Resistance of Josephson Junction Arrays at Low Temperatures

TL;DR

This paper investigates quantum vortex tunneling in Josephson junction arrays at zero temperature, revealing significant dissipation effects that influence the array's resistance.

Contribution

It introduces a detailed analysis of vortex quantum tunneling and associated dissipation in Josephson junction arrays, highlighting effects not exponentially suppressed even at large tunneling times.

Findings

Dissipation during vortex tunneling is significant even when tunneling is slow.

Energy dissipation impacts the physical resistance of the entire array.

Dissipation is not exponentially small in the tunneling parameter.

Abstract

We study motion of vortices in arrays of Josephson junctions at zero temperature where it is controlled by quantum tunneling from one plaquette to another. The tunneling process is characterized by a finite time and can be slow compared to the superconducting gap (so that $\tau \Delta >> 1$). The dissipation which accompanies this process arises from rare processes when a vortex excites a quasiparticle above the gap while tunneling through a single junction. We find that the dissipation is significant even in the case $\tau \Delta >> 1$, in particular it is not exponentially small in this parameter. We use the calculated energy dissipation for the single vortex jump to estimate the physical resistance of the whole array.