Incipient quantum spin Hall insulator under strong correlations

To assess prior mean-field studies that the interacting Kane-Mele model supports a novel antiferromagnetic Chern insulating phase (AFCI) for a wide range of sublattice potentials, we analyze the Kane-Mele-Hubbard model in the presence of a sublattice potential using determinant quantum Monte Carlo (DQMC). Instead of an AFCI, we find that the ground state is a quantum spin Hall (QSH) insulator for intermediate values of the sublattice potential $\lambda_v$, albeit with a small gap. The QSH state gives way to a trivial band insulator as the sublattice potential increases beyond a critical value. Only at small sublattice potentials does the QSH state transition into a trivial Mott insulator with xy antiferromagnetic correlations. The QAH feature is only observed at high temperature. The QAH feature crosses over to an incipient QSH state when the topological gap stabilizes. Our work is consistent with the experimental observation that in twisted bilayer MoTe$_2$ and WSe$_2$ as well as AB stacked MoTe$_2$/WSe$_2$, where QSH is consistently observed at even-integer filling over a wide range of parameters.