Universität zu Köln

Moreno Gonzalez, Mateo (2025). Localization and topology in surface states of disordered topological insulators. PhD thesis, Universität zu Köln.

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Abstract

In condensed matter physics topology has fundamentally reshaped our under- standing of phases of matter and the transitions between them. New phases, such as topological insulators, have introduced innovative perspectives on band theory, where for each band in the bulk of these systems topological invariants can be defined. One significant consequence of bulk topological invariants is the emergence of topologically protected gapless boundary states that are robust against symmetry-preserving perturbations. However, all real systems exhibit some degree of impurities or disorder. Disorder breaks translation invariance, a critical feature for band theory, and can lead to the localization of states through Anderson localization. Ander- son localization and topology act as opposing forces in electronic systems: while topology protects gapless states, Anderson localization tends to localize them. Consequently, Anderson localization can potentially drive a topological insulator through topological phase transitions. This thesis investigates the impact of disorder on topological insulators in two and three dimensions. First, it presents a comprehensive study of the disordered Chern insulator, detailing its phase diagram and identifying the energy positions of delocalized states responsible for quantized Hall responses. Secondly, it explores disordered higher-order topological insulators, examining the preservation of boundary modes and topological invariants under disorder. Lastly, it addresses the surface states of three-dimensional chiral topological insulators, revealing their fragility and localization properties. These questions are addressed using analytical methods from topological quantum field theory and by deriving non-linear σ models from microscopic models. These findings allow us to comprehend the interplay between Anderson localization and topology in some topological insulators in two and three dimensions.