Interacting holes in a gated ${\mathrm{WSe}}_2$ quantum channel: Valley correlations and zigzag Wigner crystal

We present a theory of interacting valence holes in a gate-defined one-dimensional quantum channel in a single layer of a transition metal dichalcogenide material ${\mathrm{WSe}}_2$. Based on a microscopic atomistic tight-binding model and Hartree-Fock and exact configuration-interaction tools, we demonstrate the possibility of symmetry-broken valley polarized states for strongly interacting holes. The interplay between interactions, perpendicular magnetic field, and the lateral confinement asymmetry together with the strong Rashba spin-orbit coupling present in ${\mathrm{WSe}}_2$ material is analyzed, and its impact on valley polarization is discussed. For weaker interactions, an investigation of the pair correlation function reveals a valley-antiferromagnetic phase. For low hole densities, a formation of a zigzag Wigner crystal phase is predicted. The impact of various hole liquid phases on transport in a high mobility quasi-one-dimensional channel is discussed.