Electronic liquid crystalline phases in a spin-orbit coupled two-dimensional electron gas

We argue that the ground state of a two-dimensional electron gas with Rashba spin-orbit coupling realizes one of several possible liquid crystalline or Wigner crystalline phases in the low-density limit, even for short-range repulsive electron-electron interactions (which decay with distance with a power larger than two). Depending on specifics of the interactions, preferred ground states include an anisotropic Wigner crystal with an increasingly anisotropic unit cell as the density decreases, a striped or electron smectic phase, and a ferromagnetic phase that strongly breaks the lattice point-group symmetry, i.e., exhibits nematic order. Melting of the anisotropic Wigner crystal or the smectic phase by thermal or quantum fluctuations can likely give rise to a nonmagnetic nematic phase that preserves time-reversal symmetry.