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Is the Quantum Hall Effect influenced by the gravitational field?

Friedrich W. Hehl·Yuri N. Obukhov·Bernd Rosenow
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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.

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Friedrich W. Hehl, Yuri N. Obukhov, Bernd Rosenow. 2003-10-13. Is the Quantum Hall Effect influenced by the gravitational field?. https://doi.org/10.1103/physrevlett.93.096804

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