Coulomb-Induced Nematicity in a Two-Valley Two-Dimensional Electron Gas

Recent experiments conducted in AlAs have revealed a transition as a function of decreasing electron density from a C₄ symmetric liquid to a nematic liquid phase, devoid of spin-ordering. In a separate variational Monte Carlo study [1] of an appropriate two-valley model of the two-dimensional electron gas (2DEG), we showed that for effective mass anisotropy characteristic of AlAs, such a nematic phase arises as a form of valley polarization driven purely by the Coulomb repulsion between electrons. To obtain greater insight into the essential physics, we have studied this same problem by expanding about the high density (small r_s) limit. At Hartree-Fock level, a Stoner instability to a polarized state occurs below an unrealistically small critical value of r_s, and spin and orbital polarization are degenerate instabilities. Extending the analysis of correlation energy within the random-phase approximation, we find an increase in the critical value of r_s, and prove that the nematic state consistently possesses a lower correlation energy compared to the non-nematic ferromagnetic state. This observation is valid for more general repulsive interaction. We have also studied [2] the dilute limit (large r_s) and found that the system forms a nearly triangular Wigner crystal (WC) albeit one that is also nematic in the sense that it breaks the six-fold rotational symmetry of the single component WC. This outcome can be attributed to the phonons of the Wigner crystal inheriting the inherent "nematicity" of the kinetic energy.

[1] A. Valenti, V. Calvera, S. A. Kivelson, E. Berg, and S. D.Huber, arXiv:2307.15119 (2023)

[2] V. Calvera, S. Kivelson, E. Berg, Fiz. Nyzk. Temp., 49, 747-769 (2023)