Hall coefficient of semimetals

TL;DR

This paper applies a new formula for the Hall coefficient to various semimetals and semiconductors, revealing how band structure and scattering influence Hall measurements, and proposes experiments to observe these effects.

Contribution

It introduces a novel application of a recent Hall coefficient formula to complex materials, highlighting the role of band topology and degeneracies.

Findings

Deviations from classical inverse carrier density are linked to band degeneracies.

Fermi surface topology significantly affects Hall coefficient measurements.

Proposed experiments can detect these deviations in real materials.

Abstract

A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 66601 (2018)] is applied to nodal line and Weyl semimetals (including graphene), and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drude's inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband scattering. Experiments which can measure these deviations are proposed.