Doping a Moire Mott insulator: 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 deg, 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 deg. The twist angle dependence of the Josephson critical current and the Shapiro steps are consistent with  recent experiments. Utilizing the moire structure as a  probe of correlation physics, in particular of the pair density wave state, is discussed.