Compact localized states and flat-band generators in one dimension

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 fine-tuned networks, still lacking a comprehensive generating principle. We introduce a FB ge...

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Bibliographic Details
Published in:Physical review. B 2017-03, Vol.95 (11), p.115135, Article 115135
Main Authors: Maimaiti, Wulayimu, Andreanov, Alexei, Park, Hee Chul, Gendelman, Oleg, Flach, Sergej
Format: Article
Language:English
Subjects:
Eigenvectors
Networks
Photonics
Unit cell
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Summary: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 fine-tuned 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.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.95.115135