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

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 $5$, 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.

arXiv comment13 pages, 8 figures

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Cited by in corpus (10)

• The Superconductivity of Sr${}_2$RuO${}_4$ Under $c$-Axis Uniaxial Stress
• Heat capacity double transitions in time-reversal symmetry broken superconductors
• Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate
• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• Constraints on the superconducting state of Sr${}_2$RuO${}_4$ from elastocaloric measurements
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• $\mu$SR measurements on Sr${}_2$RuO${}_4$ under $⟨110⟩$ uniaxial stress
• Multipole-fluctuation pairing mechanism of $d_{x^2-y^2}+ig$ superconductivity in Sr${}_2$RuO${}_4$
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Vortex nucleation barriers and stable fractional vortices near boundaries in multicomponent superconductors