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.
Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-307393 |
Date | January 2022 |
Creators | Zorzato, Alberto |
Publisher | KTH, Fysik |
Source Sets | DiVA Archive at Upsalla University |
Language | English |
Detected Language | English |
Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
Format | application/pdf |
Rights | info:eu-repo/semantics/openAccess |
Relation | TRITA-SCI-GRU ; 2022:003 |
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