Phases of the coupled two-dimensional superconductors with second order Josephson coupling

Time-reversal breaking superconductivity has recently been realized in twisted junction of cuprate superconductors, and the underlying mechanism is attributed to the second order Josephson coupling across the junction [1]. The theoretical model consisting of two superconducting layers coupled by second order Joesephson tunnelling has been studied [2-5] within various approximations, yielding phase diagrams not necessarily all in agreement. We note that the same physics may also be realized in ultracold spinor Bose gas in a quasi-two-dimensioanl geometry. We analyze the bilayer model with a duality transformation inspired by Peskin [6], and highlight the role played by the Z2 domain wall.

[1] Zhao et al. 2023. Science 382 (6677): eabl8371.

[2] Liu et al. 2023. Nat. Commun. 14 (1): 7926.

[3] Song and Zhang 2022. Phys. Rev. Lett. 128 (19): 195301.

[4] Zeng et al. 2024. Sci. China. Ser. G 67 (3): 237411.

[5] Maccari et al. 2023. Phys. Rev. B 107 (6): 064501.

[6] Peskin 1978. Ann. Phys.-New York 113 (1): 122–52.