# Distinguishing XY from Ising Electron Nematics

## TL;DR

This paper investigates the nature of electron nematics in quantum Hall systems, showing that their behavior aligns with the Ising universality class due to lattice interactions, and proposes tests to distinguish universality classes.

## Contribution

It demonstrates that including lattice interactions explains the temperature dependence of electron nematic anisotropy, establishing the Ising universality class for these systems.

## Key findings

- Electron nematic behavior deviates from XY model at low temperatures.
- Inclusion of 4-fold lattice symmetry breaking explains temperature dependence.
- Quantum Hall electron nematic belongs to the Ising universality class.

## Abstract

At low temperatures in ultraclean GaAs-AlGaAs heterojunctions, high fractional Landau levels break rotational symmetry, leading to increasingly anisotropic transport properties as temperature is lowered below $\sim$150mK. While the onset of transport anisotropy is well described by an XY model of an electron nematic in the presence of a weak uniform symmetry-breaking term, the low temperature behavior deviates significantly from this model. We find that inclusion of interactions between the electron nematic and the underlying crystalline lattice in the form of a 4-fold symmetry breaking term is sufficient to describe the entire temperature dependence of the transport anisotropy. This implies that the quantum Hall electron nematic is in the Ising universality class. We propose new experimental tests that can distinguish whether any two-dimensional electron nematic is in the XY or Ising universality class.