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Kaleidoscope of symmetry-protected topological phases in one-dimensional periodically modulated lattices

Kaleidoscope of symmetry-protected topological phases in one-dimensional periodically modulated lattices

We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase $\ensuremath{\pi}$ or the emergence of a pair of degenerate boundary states. It is shown that there may exist three types of …