Universal scaling in BCS superconductivity in two dimensions in non-s waves

TL;DR

This paper investigates universal scaling behaviors in two-dimensional non-s-wave BCS superconductors, revealing how key parameters like the gap, critical temperature, and specific heat exhibit universal relationships across different pairing symmetries.

Contribution

It demonstrates universal scaling laws for various superconducting properties in 2D non-s-wave BCS models, including $s$, $p$, and $d$ waves, across different physical quantities.

Findings

Universal scaling of gap parameter, $T_c$, and coherence length.

High-$T_c$-like behavior in weak-coupling limit.

Universal temperature dependence of specific heat, penetration depth, and thermal conductivity.

Abstract

The solutions of a renormalized BCS model are studied in two space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials. The gap parameter, the critical temperature $T_c$, the coherence length $\xi$ and the jump in specific heat at $T_c$ as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small $\xi$ and large $T_c$ appropriate to those for high-$T_c$ cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in $p$ and $d$ waves.