Direct measurement of Chern numbers in the diffraction pattern of a Fibonacci chain

A. Dareau, E. Levy, M. Bosch Aguilera, R. Bouganne, E. Akkermans, F. Gerbier, J. Beugnon

Published 2016-07-04Version 1

Topological properties are now understood to be a key feature of many different physical systems, from topological insulators to quasicrystals. Such properties are often encoded into integer-valued topological invariants, such as winding or Chern numbers, usually related to transport or spectral measurements. We report on an experiment where the Chern numbers of quasicrystalline structures are directly determined by an interferometric approach. We show that all the possible Chern numbers for finite-length Fibonacci chains can be observed directly in their diffraction pattern. Finally, we also demonstrate quantitatively the stability of these topological invariants with respect to structural disorder.