Effects of elastic correlations on random field disorder in electronic nematics

Electronic nematicity is a phase seen in many quantum materials in which the electrons collectively lower the point group symmetry of the underlying crystal. Due to nemato-elastic coupling, local nematic order parameter is tied to any spatial inhomogeneity within the crystal that locally lowers the same symmetry. These inhomogeneities are due to local internal strains which then serve as random field disorder for the nematic. Typically, the random field Ising model is used to model the low-energy physics of these systems. However, there is growing experimental evidence that conventional treatments with uncorrelated random fields cannot describe even the paranematic phase. Since internal strains are due to crystalline defects, we instead calculate the distribution of strains with an ensemble of dislocations via elasticity theory. These elastic defects produce correlations in the strain distribution not only through the medium, but also between different components of the strain tensor. We demonstrate the effects of these correlations in the paranematic phase of TmVO₄, treating it as an Ising model in the presence of both random longitudinal and random transverse fields generated by the same ensemble of dislocations.