Measuring topological invariants from generalized edge states in polaritonic quasicrystals

TL;DR

This paper demonstrates how generalized edge states in polaritonic Fibonacci quasicrystals can be used to measure topological invariants, revealing the connection between fractal energy spectra and topological properties.

Contribution

It introduces a method to determine topological invariants in quasicrystals via edge state analysis, linking spectral evolution to topological numbers.

Findings

Edge states traverse spectral gaps as the phason varies.

Spatial symmetry of edge states switches with the spectral evolution.

Topological invariants match the gap-labeling theorem predictions.

Abstract

We investigate the topological properties of Fibonacci quasicrystals using cavity polaritons. Composite structures made of the concatenation of two Fibonacci sequences allow investigating generalized edge states forming in the gaps of the fractal energy spectrum. We employ these generalized edge states to determine the topological invariants of the quasicrystal. When varying a structural degree of freedom (phason) of the Fibonacci sequence, the edge states spectrally traverse the gaps, while their spatial symmetry switches: the periodicity of this spectral and spatial evolution yields direct measurements of the gap topological numbers. The topological invariants that we determine coincide with those assigned by the gap-labeling theorem, illustrating the direct connection between the fractal and topological properties of Fibonacci quasicrystals.