Wannier Functions in non-Hermitian Systems

Abstract: The scope of this thesis is analyzing and characterizing certain gapless states in tight-binding non-Hermitian systems. We start by providing a pedagogical introduction to tight-binding theory, topological phases of matter, Wannier functions as real-space duals of Bloch functions and their properties, non-Hermitian systems and associated differences from standard Hermitian systems. Subsequently we show the possibility of extending pre-existing concepts of Hermitian quantum mechanics to non-Hermitian settings without losing predicting power over some peculiar observables. We conclude by providing numerical evidence for existence of certain topological states in finite one-dimensional and two-dimensional systems, also testing their robustness against symmetry-breaking and disorder.