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We propose a real-space approach explaining and controlling the occurrence ofedge-localized gap states between the spectral quasibands of binary tightbinding chains with deterministic aperiodic long-range order. The framework isapplied to the Fibonacci, Thue-Morse and Rudin-Shapiro chains, representingdifferent structural classes. Our approach is based on an analysis of theeigenstates at weak inter-site coupling, where they are shown to genericallylocalize on locally reflection-symmetric substructures which we call localresonators. A perturbation theoretical treatment demonstrates the localsymmetries of the eigenstates. Depending on the degree of spatial complexity ofthe chain, the proposed local resonator picture can be used to predict theoccurrence of gap-edge states even for stronger couplings. Moreover, we connectthe localization behavior of a given eigenstate to its energy, thus providing aquantitative connection between the real-space structure of the chain and itseigenvalue spectrum. This allows for a deeper understanding, based on localsymmetries, of how the energy spectra of binary chains are formed. The insightsgained allow for a systematic analysis of aperiodic binary chains and offers apathway to control structurally induced edge states.

Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains