Compact localized states and flat-band generators in one dimension
By Wulayimu Maimaiti, Alexei Andreanov, H. Park, Oleg V. Gendelman, Sergej Flach. 2016
158 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b56a140aa6f787c187e33d3fdffca48aae314cf3
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Artificial flat band systems: from lattice models to experiments (2018, background): “The parameter space of these flat bands (U = 2 cells) assuming short-ranged hopping was determined systematically in 2017 [41].”