Title: Understanding the gap structure and phase diagram in twisted bilayer cuprates.

Abstract-There has been a great deal of interest in the

predicted topological state of twisted bilayer cuprates[1],

potentially observed in Josephson experiments on twisted

BSCCO-2212 crystals [2]. Such a state should manifest

a type of d+id' superconducting order with chiral edge modes

when the twist angle is close to 45 degrees. Still, the

exact structure of the expected order parameter in the

twisted lattice unit cell, as might be measured by STM,

for example has not been elaborated in detail.

We present our results for a tight binding lattice model calculation with

phenomenological interlayer

tunneling, and discuss the extension to realistic Wannier-based

models. We study the phase diagram of the order

parameter with tunneling strength and twist angle,

and predict the onset of the topological transition.

Reference-

[1] Can, O., Tummuru, T., Day, R.P. et al. High-temperature topological superconductivity in twisted double-layer copper oxides. Nat. Phys. 17, 519–524 (2021).

[2] S. Y. Frank Zhao et al.,Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors.Science382,1422-1427(2023).