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Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators.

Quasiperiodic structures have recently been found to possess salient topological properties. In this Letter, we theoretically and experimentally demonstrate the topological edge states in a quasiperiodic Harper chain composed of split-ring resonators. In a finite-size Harper chain, we find that there is always a pair of edge states in the bandgaps, independent of the number of the resonators. Different from the topological edge states localized at both ends of a periodic chain, this pair of edge states is selectively localized at the left or right end of the quasiperiodic chain at different frequencies. These paired-edge states with asymmetric field distribution can be used for unidirectional propagation. Our results not only provide a versatile platform to study the topological physics beyond the periodic structures but also may be useful in some applications such as selective unidirectional power transfer.