A microscopic BdG analysis of time-reversal symmetry breaking at domain walls in a model of Sr₂RuO₄

It has been shown¹ that many seemingly contradictory experimental findings concerning the superconducting state in Sr₂RuO₄ can be accounted for as resulting from an accidental near degeneracy between d(x²-y²}and g(xy(x²-y²)) superconducting states. We perform a BdG analysis of the effect of spatially varying strain on such a state, and its impact on the transition to a state with spontaneously broken time-reversal symmetry (TRS). In the presence of finite xy-strain, the superconducting state consists of 2 possible symmetry-related TRS preserving states: d+g and d-g. However, at domain walls between two such regions, TRS is broken, resulting in a d+ig state. We find rich microscopic structure associated with such domain walls, including equilibrium orbital currents (and hence induced magnetic fields) that extend to surprisingly long distances from the domain wall. This observation suggests a resolution of the apparent inconsistency between the observation of spontaneous bulk magnetic fields by μSr with the lack of a strong feature in the specific heat marking the transition to a TRS breaking state.

[1] Kivelson, S.A., Yuan, A.C., Ramshaw, B. et al. A proposal for reconciling diverse experiments on the superconducting state in Sr₂RuO₄. npj Quantum Mater. 5, 43 (2020).