Disorder effects in the Kitaev spin liquid

Abstract

One of the long-standing open questions in condensed matter physics, which has recently garnered significant attention, is how a quantum spin liquid (QSL) state responds to the various forms of structural disorder that are inevitable in real materials. Despite numerous theoretical proposals and candidate materials for QSLs over the past half-century, the existence of this exotic magnetic phase remains contentious due to two primary challenges in experimental identification. First, the absence of long-range magnetic order in QSLs results in a featureless ground state, making its characterization largely dependent on the excitation spectrum and dynamical probes. Second, the unavoidable presence of structural disorder in real materials can significantly affect the spin-liquid phase or even lead to its destruction. This underscores the urgent need for a deeper understanding of the effects of disorder in quantum spin liquids. The Kitaev honeycomb model, discovered in 2006, is an exactly solvable model that hosts quantum spin liquid phases and holds the potential for realization in transition-metal compounds with strong spin-orbit coupling. The spin fractionalization into locally conserved fluxes and itinerant Majorana fermions underpins the model's exact solvability, even in real-space representation. This characteristic makes the Kitaev model an ideal testbed for studying disorder effects in quantum spin liquids, allowing us to address the aforementioned challenges by enabling the calculation of the energy spectrum and dynamical response without relying on translational invariance. In this dissertation, various aspects of disorder within the Kitaev spin liquid model have been explored, including disorder-induced flux binding, localization of Majorana modes, power-law divergence in the density of states, signatures of Majorana zero modes in the local dynamical correlation function, and strong-disorder criticality in the quasi-one-dimensional Kitaev model. These studies provide not only a deeper understanding of the role of disorder in the Kitaev spin liquid, but also propose potentially observable consequences in thermal conductivity, specific heat, and inelastic tunneling conductance.