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arXiv · 1610.02970

Compact localized states and flatband generators in one dimension

Wulayimu Maimaiti·Alexei Andreanov·Hee Chul Park·Oleg Gendelman·Sergej Flach
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Abstract

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.

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Wulayimu Maimaiti, Alexei Andreanov, Hee Chul Park, Oleg Gendelman, Sergej Flach. 2016-12-26. Compact localized states and flatband generators in one dimension. https://doi.org/10.1103/physrevb.95.115135

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