QST-Seminar - Impart orientations to topological line defects - from non-Abelian and non-Hermitian band nodes to optical polarization singularities

The theory of topological defects plays essential roles in many physical fields, benefiting our comprehension of the spacetime defects in the large-scale structure of universe, the dynamics of ordered media, and the band structure degeneracies in crystalline materials. As a specific kind of topological defects in 3D space, the topological line defects exhibit charming features in their evolutions. When two line defects meet in space, they may either annihilate or repel each other, or even merge into a new defect. In this talk, I will show that these mysterious evolution phenomena of different kinds of line defects can be uniformly understood by assigning an orientation to the lines. First, I will introduce the recent breakthrough of the non-Abelian nodal line theory, where the orientations to the nodal lines imparted by the non-Abelian charges around them can successfully explain the formation of nodal chains and links in PT-symmetric crystals. Following this theory, we have experimentally realized the first 3D non-Abelian phononic crystal possessing earring nodal links and have achieved the first measurement of non-Abelian topological charges in well-designed transmission-line lattices. Second , by generalizing this idea to the lines of non-Hermitian band degeneracies, so-called exceptional points (EPs), we discover that the eigenvalue braiding around an exceptional line (EL) can endow it with a positive direction and propose several mechanisms for realizing symmetry-protected exceptional chains based on the source-free principle of ELs. Finally, I will reveal that the circular polarization singularities (C-points) in 3D vector optical fields can be directly mapped to the non-Hermitian EPs. Hence, the exceptional chain theory can also predict the robust intersection morphologies of the lines of C-points in certain symmetric light fields.