Necessary and sufficient conditions for flat bands in M-dimensional N-band lattices with complex-valued nearest-neighbour hopping

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Title
Necessary and sufficient conditions for flat bands in M-dimensional N-band lattices with complex-valued nearest-neighbour hopping
Author(s)
L A Toikka; A Andreanov
Publication Date
2019-01
Journal
Journal of Physics A: Mathematical and Theoretical, v.52, no.2, pp.02LT04 -
Publisher
IOP publishing LTD
Abstract
We formulate the necessary and sufficient conditions for the existence of dispersionless energy eigenvalues (so-called flat bands ) and their associated compact localized eigenstates in M-dimensional tight-binding lattices with N sites per unit cell and complex-amplitude nearest-neighbour tunneling between the lattice sites. The degrees of freedom M can be traded for longer-range complex hopping in lattices with reduced dimensionality. We show the conditions explicitly for (M = 1, N ≤ 4), (M = 2, N = 2, 3), and (M = 3, N = 2, 3), and outline their systematic construction for arbitrary N, M. If and only if the conditions are satisfied, then the system has one or more flat bands. By way of an example, we obtain new classes of flat band lattice geometries by solving the conditions for the lattice parameters in special cases. © 2018 IOP Publishing Ltd Printed in the UK
URI
https://pr.ibs.re.kr/handle/8788114/5580
ISSN
1751-8113
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
Files in This Item:
Toikka_2019_J._Phys._A%3A_Math._Theor._52_02LT04.pdfDownload

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