Critical velocity of a clean one-dimensional superconductor

TL;DR

This paper recalculates the critical velocity of a clean one-dimensional superconductor, revealing it is smaller than previously thought due to a discontinuous phase transition, with implications for understanding superfluid stability.

Contribution

The study provides a mean-field theory analysis showing the critical velocity is reduced by a factor of rom the Landau value, highlighting a pre-emptive phase transition not previously recognized.

Findings

Critical velocity is actor smaller than Landau critical velocity.

Discontinuous phase transition causes the reduced critical velocity.

Analysis includes effects of temperature, critical currents, and impurities.

Abstract

We revisit the problem of the critical velocity of a clean one-dimensional superconductor. {\changed At the level of mean-field theory}, we find that the zero-temperature value of the critical velocity--the uniform velocity of the superfluid condensate at which the superconducting state becomes unstable--is a factor of $\sqrt{2}$ smaller than the Landau critical velocity. This is in contrast to a prior finding, which held that the critical velocity is equal to the Landau critical velocity. The smaller value of the critical velocity, which our analysis yields, is the result of a pre-emptive Clogston-Chandrasekhar--like discontinuous phase transition, and is an analog of the threshold value of the uniform exchange-field of a superconductor, previously investigated by Sarma and by Maki and Tsuneto. We also consider the impact of nonzero temperature, study critical currents, and examine metastability and its limits in the temperature versus flow-velocity phase diagram. In addition, we comment on the effects of electron scattering by impurities.