Spin and layer pseudospin order in transition metal dichalcogenide double-moire systems

We study the competition between spin, layer polarization, and layer coherence order in transition metal dichalcogenidie double-moiré systems by performing self-consistent unrestricted Hartree-Fock calculations. Spontaneous layer coherence states are counter-flow superfluids, whereas spontaneous layer polarization states are expected to lead to a hysteric dependence of layer polarization on external displacement field. At integer moiré filling factors we find that the dependence of the ground state on displacement field exhibits a series of generalized Wigner crystal states at rational layer polarizations, separated by intervals of spontaneous interlayer phase coherence. We comment on the relationship between our theoretical results and the recent experimental identification of a dipolar exciton insulator in a moire lattice [Gu, et al. arXiv:2108.06588; Zhang, et al. arXiv:2108.07131].