Non-trivial Braiding of Band Nodes in Non-Hermitian Systems

A prevailing notion in the topological band theory is that the topological charge associated with band degeneracies cannot change upon continuously tuning the Bloch Hamiltonian. Here, we show that this notion is in general incorrect in non-Hermitian systems. In particular, we present a simple three-dimensional two-band model, such that a Weyl point degeneracy flips its chiral charge after encircling an exceptional line degeneracy, upon tuning one parameter. We use the formalism of Abe homotopy to mathematically describe this phenomenon. Our work points to significant richness in the topology of non-Hermitian Hamitonians that is not shared by their Hermitian counterparts.