Short description

Quasicrystals exhibit rotational symmetries that are forbidden in periodic crystals, such as 8-, 10-, or 12-fold symmetry. Recent studies have demonstrated that photonic structures with such an order can host polarization vortices in momentum space with unusually large topological charges, as bound states in the continuum (BICs) and symmetry-protected radiation modes.

This project explores whether such high-charge polarization vortices can be understood as projections of a higher-dimensional periodic “parent” system. In the cut-and-project framework, a two-dimensional quasicrystal is obtained by projecting a periodic lattice defined in a higher-dimensional space. The central objective is to determine how the crystallographic symmetry and representation theory of this higher-dimensional system constrain the allowed vortex charges observed after projection.

By combining symmetry analysis with numerical modeling of realistic structures, the project aims to establish a predictive framework linking higher-dimensional symmetry to polarization-vortex topology in quasicrystals.

Background

  • Quantum mechanics and linear algebra
  • Basic condensed-matter or photonics concepts
  • Familiarity with band structures and lattice symmetry
  • Introductory notions of topology (helpful but not required)

What you will learn

  • The cut-and-project construction of quasicrystals
  • The role of rotational symmetry in quantizing topological charge
  • How to compute polarization vortices and winding numbers in momentum space
  • The connection between symmetry representations and topological defects
  • How to combine analytical reasoning with numerical simulations

Interested?

Feel free to contact me for more information.