Anomalous Polarization in One-Dimensional Aperiodic Insulators

Multilevel charge pumping is a feature that was recently observed in quasiperiodic systems. In this work, we show that it is more generic and appears in different aperiodic systems. Additionally, we show that for aperiodic systems admitting arbitrarily long palindromic factors, the charge pumping protocol connects two topologically distinct insulating phases. This confirms the existence of topological phases in aperiodic systems whenever their finite-size realizations admit inversion symmetry. These phases are characterized by an anomalous edge response resulting from the bulk–boundary correspondence. We show that these signatures are all present in various chains, each representing a different class of structural aperiodicity: the Fibonacci quasicrystal, the Tribonacci quasicrystal, and the Thue–Morse chain. More specifically, we calculate three quantities: the Berry phase of the periodic approximation of the finite-size systems, the polarization response to an infinitesimal static and constant electric field in systems with open boundary conditions, and the degeneracy of the entanglement spectrum. We find that all of them provide signatures of a topologically nontrivial phase.