Electronic nematicity in disordered crystals: the impact of random strain

Besides superconductivity, magnetism, and charge order, electronic interactions can also promote unusual types of electronic order analogous to liquid-crystalline phases. Indeed, electronic nematicity has been observed in a diverse set of systems, from unconventional superconductors to doped topological insulators to twisted moiré devices. In all cases, the presence of the underlying lattice (or superlattice) significantly influences the critical properties associated with the nematic phase by restricting the allowed directions of the nematic director, mediating long-range nematic interactions, and introducing random strain. The latter is ubiquitously generated in crystals by several sources, such as chemical substitution, vacancies, interstitials, and dislocations. In this talk, I will explore different aspects of the impact of random strain on electronic nematicity. First, I will discuss how surface defects can trigger a modulated nematic phase, which is the analogue of the smectic phase in liquid crystals. Then, I will show that important qualitative effects are not captured by descriptions based solely on the random-field Ising model, such as the long-range correlated nature of the random strain and the disorder-induced correlations with phases intertwined with nematicity. I will propose and explore the properties of different types of models that incorporate these effects, such as a random Baxter-field model and a transverse-field Ising model with correlated random longitudinal and transverse fields. I will conclude by arguing that the interplay between random strain and electronic nematicity leads to a unique landscape of phenomena with no counterparts in clean systems, which could explain puzzling experimental data in different materials.