Revisiting Langer-Ambegaokar-McCumber-Halperin theory of resistive transitions in one-dimensional superconductors with exact solutions

TL;DR

This paper corrects the classical Langer-Ambegaokar-McCumber-Halperin theory for 1D superconductors by providing an exact solution that revises the understanding of free energy barriers and phase slip formation.

Contribution

It offers an exact solution that revises the saddle point identification in the resistive transition theory of 1D superconductors.

Findings

Corrects the saddle point identification in the original theory

Shows the system can have zero amplitude of superconducting phase at a point

Reveals the actual free energy barrier involved in phase slips

Abstract

We present an important correction to the Langer-Ambegaokar-McCumber-Halperin theory for the resistive state of a 1D superconductor. We establish that the identification of the saddle on the free energy surface over which Langer and Ambegaokar had claimed the system to move in order to form thermally excited phase slip centres is wrong. With the help of an exact solution we show that the system has to overcome a similar free energy barrier but can actually have vanishing amplitude of superconducting phase at a point unlike the Langer-Ambegaokar solution.