Nematic metal in a multi-valley electron gas: Variational Monte Carlo analysis and application to AlAs

Abstract

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with $C_4$ (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized 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, $m_x/m_y\approx 5.2$, we obtain a transition from an anisotropic metal to a valley-polarized metal at $r_s\approx 12$ (where $r_s$ is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

arXiv comment5+20 pages

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• Theory of Coulomb driven nematicity in a multi-valley two-dimensional electron gas
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• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• An unusual first order phase transition in a 2D superconductor
• Quantum melting a Wigner crystal into Hall liquids