1D quasicrystals and topological markers

TL;DR

This paper extends a 1D topological marker to quasiperiodic and aperiodic systems, demonstrating its effectiveness in revealing topological properties in complex quasicrystal Hamiltonians and fully aperiodic systems.

Contribution

The authors modify an existing 1D topological marker to apply it to quasiperiodic and aperiodic systems, enabling new exploration of their topological features.

Findings

Effective identification of topological properties in various quasicrystal Hamiltonians

Application of the marker to systems with largely unexplored topological structures

Verification of the marker's effectiveness in fully aperiodic systems

Abstract

Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively reveal the topological properties of 2D systems. In an earlier work, the present authors have developed a marker that can be applied to 1D time-dependent systems which can be used to explore their topological properties, like charge pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against different quasicrystal Hamiltonians, some which have been addressed in previous studies using existing methods, and others which possess topological structures that have been largely unexplored. We also demonstrate that the altered 1D marker can be productively applied to systems that are fully aperiodic.