Is the Quantum Hall Effect influenced by the gravitational field?

TL;DR

This paper investigates whether gravitational fields affect the quantum Hall effect by combining macroscopic and microscopic analyses, concluding that the effect is likely unaffected by gravity due to its topological nature.

Contribution

It provides a microscopic calculation showing the quantum Hall effect's insensitivity to gravitational fields, supporting the idea of its topological independence.

Findings

QHE is metric independent in (1+2)-dimensional electrodynamics

Microscopic calculations show no coupling between gravity and Hall conductance

QHE likely unaffected by gravitational variations in experiments

Abstract

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the realm of (1 + 2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent (`topological'). This suggests that it does not couple to $\mathbf{g}(x)$. We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.