Non-perturbative microscopic theory of superconducting fluctuations near a quantum critical point

TL;DR

This paper develops a non-perturbative microscopic theory for superconducting fluctuations near a quantum critical point, revealing a crossover in magnetic susceptibility behavior and applying to various disordered superconducting systems.

Contribution

It introduces a non-perturbative approach to analyze quantum superconducting fluctuations at the critical point, connecting to antiferromagnetic quantum critical theory.

Findings

Derived a general expression for fluctuation magnetic susceptibility.

Identified a crossover from logarithmic to fractional logarithmic dependence near the transition.

Applicable to diverse superconducting systems including cuprates and disordered films.

Abstract

We consider an inhomogeneous anisotropic gap superconductor in the vicinity of the quantum critical point, where the transition temperature is suppressed to zero by disorder. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action for the superconducting order parameter. It is shown that the critical theory corresponds to the marginal case in two dimensions and is formally equivalent to the theory of an antiferromagnetic quantum critical point, which is a quantum critical theory with the dynamic critical exponent, z=2. This allows us to use a parquet method to calculate the non-perturbative effect of quantum superconducting fluctuations on thermodynamic properties. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, $\chi ~ ln(dn)$, valid beyond the Ginzburg region to $\chi ~ ln^{1/5}(dn)$ valid in the immediate vicinity of the transition (where $dn$ is the deviation from the critical disorder concentration). We suggest that the obtained non-perturbative results describe the low-temperature critical behavior of a variety of diverse superconducting systems, which include overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.