Geometric adiabatic transport in quantum Hall states

TL;DR

This paper introduces a new quantized transport coefficient in quantum Hall states, linked to geometric deformations and gravitational anomalies, expanding the understanding of topological invariants in these systems.

Contribution

It identifies a third quantized transport coefficient related to the Chern number of a vector bundle over moduli space, which is a novel topological invariant in quantum Hall physics.

Findings

The new coefficient is quantized and constant along quantum Hall plateaus.

It is related to the Chern number of a vector bundle over moduli space.

The coefficient influences forces on electronic fluid due to geometric deformations.

Abstract

We argue that in addition to the Hall conductance and the nondissipative component of the viscous tensor, there exists a third independent transport coefficient, which is precisely quantized. It takes constant values along quantum Hall plateaus. We show that the new coefficient is the Chern number of a vector bundle over moduli space of surfaces of genus 2 or higher and therefore cannot change continuously along the plateau. As such, it does not transpire on a sphere or a torus. In the linear response theory, this coefficient determines intensive forces exerted on electronic fluid by adiabatic deformations of geometry and represents the effect of the gravitational anomaly. We also present the method of computing the transport coefficients for quantum Hall states.