Indubala I Satija, Gerardo G. Naumis
The topology of quasicrystals is found to have a novel manifestation in the spatial profile of band edge states as topological invariants transform various peaks into doublets of size equals the Chern number. The Chern-dressed peaks form a self-similar pattern encoding topological fingerprints at all length scales. For quasicrystals exhibiting a localization transition, fluctuations about exponentially localized zero modes describe a critical point of the topological phase transition where Majorana modes delocalize. These exotic modes can be captured in their entirety using U(1) symmetry breaking perturbation where the localization transition is accompanied by the topological transition as edge-localized modes move to the interior, loosing topological protection.
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http://arxiv.org/abs/1210.5159
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