Incoherent tunneling and topological superconductivity in twisted cuprate bilayers

TL;DR

Twisting high-$T_c$ cuprate monolayers can induce a topological superconducting state, and this phase remains stable even with disorder-induced incoherent tunneling, relevant to real materials like Bi2212.

Contribution

This work demonstrates that incoherent tunneling due to disorder does not destroy the topological phase in twisted cuprate bilayers, extending understanding of topological superconductivity in realistic conditions.

Findings

Topological phase persists despite incoherent tunneling.

Extent of topological phase decreases with increased incoherence.

Robustness of topological phase in Bi2212 parameters.

Abstract

Twisting two monolayers of a high-$T_c$ cuprate superconductor can engender a chiral topological state with spontaneously broken time reversal symmetry $\mathcal{T}$. A crucial ingredient required for the emergence of a gapped topological phase is electron tunneling between the CuO$_2$ planes, whose explicit form (in an ideal clean sample) is dictated by the symmetry of the atomic orbitals. However, a large body of work on the interlayer transport in cuprates indicates importance of disorder-mediated incoherent tunneling which evades the symmetry constraints present in an idealized crystal. The latter arises even in the cleanest single-crystal samples through oxygen vacancies in layers separating the CuO$_2$ planes, introduced to achieve the hole doping necessary for superconductivity. Here we assess the influence of incoherent tunneling on the phase diagram of a twisted bilayer. We show that the model continues to support a fully gapped topological phase with broken $\mathcal{T}$, even in the limit of disorder-mediated interlayer coupling. Compared to the model with a constant, momentum conserving interlayer coupling, the extent of the topological phase around the 45$^\circ$ twist decreases with increasing incoherence, but remains robustly present for parameters likely relevant to Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$.