Tuning topological superconductivity within the $t$-$J$-$U$ model of twisted bilayer cuprates

TL;DR

This paper theoretically investigates how twisting bilayer cuprates influences their topological superconducting phases, revealing a rich phase diagram with novel TRS-breaking and topological states sensitive to doping and twist angle.

Contribution

It introduces a detailed phase diagram of twisted bilayer cuprates using a $t$-$J$-$U$ model and uncovers previously unreported reentrant TRS-breaking and topological superconducting phases.

Findings

Identification of a non-convex region for $d+e^{i heta}d$ states in doping-twist space.

Discovery of a reentrant TRS-breaking phase on the underdoped side.

Evidence for topological superconductivity at specific twist angles.

Abstract

We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBC) as a function of electron density and layer twist angle. The bilayer $t$-$J$-$U$ model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically-consistent Gutzwiller formulation. The constructed phase diagram encompasses both gapless $d$-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped $d+\mathrm{e}^{i\varphi}d$ phase that breaks spontaneously time-reversal-symmetry (TRS) and is characterized by nontrivial Chern number. We find that $d+\mathrm{e}^{i\varphi}d$ state occupies a non-convex butterfly-shaped region in the doping vs. twist-angle plane, and demonstrate the presence of previously unreported reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from $45^\circ$. Our analysis of the microscopically derived Landau free energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.