Flatband generator in two dimensions
| Autor: | Wulayimu Maimaiti, Alexei Andreanov, Sergej Flach |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Condensed Matter - Mesoscale and Nanoscale Physics FOS: Physical sciences Perturbation (astronomy) Disordered Systems and Neural Networks (cond-mat.dis-nn) 02 engineering and technology State (functional analysis) Condensed Matter - Disordered Systems and Neural Networks 021001 nanoscience & nanotechnology 01 natural sciences Theoretical physics Character (mathematics) Dimension (vector space) Lattice (order) Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences Flat band 010306 general physics 0210 nano-technology Degeneracy (mathematics) Generator (mathematics) |
| Popis: | Dispersionless bands -- \emph{flatbands} -- provide an excellent testbed for novel physical phases due to the fine-tuned character of flatband tight-binding Hamiltonians. The accompanying macroscopic degeneracy makes any perturbation relevant, no matter how small. For short-range hoppings flatbands support compact localized states, which allowed to develop systematic flatband generators in $d=1$ dimension in Phys. Rev. B {\bf 95} 115135 (2017) and Phys. Rev. B {\bf 99} 125129 (2019). Here we extend this generator approach to $d=2$ dimensions. The \emph{shape} of a compact localized state turns into an important additional flatband classifier. This allows us to obtain analytical solutions for classes of $d=2$ flatband networks and to re-classify and re-obtain known ones, such as the checkerboard, kagome, Lieb and Tasaki lattices. Our generator can be straightforwardly generalized to three lattice dimensions as well. 7 pages + appendices, 7 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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