Josephson diode effects in twisted nodal superconductors

• Published in: arXiv.org 2023-07
• Main Authors: Volkov, Pavel A, Lantagne-Hurtubise, Étienne, Tummuru, Tarun, Plugge, Stephan, Pixley, J H, Franz, Marcel
• Format: Article
• Language: English
• Subjects: Damping; Free energy; Interlayers; Magnetic fields; Perturbation; Reciprocation; Superconductors; Symmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2307.01261

Recent Josephson tunneling experiments on twisted flakes of high-\(T_c\) cuprate superconductor Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+x}\) revealed a non-reciprocal behavior of the critical interlayer Josephson current - i.e., a Josephson diode effect. Motivated by these findings we study theoretically the emergence of the Josephson diode effect in twisted interfaces between nodal superconductors, and highlight a strong dependence on the twist angle \(\theta\) and damping of the junction. In all cases, the theory predicts diode efficiency that vanishes exactly at \(\theta = 45^\circ\) and has a strong peak at a twist angle close to \(\theta = 45^\circ\), consistent with experimental observations. Near \(45^\circ\), the junction breaks time-reversal symmetry \({\cal T}\) spontaneously. We find that for underdamped junctions showing hysteretic behavior, this results in a \emph{dynamical} Josephson diode effect in a part of the \({\cal T}\)-broken phase. The direction of the diode is trainable in this case by sweeping the external current bias. This effect provides a sensitive probe of spontaneous \({\cal T}\)-breaking. We then show that explicit \({\cal T}\)-breaking perturbations with the symmetry of a magnetic field perpendicular to the junction plane lead to a {\em thermodynamic} diode effect that survives even in the overdamped limit. We discuss an experimental protocol to probe the double-well structure in the Josephson free energy that underlies the tendency towards spontaneous \({\cal T}\)-breaking even if \({\cal T}\) is broken explicitly. Finally, we show that in-plane magnetic fields can control the diode effect in the short junction limit, and predict the signatures of explicit \({\cal T}\)-breaking in Shapiro steps.