An analytic evaluation of Kane fermion magneto-optics in two and three dimensions

TL;DR

This paper analytically derives the magneto-optical conductivity for the Kane model in two and three dimensions, revealing how dimensionality and polarization affect optical transitions and signatures.

Contribution

It provides the first analytic expressions for Kane fermion magneto-optics in both 2D and 3D, highlighting the effects of dimensionality and polarization on optical transitions.

Findings

In 2D, no optically activated transitions occur between chiral sectors.

In 3D, intra- and inter-sector transitions are possible due to dispersion.

Circular polarization can distinguish inter-sector transitions in 3D.

Abstract

We calculate and present an analytic form of the magneto-optical conductivity for the gapped low-energy Kane model in two and three dimensions separately. The two-dimensional case maps onto the $\alpha$-$\mathcal{T}_3$ model at a particular value of $\alpha=1/\sqrt{3}$. In two dimensions, two chiral sectors exist, between which there are no optically activated transitions. In three dimensions, the extra dimension of dispersion mixes the two sectors so that intra- and inter-sector transitions can occur. The latter type of transition can be separated out via circular polarizations of light and shows a distinct signature in the transverse conductivity.