A microscopic Ginzburg--Landau theory and singlet ordering in Sr$_2$RuO$_4$

TL;DR

This paper develops a Ginzburg--Landau theory for multiband superconductors, applies it to Sr$_2$RuO$_4$, and constrains possible $d+ig$-wave order parameters based on heat capacity measurements and experimental data.

Contribution

It introduces a general multiband Ginzburg--Landau framework and applies it to restrict theories of $d+ig$ order in Sr$_2$RuO$_4$ based on thermodynamic predictions.

Findings

Heat capacity jump at second order parameter onset exceeds experimental bounds.

Constraints on $d+ig$-wave and near-degenerate order parameters in Sr$_2$RuO$_4$.

Theoretical predictions challenge the viability of certain proposed order parameters.

Abstract

The long-standing quest to determine the superconducting order of Sr$_2$RuO$_4$ (SRO) has received renewed attention after recent nuclear magnetic resonance (NMR) Knight shift experiments have cast doubt on the possibility of spin-triplet pairing in the superconducting state. As a putative solution, encompassing a body of experiments conducted over the years, a $d+ig$-wave order parameter caused by an accidental near-degeneracy has been suggested [S. A. Kivelson et al., npj Quantum Materials $\bf{5}$, 43 (2020)]. Here we develop a general Ginzburg--Landau theory for multiband superconductors. We apply the theory to SRO and predict the relative size of the order parameter components. The heat capacity jump expected at the onset of the second order parameter component is found to be above the current threshold deduced by the experimental absence of a second jump. Our results tightly restrict theories of $d+ig$ order, and other candidates caused by a near-degeneracy, in SRO. We discuss possible solutions to the problem.