This article has an erratum: [erratum]
Volume 105, Number 3, February 2014
|Number of page(s)||6|
|Published online||10 February 2014|
Detangling flat bands into Fano lattices
1 New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University 0745 Auckland, New Zealand
2 Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University Canberra ACT 0200, Australia
3 Moscow Institute for Physics and Technology (State University) - 9 Institutskiy pereulok, Dolgoprudny, Moskovskaya obl., 141700 Russia
Received: 14 January 2014
Accepted: 24 January 2014
Macroscopically degenerate flat bands (FB) in periodic lattices host compact localized states which appear due to destructive interference and local symmetry. Interference provides a deep connection between the existence of flat band states (FBS) and the appearance of Fano resonances for wave propagation. We introduce generic transformations detangling FBS and dispersive states into lattices of Fano defects. Inverting the transformation, we generate a continuum of FB models. Our procedure allows us to systematically treat perturbations such as disorder and explain the emergence of energy-dependent localization length scaling in terms of Fano resonances.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 73.20.Fz – Weak or Anderson localization
© EPLA, 2014
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