Hall effect and geometric phases in Josephson junction arrays
P. Ao, Y. Tan, and X.-M. Zhu
TL;DR
This paper predicts a zero classical Hall effect in Josephson junction arrays due to the Magnus force, but reveals a complex quantum Hall effect arising from geometric phases and superfluid density effects.
Contribution
It introduces the role of geometric phases and superfluid density in generating a quantum Hall effect in Josephson junction arrays, contrasting with classical predictions.
Findings
Zero classical Hall effect predicted in the array.
Rich and complex quantum Hall effect due to geometric phases.
Quantum Hall effect linked to the Thouless-Kohmoto-Nightingale-den-Nijs effect.
Abstract
Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect.
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