Eur. Phys. J. B (2017) 90: 1
https://doi.org/10.1140/epjb/e2016-70551-2

Regular Article

Localization of weakly disordered flat band states

¹ Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore
² Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, ACT 2601 Canberra, Australia
³ New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, 0745 Auckland, New Zealand
⁴ Physics Department, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave., Astana, Kazakhstan
⁵ Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea

^a e-mail: dleykam@ntu.edu.sg

Received: 20 September 2016
Received in final form: 7 November 2016
Published online: 11 January 2017

Abstract

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths ξ that diverge with a variety of unconventional exponents ν, ξ ~ 1 /W^ν.