Bulk topological signatures of a quasicrystal

TL;DR

This paper demonstrates that measuring real space charge density in a Fibonacci quasicrystal reveals topological properties, with charge oscillations linked to the Chern number, robust against interactions and disorder.

Contribution

It introduces a method to infer topological invariants from real space charge measurements in quasicrystals, connecting charge oscillations to the Chern number.

Findings

Charge oscillations correspond to the Chern number of the gap.

The effect persists under moderate interactions and disorder.

Two interpretations of oscillations are provided: valence bond and perturbative.

Abstract

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.