Effects of Interaction and Percolation on Topological Edge States

Abstract

In this thesis we studied two important Topological Insulators (TIs), where we focused particularly on the role of interactions and percolation on the topological edge states. First, we analyzed the role of nearest-neighbor interactions in a prototype one-dimensional TI, namely the Su-Schrieffer-Heeger (SSH) model. Based on a Green s function formalism, we applied Dyson s equation in combination with T-matrix approximation to verify the bulk-edge correspondence in the presence of interactions. The critical exponents near topological phase transitions are found to be the same as the noninteracting SSH model, indicating that the system stays in the same universality class despite the presence of interactions. The second system is a two-dimensional timereversal symmetric TI, namely the Bernevig-Hughes-Zhang (BHZ) model in conjunction with a time-reversal breaking ferromagnetic metal (FMM), where we investigated the percolation of the quantum spin Hall state from the TI layer to the FMM by means of a tight-binding model. We demonstrated that depending on whether the edge state Dirac cone submerges into the FMM subbands and the direction of the magnetization of the FMM, the percolation of the edge state and its spin-momentum locking are affected in different ways. Surprisingly, we uncover that the equilibrium edge spin current in the BHZ model, naturally expected from the spin polarized propagating edge states, is in fact absent due to the cancellation from the valence bands. Nevertheless, laminar flows of room temperature persistent charge and spin currents are produced near the interface of the BHZ/FMM junction. Using a linear response theory, we investigate the current-induced spin polarization caused by the percolation of the edge state, which serves as a spin torque that is found to be predominantly field-like. Moreover, the spin polarization is dramatically enhanced near the impurities at the edge of the BHZ model.

En esta tesis estudiamos dos importantes aislantes topológicos (TI), donde nos enfocamos en el rol que tienen las interacciones y la percolación sobre los estados topológicos de borde. Primero, analizamos el papel de las interacciones en un prototipo TI unidimensional, llamado modelo Su-Schrieffer-Heeger (SSH). Usando el formalismo de la función de Green, resolvemos la ecuación de Dyson en combinación con la aproximación de la matriz-T para verificar la correspondencia bulk-edge en presencia de interacciones y estudiar el comportamiento crítico de la transición de fase topológica. El segundo sistema es un TI bidimensional simétrico bajo reversión temporal, conocido como modelo Bernevig-Hughes-Zhang (BHZ), en contacto con un metal ferromagnético (FMM). Aquí estudiamos la percolación del estado Hall de espín cuántico del modelo BHZ hacia el FMM por medio de un modelo tight-binding. Observamos una serie de efectos sobre la percolación del estado y el espín-momentum-locking dependientes de la estructura de bandas y la dirección de la magnetización del FMM. Calculamos flujos laminares de corrientes locales de carga y espín cerca del contacto y, aplicando teoría de la respuesta lineal, la polarización de espín inducida, la misma que sirve como un torque de espín y resulta ser predominantemente de tipo field-like.