Two phase transitions in ${(d_{x^2-y^2}+is)}$-wave superconductors

TL;DR

This paper investigates two second-order phase transitions in a $(d_{x^2-y^2}+is)$-wave superconductor, revealing changes in thermodynamic properties and symmetry as temperature decreases, on both square and orthorhombic lattices.

Contribution

It numerically demonstrates the existence of two distinct phase transitions in a coupled $d$-wave and $s$-wave superconductor with detailed thermodynamic analysis.

Findings

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

Observable jumps in specific heat at both transitions

Change from power-law to exponential behavior in superconducting observables

Abstract

We study numerically the temperature dependencies of specific heat, susceptibility, penetration depth, and thermal conductivity of a coupled $(d_{x^2-y^2}+is)$-wave Bardeen-Cooper-Schreiffer superconductor in the presence of a weak s-wave component (1) on square lattice and (2) on a lattice with orthorhombic distorsion. As the temperature is lowered past the critical temperature $T_c$, a less ordered superconducting phase is created in $d_{x^2-y^2}$ wave, which changes to a more ordered phase in $(d_{x^2-y^2}+is)$ wave at $T_{c1}$. This manifests in two second-order phase transitions. The two phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of the superconducting observables exhibit a change from power-law to exponential behavior as temperature is lowered below $T_{c1}$ and confirm the new phase transition.