Nematic, Ferroelectric, Quantum Hall States in Odd-layer Transition Metal Dichalcogenides

Three-fold rotational symmetry in transition metal dichalcogenides (TMDCs) leads to three elliptical electron pockets, with each of them centered at $Q$, a region between $\Gamma$ and $K$ in the momentum space. When this odd-layer triple-valley system is subject to a perpendicular magnetic field, spontaneous rotational symmetry breaking occurs when the lowest Landau levels are 1/3 or 2/3 filled. The resulting nematic state and the lack of inversion center for each pocket lead to a spontaneous electric polarization. This ferroelectric characteristic makes manipulation of electrons into a preferred single valley-polarized state by an applied electric field possible.