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

TL;DR

This paper investigates the temperature-driven phase transition in cuprate superconductors from a pure $d_{x^2-y^2}$ state to a mixed $d_{x^2-y^2}+d_{xy}$ state, analyzing thermodynamic properties and identifying two distinct phase transitions.

Contribution

It introduces a detailed study of the phase transition sequence in cuprates, highlighting the emergence of a mixed superconducting state at lower temperatures.

Findings

Two phase transitions identified at temperatures T_c and T_{c1}

Specific heat exhibits two jumps at the transition points

Order parameter and spin susceptibility show characteristic temperature dependencies

Abstract

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $ d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $ d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.