Topological properties of Fibonacci quasicrystals : A scattering analysis of Chern numbers

Understand

We report on a study of topological properties of Fibonacci quasicrystals.

• Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry.
• Topological and spectral features are related to the two independent phases of the scattering matrix: the total phase shift describing the frequency spectrum and the chiral phase sensitive to topological features.
• Conveniently designed gap modes with spectral properties directly related to the Chern numbers allow to scan these phases.