Landau levels in a gravitational field: The Levi-Civita and Kerr spacetimes case

TL;DR

This paper explores how different gravitational fields, including those of a cylinder and a rotating sphere, affect Landau levels, removing degeneracy and enabling potential quantum tests of gravity and frame-dragging effects.

Contribution

It extends previous work by analyzing Landau level splitting in new gravitational scenarios using Levi-Civita and Kerr spacetimes, proposing experimental tests.

Findings

Gravitational fields remove Landau level degeneracy in cylindrical and Kerr spacetimes.

The approach uses Levi-Civita metric for self-consistent analysis.

Potential quantum tests of gravity and frame-dragging effects are identified.

Abstract

We have recently found that the gravitational field of a static spherical mass removes the Landau degeneracy of the energy levels of a particle moving around the mass inside a magnetic field by splitting the energy of the Landau orbitals. In this paper we present the second part of our investigation of the effect of gravity on Landau levels. We examine the effect of the gravitational fields created by an infinitely long massive cylinder and a rotating spherical mass. In both cases, we show that the degeneracy is again removed thanks to the splitting of the particle's orbitals. The first case would constitute an experimental test - which is quantum mechanical in nature - of the gravitational field of a cylinder. The approach relies on the Newtonian approximation of the gravitational potential created by a cylinder but, in view of self-consistency and for future higher-order approximations, the formalism is based on the full Levi-Civita metric. The second case opens up the possibility for a novel quantum mechanical test of the well-known rotational frame-dragging effect of general relativity.