Quantum Hall Ferroelectrics and Nematics in Multivalley Systems

Abstract

We study broken symmetry states at integer Landau-level fillings in multivalley quantum Hall systems whose low-energy dispersions are anisotropic. When the Fermi surface of individual pockets lacks twofold rotational symmetry, like in bismuth (111) [Feldman et al., Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth, Science 354, 316 (2016)] and in Sn[subscript 1-x]Pb[subscript x]Se (001) [Dziawa et al., Topological Crystalline Insulator States in Pb[subscript 1-x]Sn[subscript x]Se, Nat. Mater. 11, 1023 (2012)] surfaces, interactions tend to drive the formation of quantum Hall ferroelectric states. We demonstrate that the dipole moment in these states has an intimate relation to the Fermi surface geometry of the parent metal. In quantum Hall nematic states, like those arising in AlAs quantum wells, we demonstrate the existence of unusually robust Skyrmion quasiparticles.