Critical point of the transition between $s_\pm$ and $s_{++}$ states of a two-band superconductor with nonmagnetic impurities

TL;DR

This paper investigates the transition between $s_$ and $s_{++}$ states in a two-band superconductor with nonmagnetic impurities, revealing a smooth crossover at high temperatures and a first-order transition at low temperatures, with a critical end point indicating a potential quantum phase transition.

Contribution

It demonstrates the existence of a critical end point in the phase diagram of an $s_$ superconductor with impurities, highlighting the temperature-dependent nature of the transition.

Findings

Transition is smooth at high temperatures.

Transition becomes first order at low temperatures.

Critical end point exists on the phase diagram.

Abstract

Behavior of the Grand thermodynamic potential along with its derivatives, entropy and specific heat, is considered within a two-band model of an unconventional $s_\pm$ superconductor with nonmagnetic impurities. The transition $s_\pm \to s_{++}$ is shown to be a smooth crossover at high temperatures, while it becomes the first order phase transition at low temperatures. Thus, on a phase diagram `temperature'-`impurity scattering rate' there appears to be a critical end point. Temperature at which the behavior of the transition is changed is maximal in the Born limit and tends to zero away from the limit, which points out to the possible realization of a quantum phase transition.