Z2 nontrivial Moiré minibands and interaction-driven Quantum anomalous Hall insulators in Topological Insulator based Moiré Heterostructures

We studied the electronic band structure and its topological property of a topological insulator thin film under a Moir'e superlattice potential. The $mathbb Z_2$ non-trivial isolated mini-bands can generally appear for the low-energy Moir'e mini-band spectrum in the phase diagram when the Moir'e potential form a hexagonal lattice with six-fold rotation symmetry. The conduction (valence) mini-bands can be topologically non-trivial when the hexagonal lattice has two minima (maxima). For the nontrivial conduction mini-band case, we find both the two isolated lowest Kramers' pairs of conduction mini-bands have nontrivial $mathbb Z_2$ invariant when there is inversion, while only the isolated lowest Kramers' pair of mini-bands is topologically non-trivial when the inversion symmetry is broken. The Coulomb interaction can potentially drive the lowest conduction Kramers' mini-bands into the quantum anomalous Hall state at half-filling, which is further stablized in the inversion asymmetric case. We propose the atomic Sb layer on top of Sb$_2$Te$_3$ films to realize our model via the first principles calculations.