TOPOLOGICAL PHASES OF MATTER FOR QUANTUM MATERIALS AND DEVICES

Spin related phenomena play an important role in quantum physics. In this dissertation, we look into the spin dynamics of both nuclear and electron spins. Recently, physicists achieved considerable progress in understanding non-abelian and topological matter. Some feasible breeding ground for experimental observation of these phenomena are quantum Hall effect settings and structures with topological insulators. We therefore are interested in role of electron and nuclear spins in transport phenomena in these systems.

We briefly introduce the subject of integer and fractional quantum Hall effect and topological insulators and discuss relevant mathematical methods such as K-matrix theory and quantum kinetic theory in Chapter 1. We also discuss Majorana Fermions, parafermions and Fibonacci anyons.

In Chapter 2, we discuss interaction between nuclear spins and quantum Hall edge state electron spins via hyperfine interaction. In particular, we consider an experimental setting developed in prof. Rokhinson group, that studied a quantum device built to explore the possibility of creating parafermion zero modes. We used a simplified model with $k=\frac{1}{3}$ Luttinger Liquid counter propagating opposite spin edge states interacting with nuclear spins, and considered the polarization of nuclear spins caused by electric current flow and studied its dependence on bias and temperature. We also performed an renormalization group analysis of the hyperfine interaction. We evaluated the effects of Overhauser field generated by polarized nuclear spins on polarized and unpolarized FQH phases, and suggested a novel dynamical nuclear polarization mechanism, in which the polarization is not only spread by dipole-dipole interaction but also dynamically shifts the boundary between polarized and unpolarized phases. We further discussed the obstacles for observation of parafermion zero modes due to nuclear spins and proposed possible remedies.

In chapter 3, we discuss the role of electron spins in the magneto-chiral anisotropy of resistance. We propose that polarization and relaxation of electron spins in quantum wells with spin-orbit interactions or on the surface state of a topological insulator under external magnetic field $B$ can induce an electric current that is quadratic in electric and linear in magnetic field resulting in non-reciprocity of resistance. We used the kinetic equation to analyze this mechanism.