UC Berkeley

In this dissertation we will describe aspects of the interplay of anisotropy and disorder with fractionalized phases of matter through three studies.

The first study concerns a material, $\alpha$-RuCl$_3$, which has been suggested to be proximate to a fractionalized phase called the Kitaev spin liquid. Despite the presence of traditional magnetic order at low temperatures, ab-initio predictions, and an observed continuum of magnetic excitations at high energies has led to excitement that the material is close to the spin liquid phase. In this study, we describe the magnetic excitations of $\alpha$-RuCl$_3$ as observed by time-domain terahertz spectroscopy. In the presence of a small ($1.5$T) magnetic field, a discontinuity in the spectra of magnetic excitations as well as a continuum of magnetic absorption is observed. These observations are suggestive of a field induced transition or proximity to the Kitaev spin liquid. However, with the assumption of random bond anisotropy, we show that a conventional magnetic order is sufficient to explain all observed features. While we find that the experiment can be qualitatively fit to a Hamiltonian with large Kitaev coupling, all aspects of the experiment are shown to be well described by non-fractionalized excitations.

In the second study we consider the impact of lattice vacancies in the Kitaev spin liquid, which represents an expected form of disorder in any physical realization of the phase. In Kitaev's exactly solvable honeycomb model, it has been shown that introducing a lattice vacancy binds an emergent $Z_2$ flux. This offers a feasible route to creating and trapping this fractionalized excitation. However, it is unclear if this would hold generally for Kitaev spin liquids or only for Kitaev's integrable model. To address this, we introduce a universal low-energy effective theory for the spin liquid with vacancies and $Z_2$ fluxes. Using this low-energy theory in the gapless phase we find that the binding energy can be attributed to the suppression of a scattering resonance caused by the vacancy. In the non-abelian phase, where $Z_2$ fluxes are Ising anyons, we find that the binding energy has a topological origin. Identifying the doubled spin liquid as a quantum Hall state allows us to argue that spectral flow as flux is threaded through the vacancy induces the binding energy. Our results show that lattice vacancies offer a robust method of creating and trapping Ising anyons in realistic instances of the Kitaev spin liquid. Additionally, this finding indicates that in the presence of vacancy disorder, the Kitaev spin liquid should be expected to have a ground state with $Z_2$ fluxes pinned to the vacancies.

In the final chapter we introduce exactly solvable models of the phase transition between a Fermi Liquid and a fractionalized Fermi Liquid (FL$^{\ast}$) defined by the emergence of a $U(1)$ gauge field. We compare the cases where the interactions of this model are spatially disordered or translationally invariant. Unlike previous attempts to analytically describe this phase transition, the approach that we introduce allows for the description of strongly coupled fixed points. In particular, we find that it can describe the ubiquitous linear in temperature strange metal resistivity observed near many metallic critical points. For spatially disordered couplings this strange metal phenomenology only appears if the spin liquid deconfines anisotropically into two-dimensional planes of the three-dimensional material. In the limit of strong damping of the critical boson, the model describes a Planckian strange metal in which quasiparticle lifetimes are set only by fundamental constants and the temperature.