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We study a one-band Hubbard model of twisted bilayer cuprates with a twistangle of $53.13^\circ$. By introducing an inter-layer bias, we simulateheterobilayers of different dopings. Using the variational clusterapproximation (VCA) we probe the effect of this bias on thetime-reversal-symmetry (TRS) breaking phase. Doping differences between layersaffect the region where TRS-breaking occurs; we construct a phase diagrammapping out the TRS-breaking phase in the $n_1$-$n_2$ plane, $n_\ell$ being theelectron density on layer $\ell$. We also map the spontaneous supercurrent onthe same plane.

Inter-layer bias effect on time-reversal symmetry breaking in twisted bilayer cuprates