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Compact localized states and flat-band generators in one dimension
Maimaiti, Wulayimu,Andreanov, Alexei,Park, Hee Chul,Gendelman, Oleg,Flach, Sergej American Physical Society 2017 Physical Review B Vol.95 No.11
<P>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.</P>