Doping phase diagram of a Hubbard model for twisted bilayer cuprates

TL;DR

This paper investigates the phase diagram of a twisted Hubbard model for cuprate bilayers, revealing a time-reversal symmetry breaking phase at strong interlayer tunneling near optimal doping, using variational cluster approximation.

Contribution

It introduces a detailed analysis of the twisted Hubbard model for cuprates, identifying a novel time-reversal symmetry breaking phase with a continuous phase difference transition.

Findings

Time-reversal symmetry breaking phase near optimal doping at strong interlayer tunneling

Phase difference between layers varies from 0 to π, indicating a continuous transition

Cluster extension of dynamical mean field theory did not detect the TRSB phase

Abstract

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $\theta=53.13^{\circ}$ using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference $\phi$ between the $d$-wave order parameters of two layers is $\pi$ in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference $\phi$ changes continuously from 0 to $\pi$. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.