Braid-protected topological band structures with unpaired exceptional points

Abstract

A class of systems is presented in which a particle-antiparticle pair cannot annihilate each other after they have moved along a loop and instead form a new type of composite particle. This occurs in so-called non-Hermitian systems: classical metamaterials or ``open'' quantum systems that are coupled to the rest of the Universe. In two dimensions, their excitations are massless ``particles'' that can be created as a pair or annihilate each other pairwise. Each particle is associated with the mathematical structure of a knot in a rope. After moving one particle along a loop and bringing it near its former antiparticle, their knots are combined differently. The two can no longer annihilate pairwise and instead form a new particle corresponding to a more complicated knot. This shows that non-Hermitian particles in two dimensions remember their movement history.