Doping a moir\'e Mott Insulator: A t-J model study of twisted cuprates

We theoretically investigate twisted structures where each layer is composed of a strongly correlated material. In particular, we study a twisted t-J model of cuprate multilayers within the slave-boson mean field theory. This treatment encompasses the Mott physics at small doping and self consistently generates d-wave pairing. Furthermore, including the correct inter-layer tunneling form factor consistent with the symmetry of the Cu $d_{x^2-y^2}$ orbital proves to be crucial for the phase diagram. We find spontaneous time reversal (T) breaking around twist angle of $45^\circ$, although only in a narrow window of twist angles. Moreover, the gap obtained is small and the Chern number vanishes, implying a non-topological superconductor. At smaller twist angles, driving an interlayer current however 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 $45^o$. The twist angle dependence of the Josephson critical current and the Shapiro steps are consistent with recent experiments. Utilizing the moir\'e structure as a probe of correlation physics, in particular of the pair density wave state, is discussed.