Phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+id_{xy}$ superconductor

TL;DR

This paper investigates the phase transition from a pure $d_{x^2-y^2}$ superconductor to a mixed $d_{x^2-y^2}+id_{xy}$ phase, revealing two second-order transitions characterized by specific heat jumps and changes in temperature dependence.

Contribution

It provides a detailed analysis of the temperature-driven phase transition between different superconducting states in a lattice model, highlighting the emergence of a new phase with distinct thermodynamic signatures.

Findings

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

Change from power-law to exponential temperature dependence below $T_{c1}$

Identification of a transition to a $d_{x^2-y^2}+id_{xy}$ superconductor

Abstract

The temperature dependencies of specific heat and spin susceptibility of a coupled $d_{x^2-y^2} +id_{xy}$ superconductor in the presence of a weak $d_{xy}$ component are investigated in the tight-binding model (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature $T_c$, first a less ordered $d_{x^2-y^2}$ superconductor is created, which changes to a more ordered $d_{x^2-y^2} +id_{xy}$ superconductor at $T_{c1} (<T_c)$. This manifests in two second order phase transitions 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.