A fresh look at the influence of gravity on the quantum Hall effect
Department of Physics and Astronomy, Bishop’s University, 2600 College Street, J1M 1Z7, Sherbrooke, QC, Canada
2 Physics Department, Champlain College-Lennoxville, 2580 College Street, J1M 0C8, Sherbrooke, QC, Canada
3 Département de Physique, Université de Montréal, 2900 Boulevard Édouard-Montpetit, H3T 1J4, Montréal, QC, Canada
Accepted: 20 May 2020
Published online: 2 June 2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020