Nematic metal in a multi-valley 2D electron gas: a variational Monte Carlo study

The two-dimensional electron gas (2DEG) is of fundamental importance in quantum many-body physics. At low densities, the Coulomb interaction cannot be treated perturbatively. In this presentation, I will discuss results of a variational Monte Carlo study of a minimal extension of the simplest model to the case in which the 2DEG derives from two valleys, each with anisotropic effective mass tensors related in such a way that the full system posesses a C₄ (as opposed to full rotational) symmetry. In particular, we find a broad intermediate range of densities where the system exhibits a fluid valley-polarized ground state. Our results are of direct relevance to the recently discovered nematic state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_x/m_y ≈ 5.2, we obtain a transition from an anisotropic fluid to a valley-polarized fluid at r_s ≈ 12 (where r_s is the dimensionless Wigner-Seitz radius).