Symmetric topological Mott insulator and Mott semimetal

Correlated physics in nearly flat topological bands is a central theme in the study of moir\'e materials. While ground states at integer fillings are typically identified as quantum Hall ferromagnets within a Hartree-Fock framework, we propose the existence of symmetric topological Mott insulators (STMIs) that transcend this Slater determinant picture. Focusing on half-filling of each flavor per unit cell, we demonstrate the existence of STMIs which exhibit a quantized charge or spin Hall response. We first establish this phase in a bilayer Haldane-Hubbard model with localized orbitals on the $A$ sublattice and dispersive band on the $B$ sublattice. Starting from a trivial Mott insulator on the $A$ sublattice, tuning the sublattice potential drives a Bose-Einstein-condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) transition of the associated $p-\mathrm{i}p$ exciton pairing, realizing a topological Mott insulator with $C=1$ per flavor. We further generalize this construction to a single-layer spinful model, where the resulting STMI hosts charge edge modes coexisting with bulk local moments. A Mott semimetal is identified at the quantum critical point between the STMI and the trivial Mott insulator. Finally, we discuss applications to AA-stacked MoTe$_2$/WSe$_2$, proposing a ferromagnetic Chern insulator phase as a low-temperature descendant of the symmetric Mott semimetal.