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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