Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature

TL;DR

This paper investigates the effects of Berry curvature on quantized nonlinear transport in Fermi gases, revealing conditions under which quantization persists or breaks down, especially in inhomogeneous systems like trapped ultracold atoms.

Contribution

It demonstrates that Berry curvature does not influence quantized nonlinear transport in translationally invariant Fermi gases but causes breakdown when spatial inhomogeneity is present.

Findings

Berry curvature does not affect quantization in uniform systems

Inhomogeneity leads to breakdown of quantized transport due to Berry curvature and potential gradients

Breakdown of quantization observable in ultracold atom experiments

Abstract

Quantized transport not only exist in gapped topological states but also in metallic states. Recently, Kane proposed a quantized nonlinear conductance in ballistic metals whose value is determined by the Euler characteristic of the Fermi sea [Phys. Rev. Lett. 128, 076801 (2022)]. In this paper, we consider two-dimensional noninteracting fermionic systems whose Fermi surface has nonvanishing Berry curvature. We find that the Berry curvature at the Fermi surface does not affect the quantized nonlinear transport for translationally invariant systems. When spatial inhomogeneity is introduced, such quantization breaks down due to the combined effect of Berry curvature and the gradient of local potential. Such breakdown of quantization can be observed in trapped ultracold atoms with topological bands.