Symmetry-protected topological exceptional chains in non-Hermitian crystals

In non-Hermitian systems, the defective band degeneracies, so-calledexceptional points (EPs), can form robust exceptional lines (ELs) in 3Dmomentum space in the absence of any symmetries. Here, we show that a naturalorientation can be assigned to every EL according to the eigenenergy braidingaround it, and prove the source-free principle of ELs as a corollary of thegeneralized Fermion doubling theorem for EPs on an arbitrary closed orientedsurface, which indicates that if several ELs flow into a junction, the samenumber of outflow ELs from the junction must exist. Based on this principle, wediscover three different mechanisms that can stabilize the junction of ELs andtherefore guarantee the formation of various types of exceptional chains (ECs)under the protection of mirror, mirror-adjoint, or ${C}_2\mathcal{T}$symmetries. Furthermore, we analyze the thresholdless perturbations to aHermitian nodal line and map out all possible EC configurations that can beevolved. By strategically designing the structure and materials, we furtherexhibit that these exotic ECs can be readily observed in non-Hermitian photoniccrystals. Our results directly manifest the combined effect of spatial symmetryand topology on the non-Hermitian singularities and pave the way formanipulating the morphology of ELs in non-Hermitian crystalline systems.