Transport in quantum materials: lessons from (almost) exactly solvable models

In this dissertation, I develop new approaches, and apply and extend known techniques towards theoretical understanding of transport experiments in two quantum materials: alpha-RuCl3 and CeCoIn5. The first material, alpha-RuCl3, is a candidate Kitaev material as it may realize the Kiteav model, a rare example of an exactly solvable two-dimensional (2D) quantum spin system. The Kitaev model exhibits a spin liquid ground state, where the spins do not align even at zero temperature, with anyonic elementary excitations, a kind of excitation unique to 2D. Being able to generate and manipulate these anyons may form some of the key components of topological quantum computers. The second material, CeCoIn5, has a similar phase diagram to the high-temperature superconductors, implying that insights gained from understanding this material may lead to breakthroughs in other high-temperature superconductors./nAfter the introduction, in the second chapter of this thesis, I discuss the Kitaev model, its exact solution, and time-dependent mean-field theory (TDMFT). Although TDMFT was developed by other authors, I rederive and extend it to be able to compute any experimentally relevant quantity. With this approach, TDMFT agrees with exact results, and its main advantage is that it can be applied for more general models than the Kitaev model, unlike the exact solution. We demonstrate the value of the technique via computation of the expected results of an inelastic neutron experiment on a hypothetical Kitaev material./nIn the third chapter, I start by briefly discussing the key experiments performed on alpha-RuCl3 and focus on two experiments in particular that measure the longitudinal and Hall conductivity. Recent experiments have observed what appear to be quantum oscillations in the low-temperature longitudinal thermal conductivity. I will set up an application of our newly formulated TDMFT approach to theoretically predict the longitudinal thermal transport for the Kitaev model in a magnetic field, since not many methods can compute the necessary quantities for a 2D system and it is not known what the effect of the field will be. Furthermore, in the absence of an in-plane magnetic field, alpha-RuCl3 becomes an antiferromagnet at around seven Kelvin. In this phase, I am able to compute the thermal Hall effect via spin-wave theory (SWT), a well-established theory that works for systems with magnetic ordering, and compare the results directly with experiments on alpha-RuCl3./nStarting part two of the thesis, in chapter four, I discuss a series of experiments on CeCoIn5. I interpret these experiments as observing an exotic quantum critical point (QCP) separating two Fermi liquids with different sized Fermi surfaces. I discuss a theoretical model exhibiting such a phase transition and compute the electrical Hall resistivity expected near this QCP. In doing so, I explain one of the most surprising features of the experiment—a large peak in the Hall resistivity as a function of temperature. The computation, however, cannot perfectly capture all the features of the experiment, including the T-linear longitudinal resistivity that is a hallmark of the high-temperature superconductors in the normal state./nIn the fifth chapter, I introduce a new model for the above QCP that is exactly solvable in the same way as the Sachdev-Ye-Kitaev (SYK) model, a model that exhibits T-linear resistivity. Within my model, I compute the longitudinal and Hall resistivities and find T-linear resistivity in the critical fan above the QCP, which compares favorably with experiments on high-temperature superconductors, particularly CeCoIn5./nIn the final chapter, I discuss other potential uses for TDMFT and these SYK inspired models, and the large open questions that remain about these two materials.

Advisor: Moore, Joel E