Topological classification of time-reversal invariant quantum materials

Tyner, Alexander Conkey

doi:https://doi.org/10.21985/n2-bacy-6046

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Topological classification of time-reversal invariant quantum materials

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In recent years, the understanding and identification of quantum materials supporting non-trivial band topology has progressed rapidly. This progress has been motivated in part by the potential application of topological quantum materials in quantum computers, sensors, and other next-generation devices. Despite this progress, the computation of bulk topological invariants in time-reversal symmetric materials remains a largely open question in the absence of enhanced crystalline symmetries. In this thesis, we establish generalized procedures for computing topological invariants of time-reversal symmetric systems in one, two, and three dimensions without imposing severe symmetry constraints. We develop these methods in both momentum and real space, providing a route for cross-validation. In each case, emphasis is placed on integration with ab initio simulations to allow for connection to experiment. The outcome of this work is the establishment of novel theoretical diagnostics, conceptual advancements in bulk topological classification, and the identification of multiple high-quality topological materials that had evaded detection in the literature prior to this point. The materials identified are energetically stable and experimentally controlled, offering potential for use in future devices.

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