Exactly Solvable Model of Randomly Coupled Twisted Superconducting Bilayers

Abstract

Motivated by recent experiments on twisted junctions of cuprate superconductors (SC), it was proposed [1] that at zero temperature, a random first order Josephson coupling $J_1(\text{r})\cos \varphi$ generates an "effective" global second order coupling, $J_2\cos (2\varphi )$, with a sign that favors $\varphi =\pm \pi /2$, i.e., spontaneous breaking of time reversal symmetry (TRS). To obtain a more controlled understanding of the suggested "disorder-induced-order" mechanism, we construct an exactly solvable lattice mean field model and prove that when the disorder-average ${\bar{J}}_1=0$, the model exhibits a TRS breaking phase for all temperatures below the SC transition, i.e., $T_c=T_{\mathrm{TRSB}}$, regardless of the specific form of disorder. In the presence of nonzero ${\bar{J}}_1\ne 0$, we show that the two transitions split linearly for small ${\bar{J}}_1\ll \kappa$ (where $\kappa$ is the in-plane SC stiffness), and that $T_{\mathrm{TRSB}}$ vanishes for ${\bar{J}}_1>J_c$ where $J_c=\overline{J_1^2}/\kappa$ in the weak disorder limit. [1] A. C. Yuan, Y. Vituri, E. Berg, B. Spivak, and S. A. Kivelson, Inhomogeneity-induced time-reversal symmetry breaking in cuprate twist-junctions, arXiv preprint arXiv:2305.15472 (2023)

arXiv comment21 pages (5 main + 16 appendix), 2 figures

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