Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials

TL;DR

This paper demonstrates that 1D charge-ordered materials with quasiperiodicity exhibit 2D topological properties, linking quasicrystals to topological insulators and proposing experimental tests for their topological nature.

Contribution

It establishes the equivalence between 1D quasicrystals and incommensurate charge order, revealing their topological properties via a 2D parameter space.

Findings

Topological edge modes in 1D quasicrystals can be understood through 2D topological invariants.

Incommensurate charge order spectra are fractal, connecting to the topology of commensurate states.

Proposes an experimental test involving quantized adiabatic particle transport.

Abstract

It has recently been argued that individual 1D quasicrystals can be ascribed 2D topological quantum numbers and a corresponding set of topologically protected edge modes. Here, we demonstrate the equivalence of such 1D quasicrystals to a mean-field treatment of incommensurate charge order in 1D materials. Using the fractal nature of the spectrum of commensurate charge-ordered states we consider incommensurate order as a limiting case of commensurate orders. We show that their topological properties arise from a 2D parameter space spanned by both phase and wave vector, bringing the observation of 2D edge modes in line with the standard classification of topological order.The equivalence also provides a set of real-world quasiperiodic materials which can be readily experimentally examined. We propose an experimental test of both the quasicrystalline and topological character of these systems in the form of a quantized adiabatic particle transport upon dragging the charge-ordered state.