Doping phase diagram of a Hubbard model for twisted bilayer cuprates

We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle $θ=53.13^{\circ}$ using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference $ϕ$ between the $d$-wave order parameters of two layers is $π$ 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 $ϕ$ changes continuously from 0 to $π$. 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.

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