Topological Invariants of Metals and Related Physical Effects

TL;DR

This paper explores how topological invariants in metals, like Weyl metals, relate to observable physical effects such as valley currents induced by magnetic fields and strain, revealing hidden topological properties.

Contribution

It establishes a connection between topological invariants in metals and measurable transport phenomena, including valley currents and strain-driven electric currents.

Findings

Non-zero topological invariants in Weyl metals' Fermi surfaces

Magnetic fields induce valley currents related to topological invariants

Strain fields can generate electric currents via second Chern invariants

Abstract

The total reciprocal space magnetic flux threading through a closed Fermi surface is a topological invariant for a three-dimensional metal. For a Weyl metal, the invariant is non-zero for each of its Fermi surfaces. We show that such an invariant can be related to magneto-valley-transport effect, in which an external magnetic field can induce a valley current. We further show that a strain field can drive an electric current, and the effect is dictated by a second class Chern invariant. These connections open the pathway to observe the hidden topological invariants in metallic systems.