Zhu, X.M. and Tan, Yong and Ao, P. (1996) Effects of geometric phases in Josephson junction arrays. Physical Review Letters, 77 (3). pp. 562-565. ISSN 0031-9007
We show that the en route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect in the classical limit. However, geometric phases due to the finite superfluid density at superconductor grains have a profound influence on the quantum dynamics of vortices. Subsequently we find rich and complex Hall behaviors analogous to the Thouless-Kohmoto-Nightingale-den Nijs effect in the quantum regime.
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