Distinguishing XY from Ising electron nematics

Electron nematic phases, which break the rotational symmetry of the host crystal while retaining liquidity, have been observed in a variety of systems, including strontium ruthenates, iron superconductors, cuprate superconductors, the (111) surface of bismuth, and high fractional Landau levels. Depending upon interactions with the lattice, the nematic may either be in the XY or the Ising universality class. We propose new experimental tests that can reveal the universality class, based on hysteresis: Upon cycling an applied orienting field, a 2D XY electron nematic will show no hysteresis, whereas an Ising nematic will show robust hysteresis. We discuss this in the context of ultraclean GaAs-AlGaAs heterojunctions, in which high Landau levels near half-integral filling break rotational symmetry. This leads to a temperature dependence of the transport anisotropy, which is better described by an Ising model than an XY model, indicating that this electron nematic is in the Ising universality class. The hysteresis test we propose can be used to test this hypothesis.[1]
[1] S. Basak and E. W. Carlson, Phys. Rev. B 96, 081303(R) (2017).