| What is the connection between the Fibonacci chain, a material without periodicity—and the quantum Hall effect in a two-dimensional crystal? This is the question addressed by Anuradha Jagannathan (CNRS, Laboratoire de Physique des Solides – Université Paris-Saclay) in a study published in Physical Review B. |
By introducing a new model, the Fibonacci–Hall model, the researcher shows that a one-dimensional quasicrystal can inherit topological properties originating from a two-dimensional quantum system. In other words, even without a real magnetic field, the geometric structure of the quasicrystal generates a “geometric” flux that endows the material with characteristics similar to those observed in the quantum Hall effect.
This result highlights a deep link between geometry and quantum topology, two key concepts for understanding complex electronic states of matter.
Beyond this theoretical discovery, the model opens up perspectives for exploring higher-dimensional quasicrystals, where even richer topological phenomena could emerge.
Reference
A. Jagannathan, “Missing link between the two-dimensional quantum Hall problem and one-dimensional quasicrystals”, Physical Review B 112, L100102 (2025). DOI : 10.1103/stk9-d9vf
Contact:
Anuradha Jagannathan, Emeritus Professor at Université Paris-Saclay, Laboratoire de Physique des Solides, Orsay
anuradha.jagannathan@universite-paris-saclay.fr