Quantum fluctuations in thin superconducting wires of finite length

TL;DR

This paper investigates how finite length and environmental coupling affect quantum phase transitions in one-dimensional superconducting wires, revealing conditions for the persistence or disappearance of superconductivity.

Contribution

It analyzes the impact of finite size and environmental conductance on the superconductor-insulator transition in thin wires, extending previous infinite-wire models.

Findings

Finite length suppresses the superconductor-insulator transition.

Environmental coupling can restore superconducting order.

The phase diagram depends on wire admittance and conductance.

Abstract

In one dimensional wires, fluctuations destroy superconducting long-range order and stiffness at finite temperatures; in an infinite wire, quasi-long range order and stiffness survive at zero temperature if the wire's dimensionless admittance $\mu$ is large, $\mu > 2$. We analyze the disappearance of this superconductor-insulator quantum phase transition in a finite wire and its resurrection due to the wire's coupling to its environment characterized through the dimensionless conductance $K$. Integrating over phase slips, we determine the flow of couplings and establish the $\mu$--$K$ phase diagram.