Anomalous Polarization in One-dimensional Aperiodic Insulators

TL;DR

This paper demonstrates the existence of topological phases in one-dimensional aperiodic insulators through charge pumping, revealing anomalous edge responses and topological signatures across various aperiodic chains.

Contribution

It introduces a charge pumping scheme to identify topological phases in aperiodic chains, analyzing multiple structural classes and their topological signatures.

Findings

Topological phases confirmed in Fibonacci, Tribonacci, and Thue-Morse chains.

Multiple signatures such as Berry phase, polarization response, and entanglement spectrum degeneracy indicate nontrivial topology.

Aperiodic chains exhibit anomalous edge responses consistent with bulk-boundary correspondence.

Abstract

By implementing a charge pumping scheme for one-dimensional aperiodic chains, we confirm the existence of topological phases in these systems whenever their finite-size realizations admit inversion symmetry. These phases are usually characterized by an anomalous edge response as a result of 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 crystalline approximation of the finite-size systems, the polarization response to an inifintesimal 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.