Superfluid Flow Past an Array of Scatterers

TL;DR

This paper models superfluid flow past a periodic array of scatterers to predict the critical current in a Josephson array near its critical temperature, considering electron interactions and temperature effects.

Contribution

It introduces a model linking superfluid flow, scatterers, and electron interactions to determine critical current behavior near $T_c$ in Josephson arrays.

Findings

Critical current depends linearly on (Tc - T).

Critical current vanishes at a temperature T* below Tc.

The coefficient A is sensitive to region sizes and interactions.

Abstract

We consider a model of nonlinear superfluid flow past a periodic array of point-like scatterers in one dimension. An application of this model is the determination of the critical current of a Josephson array in a regime appropriate to a Ginzburg-Landau formulation. Here, the array consists of short normal-metal regions, in the presence of a Hartree electron-electron interaction, and embedded within a one-dimensional superconducting wire near its critical temperature, $Tc$. We predict the critical current to depend linearly as $A (Tc-T)$, while the coefficient $A$ depends sensitively on the sizes of the superconducting and normal-metal regions and the strength and sign of the Hartree interaction. In the case of an attractive interaction, we find a further feature: the critical current vanishes linearly at some temperature $T*$ less than $Tc$, as well as at $Tc$ itself. We rule out a simple explanation for the zero value of the critical current, at this temperature $T*$, in terms of order parameter fluctuations at low frequencies.