Resistance of 2D superconducting films

TL;DR

This paper analyzes the mechanisms of finite resistance in 2D superconducting films at near-zero temperature, focusing on vortex configurations and quantum phase slips, and predicts a quantum phase transition to an insulator.

Contribution

It develops a theoretical framework connecting vortex tunneling and quantum phase slips to the resistance in 2D superconducting films, revealing a quantum phase transition at low conductance.

Findings

Resistance scales as ^{-gW/\xi} with film width W and conductance g.

Quantum fluctuations induce a transition to an insulating state at g  1.

Vortex tunneling trains are equivalent to quantum phase slips in the model.

Abstract

We consider the problem of finite resistance $R$ in superconducting films with geometry of a strip of width $W$ near zero temperature. The resistance is generated by vortex configurations of the phase field. In the first type of process, quantum phase slip, the vortex worldline in 2+1 dimensional space-time is space-like (i.e., the superconducting phase winds in time and space). In the second type, vortex tunneling, the worldline is time-like (i.e., the phase winds in the two spatial directions) and connects opposite edges of the film. For moderately disordered samples, processes of second type favor a train of vortices, each of which tunnels only across a fraction of the sample. Optimization with respect to the number of vortices yields a tunneling distance of the order of the coherence length $\xi$, and the train of vortices becomes equivalent to a quantum phase slip. Based on this theory, we find the resistance $\ln R \sim -g W/\xi$, where $g$ is the dimensionless normal-state conductance. Incorporation of quantum fluctuations indicates a quantum phase transition to an insulating state for $g \lesssim 1$.