Charge and spin properties of a generalized Wigner crystal realized in the moiré WSe 2 / WS 2 heterobilayer

We examine the charge and spin properties of an effective single-band model representing a moir\'e superlattice of the ${\mathrm{WSe}}₂/{\mathrm{WS}}₂$ heterobilayer. We focus on the $2/3$ electron filling, which corresponds to the formation of a generalized Wigner crystal, as evidenced experimentally. Our approach is based on the extended Hubbard model on a triangular lattice, with a noninteracting part effectively describing a spin-split band caused by Ising-type spin-orbit coupling. We investigate the system in the regime of strong on-site Coulomb repulsion and the ground state of the Hamiltonian is obtained using the density matrix renormalization group formulated within the matrix product state approach. According to our analysis, on the basis of the density-density correlation functions resolved in momentum space, a transition from the metallic to the insulating state appears with increasing intersite electron-electron interactions. This transition is identified as concomitant with the emergence of a generalized Wigner crystal that realizes the honeycomb lattice pattern. We investigate the magnetic properties of such a Wigner crystal state and find that increasing intersite repulsion results in out-of-plane antiferromagnetic correlations and in-plane canted spin-spin ferromagnetic correlations. The latter are shown to become antiferromagnetic when the ground state is subjected to a transform, which simultaneously converts the Hamiltonian into an SU(2)-invariant form.