Quantum Hall and Light Responses in a 2D Topological Semimetal

TL;DR

This paper explores the topological properties of a 2D semimetal in graphene, demonstrating how Hall and light responses reveal its $ ext{Z}$ and $ ext{Z}_2$ invariants, and linking bulk-edge correspondence with spin-polarized transport.

Contribution

It introduces a method to measure topological invariants via light response at Dirac points and discusses the bulk-edge correspondence in a protected topological half metal.

Findings

Hall conductivity relates to $ ext{Z}$ invariant measurable by circularly polarized light.

Intermediate energy bands exhibit a $ ext{Z}_2$ invariant through conductivity responses.

Edge conductance shows a quantized half-integer value for spin-polarized transport.

Abstract

We have recently identified a protected topological semimetal in graphene which presents a zero-energy edge mode robust to disorder and interactions. Here, we address the characteristics of this semimetal and show that the $\mathbb{Z}$ topological invariant of the Hall conductivity associated to the lowest energy band can be equivalently measured from the resonant response to circularly polarized light resolved at the Dirac points. The (non-quantized) conductivity responses of the intermediate energy bands, including the Fermi surface, also give rise to a $\mathbb{Z}_2$ invariant. We emphasize on the bulk-edge correspondence as a protected topological half metal, i.e. one spin-population polarized in the plane is in the insulating phase related to the robust edge mode while the other is in the metallic regime. The quantized transport at the edges is equivalent to a $\frac{1}{2}-\frac{1}{2}$ conductance for spin polarizations along $z$ direction. We also build a parallel between the topological Hall response and a pair of half numbers (half Skyrmions) through the light response locally resolved in momentum space and on the sphere.