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Effects of geometric phases in Josephson junction arrays

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

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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.