The Hall number across a van Hove singularity

TL;DR

This paper investigates the behavior of the Hall number near a Lifshitz transition in metals, revealing universal non-analytic behavior at high fields and its relevance to nematic transitions in high-temperature superconductors.

Contribution

It provides a theoretical analysis of the Hall number's behavior across a Lifshitz transition, highlighting universal features and connections to experimental observations.

Findings

Universal non-analytic dependence of $n_H$ at high magnetic fields.

Non-singular $n_H$ dependence at low fields.

Doping-dependent $n_H$ similar to experimental data in YBa$_2$Cu$_3$O$_{7-x}$.

Abstract

In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal non-analytic dependence of $n_H$ on the electron density in the high field limit, but a non-singular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent $n_H$ similar to that observed in recent experiments in the high temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$.