Topological transport of mobile impurities

TL;DR

This paper investigates the Hall response of mobile impurities in a topologically trivial background, revealing how impurity Hall drag depends on interactions and phase transitions, with implications for ultracold gas experiments.

Contribution

It introduces a controlled diagrammatic approach to quantify impurity Hall drag and uncovers its dependence on particle-hole breaking terms and topological phase transitions.

Findings

Impurity Hall drag is not solely determined by the Chern number.

A sharp jump in Hall drag occurs at topological phase transitions.

Hall drag can be measured via circular dichroic impurity excitation rates.

Abstract

We study the Hall response of topologically-trivial mobile impurities (Fermi polarons) interacting weakly with majority fermions forming a Chern-insulator background. This setting involves a rich interplay between the genuine many-body character of the polaron problem and the topological nature of the surrounding cloud. When the majority fermions are accelerated by an external field, a transverse impurity current can be induced. To quantify this polaronic Hall effect, we compute the drag transconductivity, employing controlled diagrammatic perturbation theory in the impurity-fermion interaction. We show that the impurity Hall drag is not simply proportional to the Chern number characterizing the topological transport of the insulator on its own - it also depends continuously on particle-hole breaking terms, to which the Chern number is insensitive. However, when the insulator is tuned across a topological phase transition, a sharp jump of the impurity Hall drag results, for which we derive an analytical expression. We describe how the Hall drag and jump can be extracted from a circular dichroic measurement of impurity excitation rates, particularly suited for ultracold gas experiments.