Exactly Solvable Model of Randomly Coupled Twisted Superconducting Bilayers

TL;DR

This paper presents an exactly solvable model demonstrating how disorder can induce time-reversal symmetry breaking in twisted superconducting bilayers, with implications for understanding experimental observations in cuprate junctions.

Contribution

It provides a controlled, exactly solvable lattice mean field model showing disorder-induced TRS breaking in superconductors, extending previous phenomenological proposals.

Findings

TRS breaking occurs at all temperatures below Tc when disorder average is zero.

Splitting of transition temperatures occurs linearly with small nonzero average disorder.

TRS breaking vanishes when disorder exceeds a critical threshold J_c.

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 $J_1(\textbf{r}) \cos \phi$ generates an "effective" global second order coupling, $J_2\cos(2\phi)$, with a sign that favors $\phi = \pm \pi/2$, 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^2_1}/\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)