Fluctuation and strain effects in a chiral $p$-wave superconductor

TL;DR

This paper investigates how thermal fluctuations influence the strain-temperature phase diagram of a chiral p-wave superconductor, potentially changing the nature of phase transitions and affecting the material Sr$_2$RuO$_4$.

Contribution

It introduces a Ginzburg-Landau framework to analyze fluctuation effects on strain-induced phase transitions in chiral p-wave superconductors, revealing possible weakly first-order transitions.

Findings

Fluctuations can turn a mean-field discontinuity into a weakly first-order transition.

A second-order transition into a non-superconducting phase is possible.

Implications for the superconductor Sr$_2$RuO$_4$ are discussed.

Abstract

For a tetragonal material, order parameters of $p_x$ and $p_y$ symmetry are related by rotation and hence have the same $T_{\rm c}$ at a mean-field level. This degeneracy can be lifted by a symmetry-breaking field, like (uniaxial) in-plane strain, such that at $T_{\rm c}$, the order parameter is only of $p_x$ or $p_y$ symmetry. Only at a lower temperature also the respective other order parameter condenses to form a chiral $p$-wave state. At the mean-field level, the derivative of $T_{\rm c}$ with strain is discontinuous at zero strain. We analyze consequences of (thermal) fluctuations on the strain-temperature phase diagram within a Ginzburg-Landau approach. We find that the order-parameter fluctuations can drive the transition to be weakly first order, rounding off this discontinuity. We discuss the possibility of a second-order transition into a non-superconducting time-reversal-symmetry-breaking phase and consequences for the spin-triplet superconductor Sr$_2$RuO$_4$.