Meese, William2024-07-242024-07-242024-05https://hdl.handle.net/11299/264332University of Minnesota Ph.D. dissertation. May 2024. Major: Physics. Advisor: Rafael Fernandes. 1 computer file (PDF); xii, 209 pages.Electronic nematicity – a state of broken rotational symmetry but preserved translational symmetry – appears to be a general feature of quantum materials, and it often develops in the vicinity of unconventional superconductivity. Strains are conjugate fields for the electronic nematic order parameter – a relationship known as nematoelasticity. While external, homogeneous strains are useful tools in studying electronic nematicity, crystals simultaneously contain inhomogeneous strains because of structural disorder generated by crystalline defects. In this thesis, I demonstrate that these unavoidable, internal, random strains lead to a host of new electronic and relaxational behavior in electronic nematics. Electronic nematicity manifests as either an isolated instability or a vestigial one. The latter is a partially melted phase of some underlying primary order, meaning it is borne out of the fluctuations of the primary order parameter. In the former case, the impact of random strains has been studied before using the random-field Ising model (RFIM). In the case of vestigial nematicity, the RFIM description is incomplete, as random strain plays the simultaneous role of both a random field for the nematic order parameter and a random mass for the primary order parameter. I generalized the RFIM to a new model that is then applied to systems such as the iron pnictide superconductors. This disorder-free limit is built upon the Ashkin-Teller model, whose composite “Baxter” order parameter plays the role of the vestigial nematic comprised of two primary magnetic degrees of freedom. These magnetic degrees of freedom are mapped onto the interpenetrating Néel vectors in the pnictides. The Baxter variable is then subject to a random field, making this random “Baxter field” act as both a random field and a random mass. In analogy with the RFIM, the model is dubbed the random-Baxter-field model (RBFM), and massively-parallel Monte Carlo simulations were used to characterize its impact on nematicity. It was found that the random strains break the vestigial nematic order into domains while creating new correlations in the primary order parameters, enhancing their fluctuations. In a following experimental collaboration, electronic nematic domain formation was then used to explain optical dichroism measurements on the compound FePSe3 which showed evidence of vestigial 3-state Potts nematic domains. In the limit of nearly perfect crystals, however, neither the RFIM nor the RBFM account for the nature of long-ranged strains from crystalline defects. Recent heat capacity measurements on the nematic insulator, Tm1–xYxVO4, show that, even in the purest samples, random strains are ubiquitous and correlated. To this end, I reexamined nematoelastic interactions in structurally disordered elastic media. I developed a realistic description of elastically generated random strains from a veritable zoo of different crystalline defects, and used numerical simulations of dislocations to qualitatively account for the experimental results. It was found that even simple ensembles of defects – in this case, dislocations – can generate strain distributions that can fit the data just as well as conventional, uncorrelated random strains can without needing to overfit. These elastically generated random strains contain not only long-ranged and anisotropic correlations, but also higher-order statistics that are frequently omitted in random field models. This way of viewing random strains constitutes a new type of random field disorder and will lead to exciting new phenomena in future work.enCrystalline defectsDisorderElasticityElectronic nematicityMonte Carlo simulationsVestigial phaseThesis or Dissertation