Quantum Hall ferroelectrics and nematics in multivalley systems

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) and in Sn$_{1-x}$Pb$_x$Se (001) 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.