We theoretically explore twisted cuprate multilayers, a moiré material family where the individual layers are themselves strongly correlated. We study the twisted t-J model, using a slave-boson mean field treatment that is compatible with Mott physics at small doping. Furthermore, we incorporate the interlayer tunneling form-factor dictated by the symmetry of the Cu $d_{x^2-y^2}$ orbital. Including both these features leads to a phase diagram distinct from earlier weak-coupling treatments that predicted large gap spontaneous topological superconductors. Instead, we find that spontaneous time reversal (T) breaking occurs around twist angle of $\theta ={45}^{\circ }$, but only in a narrow window. Moreover, a nearly gapless superconductor is obtained, whose spectroscopic features parallels that in monolayer cuprates, despite the broken time reversal and reflection symmetries. At smaller $\theta$ however, driving an interlayer current can lead to a gapped topological phase. The energy-phase relation of the interlayer Josephson junction displays notable double-Cooper-pair tunneling which dominates around ${45}^{\circ }$. The $\theta$ dependence of the Josephson critical current and the Shapiro steps are consistent with recent experiments. Utilizing the moiré structure as a probe of correlation physics, e.g., the pair density wave state, is discussed.

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• Holon
• Josephson effect
• Kerr effect
• Spinon
• Superconducting gap
• Superconductivity
• Bilayer films
• Josephson junctions
• Mott insulators
• Slave bosons
• t-J model