Heat capacity double transitions in time-reversal symmetry broken superconductors

TL;DR

This paper develops a theoretical framework to analyze the second heat capacity jump in unconventional superconductors with broken time-reversal symmetry, explaining its elusive experimental detection in Sr$_2$RuO$_4$.

Contribution

It introduces a multi-band model to predict the ratio of heat capacity jumps and applies it to Sr$_2$RuO$_4$, revealing conditions for the second jump's suppression.

Findings

The second heat capacity jump can be strongly suppressed in certain order parameter configurations.

Spatial inhomogeneity may further diminish the detectability of the second jump.

The model explains why the second jump has not been observed experimentally in Sr$_2$RuO$_4$.

Abstract

Standard superconductors display a ubiquitous discontinuous jump in the electronic specific heat at the critical superconducting transition temperature. In a growing class of unconventional superconductors, however, a second order parameter component may get stabilized and produce a second heat capacity jump at a lower temperature, typically associated with the spontaneous breaking of time-reversal symmetry. The splitting of the two specific heat discontinuities can be controlled by external perturbations such as chemical substitution, hydrostatic pressure, or uniaxial strain. We develop a theoretical quantitative multi-band framework to determine the ratio of the heat capacity jumps, given the band structure and the order parameter momentum structure. We discuss the conditions of the gap profile which determine the amplitude of the second jump. We apply our formalism to the case of Sr$_2$RuO$_4$, and using the gap functions from a microscopic random phase approximation calculation, we show that recently-proposed accidentally degenerate order parameters may exhibit a strongly suppressed second heat capacity jump. We discuss the origin of this result and consider also the role of spatial inhomogeneity on the specific heat. Our results provide a possible explanation of why a second heat capacity jump has so far evaded experimental detection in Sr$_2$RuO$_4$.