Superconducting Quantum Critical Point

TL;DR

This paper investigates the quantum critical point in BCS superconductors caused by pair-breaking, analyzing fluctuation effects on conductivity across different dimensions and temperature regimes.

Contribution

It provides a detailed theoretical analysis of fluctuation-induced conductivity corrections near the superconducting quantum critical point in various dimensions.

Findings

Anomalous conductivity scales as √T in 3D at higher temperatures.

In 2D, conductivity scales as 1/T at higher temperatures.

At very low temperatures, conductivity varies as T^{1/4} in 3D and as ln(1/T) in 2D.

Abstract

We study the properties of a quantum critical point which develops in a BCS superconductor when pair-breaking suppresses the transition temperature to zero. The pair fluctuations are characterized by a dynamical critical exponent z=2. Except for very low temperatures, anomalous contribution to the conductivity is proportional to the square root of T in three dimensions, but to 1/T in two dimensions. At lowest temperatures, the conductivity correction varies as T to the power 1/4 in three dimensions, and as ln(1/T) in two.