Knotted non-Hermitian metals

Abstract

Topology, the theory of global properties invariant under continuous deformation, has proven essential for understanding the variety of forms of matter occurring in nature. Here, two paradigmatic concepts of topology in physics, namely, knots and topological properties of energy bands, are brought together to introduce a form of topological matter, best labeled as knotted non-Hermitian metals. Remarkably, non-Hermitian terms accounting for the dissipative coupling of the system to its environment are crucial for the generic stability of these exotic systems.