Localization of weakly disordered flat band states |
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| Authors: | Daniel Leykam Joshua D Bodyfelt Anton S Desyatnikov Sergej Flach |
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| Institution: | 1.Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University,Singapore,Singapore;2.Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University,Canberra,Australia;3.New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University,Auckland,New Zealand;4.Physics Department, School of Science and Technology, Nazarbayev University,Astana,Kazakhstan;5.Center for Theoretical Physics of Complex Systems, Institute for Basic Science,Daejeon,Korea |
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| 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 . |
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