Compact localized states and flatband generators in one dimension
| Autor: | Oleg Gendelman, Wulayimu Maimaiti, Hee Chul Park, Alexei Andreanov, Sergej Flach |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
Condensed Matter - Materials Science Periodic lattice Condensed Matter - Mesoscale and Nanoscale Physics business.industry Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences 02 engineering and technology Sawtooth wave 021001 nanoscience & nanotechnology 01 natural sciences symbols.namesake Transverse plane Quantum mechanics 0103 physical sciences Mesoscale and Nanoscale Physics (cond-mat.mes-hall) symbols Dissipative system Flat band Photonics 010306 general physics 0210 nano-technology Hamiltonian (quantum mechanics) business Eigenvalues and eigenvectors |
| DOI: | 10.48550/arxiv.1610.02970 |
| Popis: | Flat bands (FB) are strictly dispersionless bands in the Bloch spectrum of a periodic lattice Hamiltonian, recently observed in a variety of photonic and dissipative condensate networks. FB Hamiltonians are finetuned networks, still lacking a comprehensive generating principle. We introduce a FB generator based on local network properties. We classify FB networks through the properties of compact localized states (CLS) which are exact FB eigenstates and occupy $U$ unit cells. We obtain the complete two-parameter FB family of two-band $d=1$ networks with nearest unit cell interaction and $U=2$. We discover a novel high symmetry sawtooth chain with identical hoppings in a transverse dc field, easily accessible in experiments. Our results pave the way towards a complete description of FBs in networks with more bands and in higher dimensions. Comment: 11 pages, 4 figures |
| Databáze: | OpenAIRE |
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