Superconductor-insulator quantum critical point in 1+\epsilon dimensions

TL;DR

This paper investigates the quantum phase transition between superconducting and insulating states in a disordered, low-dimensional fermionic system using perturbative renormalization group methods, revealing a critical point at infinitesimal disorder.

Contribution

It introduces a theoretical analysis of a superconductor-insulator transition in 1+ε dimensions, providing calculations of critical exponents and scaling behaviors near the quantum critical point.

Findings

Identifies a superconductor-to-insulator quantum fixed point at infinitesimal disorder.

Calculates correlation length and dynamical exponents near the transition.

Determines the scaling of conductivity and characteristic temperature scales.

Abstract

A system of spinless fermions in $d=1+\epsilon$ dimensions, at zero-temperature and in random potential is studied using the perturbative renormalization group to first order in disorder and to second order in interaction. We find a superconductor-to- Anderson insulator quantum fixed point at an infinitesimal value of disorder and calculate the correlation length and the dynamical exponents to the lowest order in $\epsilon$ and in interaction. The scaling of conductivity with temperature and the behavior of characteristic temperature scales on both sides of the transition is determined. The model may have relevance for a p-wave superconductor at low temperatures in strongly disordered media.