead to a non-zero Hall current in time reversal symmetric systems.