QUANTUM VORTEX DYNAMICS IN JOSEPHSON-JUNCTION ARRAYS

We investigate the properties of vortices in Josephson junction arrays. In arrays of low capacitance Josephson junctions these vortices behave as quantum particles showing tunneling and interference effects. An applied current exerts a force on vortices. Classical arguments based on theories in which the junctions are shunted by Ohmic resistances predict a vortex mass, but simultaneously a strong damping due to the excitation of spin waves. In high quality SIS Josephson junctions, there are no Ohmic shunts and charge can only flow by the tunneling of Cooper pairs. We show that the discrete (in units of 2e) nature of the charges on the islands leads to qualitatively new results, if the electrostatic interaction between the Cooper pairs is long range. The spin-wave spectrum becomes stiffer, which substantially reduces the dissipation. Ballistic motion of vortices becomes possible in a wide range of velocities, consistent with recent experiments. The vortex properties change further near the superconductor-insulator transition found in these arrays. Furthermore, an external potential acts as a gauge field on vortices in the same way as a magnetic flux acts on a charged particle, which leads to the Aharonov-Casher and Hail effect. This may lead to interference phenomena that are similar to the Aharonov-Bohm effect for electrons.