
TL;DR
This paper develops systematic methods to identify and construct flatband Hamiltonians in 1D, 2D, and non-Hermitian systems, enabling better design and understanding of flatband phenomena in various physical contexts.
Contribution
It introduces a comprehensive flatband generator scheme for different lattice dimensions and types, expanding the toolkit for flatband lattice design and analysis.
Findings
Classified flatband lattices by their compact localized states properties
Generated all possible 1D flatband Hamiltonians with arbitrary bands and CLS sizes
Proposed a 2D flatband generator with CLSs in a 2x2 plaquette
Abstract
Flatbands (FBs) are dispersionless energy bands in the single-particle spectrum of a translational invariant tight-binding network. The FBs occur due to destructive interference, resulting in macroscopically degenerate eigenstates living in a finite number of unit cells, which are called compact localized states (CLSs). Such macroscopic degeneracy is in general highly sensitive to perturbations, such that even slight perturbation lifts the degeneracy and leads to various interesting physical phenomena. In this thesis, we develop an approach to identify and construct FB Hamiltonians in 1D, 2D Hermitian, and 1D non-Hermitian systems. First, we introduce a systematic classification of FB lattices by their CLS properties, and propose a scheme to generate tight-binding Hamiltonians having FBs with given CLS properties---a FB generator. Applying this FB generator to a 1D system, we identify…
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