Hysteresis response of 2D electron nematics in the presence of material disorder

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.
Previously, we proposed new experimental tests [1] that can reveal the universality class, based on hysteresis: Upon cycling an applied orienting field, a clean 2D XY electron nematic will show no hysteresis, whereas a clean Ising nematic will show robust hysteresis.
However, no material system is defect-free, and no spontaneous symmetry breaking can occur in the 2D Ising model in the presence of random fields.. In this talk, we discuss the hysteresis characteristics of XY and Ising nematics in the presence of material disorder.

[1] S. Basak and E. W. Carlson, Phys. Rev. B 96, 081303(R) (2017).