A fresh look at the influence of gravity on the quantum Hall effect

TL;DR

This paper explores how gravitational fields influence the quantum Hall effect, revealing modifications to Landau levels and Hall resistivity, and discusses potential for using quantum Hall measurements to test gravity laws.

Contribution

It provides a detailed analysis of gravitational effects on quantum Hall phenomena and proposes using these effects to probe the inverse-square law of gravity.

Findings

Gravitational field alters Landau level degeneracy and spacing.

Quantum Hall resistivity is affected by Earth's gravity.

Potential to use quantum Hall effect to test gravity laws.

Abstract

We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical direction, we compute the affected quantized Hall resistivity. Then, we investigate how the gravitational field modifies the Landau levels of a particle moving between two massive hemispheres in the presence of a constant and uniform magnetic field perpendicular to the plane of motion. We find that the familiar degeneracy of the Landau levels is removed and the spacing between the latter becomes dependent on the mass density of the hemispheres and on the gravitational constant $G$. We use this result to show that the quantum Hall effect in a thin conductor, sandwiched between two massive hemispheres, should yield a slightly different variation of the Hall resistivity with the applied magnetic field. We then argue that the well-known problem of the gravitationally induced electric field, that might a priori be thought to hinder the effect of gravity, has actually a beneficial role as it amplifies the latter. We finally discuss whether there is a possibility of using the quantum Hall effect to probe the inverse-square law of gravity.