# Quantum Hall ferroelectrics and nematics in multivalley systems

## TL;DR

This paper investigates how anisotropic Fermi surfaces in multivalley quantum Hall systems lead to ferroelectric and nematic broken symmetry states, revealing new insights into their electronic properties and quasiparticle excitations.

## Contribution

It demonstrates the formation of quantum Hall ferroelectric states linked to Fermi surface geometry and identifies robust skyrmion quasiparticles in nematic states.

## Key findings

- Ferroelectric states are driven by Fermi surface anisotropy.
- Dipole moments relate to the parent metal's Fermi surface geometry.
- Skyrmion quasiparticles are notably robust in nematic states.

## 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) 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.