Theory of Coulomb driven nematicity in a multivalley two-dimensional electron gas

The properties of a two-dimensional electron gas (2DEG) in a semiconductor host with two valleys related by an underlying ${C}_{4}$ rotational symmetry are studied using Hartree-Fock and various other many-body approaches. A familiar artifact of the HF approach is a degeneracy between the valley-polarized---``Ising nematic''---and spin-polarized---ferromagnetic---phases, which is inconsistent with recent variational Monte Carlo (VMC) results. Correlation effects, computed either within the random phase approximation (RPA) or the T-matrix approximation, enhance the valley susceptibility relative to the spin susceptibility. Extrapolating the results to finite interaction strength, we find a direct first-order transition from a symmetry-unbroken state to a spin-unpolarized Ising nematic fluid with full valley polarization, in qualitative agreement with VMC. The RPA results are also reminiscent of experiments on the corresponding 2DEG in AlAs heterostructures.