Quantized Nonlinear Conductance in Ballistic Metals

TL;DR

This paper introduces a quantized nonlinear conductance in ballistic metals that generalizes Landauer conductance to higher dimensions and reveals topological properties of the Fermi sea, with implications for experiments in 2D materials.

Contribution

It proposes a new nonlinear conductance measure for D-dimensional Fermi gases that captures topological features and extends Landauer's framework beyond one dimension.

Findings

Quantized conductance in 2D ballistic conductors

Probes the Euler characteristic of the Fermi sea

Suggests experimental setups in graphene

Abstract

We introduce a non-linear frequency dependent D+1 terminal conductance that characterizes a D dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a 2D ballistic conductor we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and of Fermi liquid interactions, and we propose experiments on 2D Dirac materials such as graphene using a triple point contact geometry.