Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

TL;DR

This paper investigates the temperature-dependent behavior of (s+id)-wave BCS superconductors, revealing two distinct second-order phase transitions characterized by observable jumps in specific heat and changes in other physical properties.

Contribution

It demonstrates the existence of two phase transitions in (s+id)-wave superconductors and characterizes their universal temperature dependencies and observable signatures.

Findings

Two second-order phase transitions at T_c and T_{c1}

Observable jumps in specific heat at both transitions

Changes in susceptibility, penetration depth, and thermal conductivity

Abstract

We establish universal behavior in temperature dependencies of some observables in $(s+id)$-wave BCS superconductivity in the presence of a weak $s$ wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature $T_c$, a less ordered superconducting phase is created in $d$ wave, which changes to a more ordered phase in $(s+id)$ wave at $T_{c1}$ ($< T_c$). The presence of two phase transitions manifest in two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of susceptibility, penetration depth, and thermal conductivity also confirm the new phase transition.