Inhomogeneity-induced time-reversal symmetry breaking in cuprate twist junctions

The lowest-order Josephson coupling, Formula Presented, between two Formula Presented-wave superconductors with a phase difference Formula Presented across the junction vanishes when their relative orientation is rotated by Formula Presented. However, in the presence of inhomogeneity, Formula Presented is nonzero locally, with a sign that fluctuates in space. We show that such a random Formula Presented generates a global second-harmonic Josephson coupling, Formula Presented, with a sign that favors Formula Presented, i.e., spontaneous breaking of time-reversal symmetry. The magnitude of Formula Presented is substantially enhanced if the spatial correlations of Formula Presented extend over large distances, such as would be expected in the presence of large-amplitude twist-angle disorder or significant local electronic nematicity. We argue that this effect likely accounts for the recent observations in twisted Josephson junctions between high-temperature superconductors.