Fig. 1: Orientation of exceptional lines (ELs) and source-free principle.
From: Symmetry-protected topological exceptional chains in non-Hermitian crystals
a An order-2 EL manifests as the phase singularity of the discriminant Δf(k), where the sign of phase vortex assigns a positive orientation (arrow on the EL) to the EL in compliance with the right-hand rule of the loop ΓEL (white dashed). b Real and imaginary parts of two intersecting bands on the transverse plane in (a), and the red and light-blue trajectories denote the two modes along the path ΓEL. c Braiding and mode switching of two eigenenergies along the loop ΓEL in (a). d Schematic of the generalized doubling theorem for exceptional points. Several directed ELs meet at a junction that is enclosed by a surface S. Colormap on the surface: \(\arg [{\Delta }_{f}({{{{{{{\bf{k}}}}}}}})]\).
