Exceptional lines in topological semimetals and superconductors*

We consider the impact of the disorder on the spectrum of three-dimensional Weyl and nodal-line semimetals. We show that the combination of disorder and a tilted spectrum leads to a non-Hermitian self-energy contribution that can split a Weyl node and nodal line into a single nodal ring and pair of exceptional lines, respectively. In nodal-line semimetals, these exceptional lines form the boundary of an open and orientable bulk Fermi ribbon in reciprocal space on which the energy gap vanishes. We find that the surface of such a disorder-induced bulk Fermi ribbon in general lies orthogonal to the direction of the tilt, which can be exploited to realize a bulk Fermi ribbon with nontrivial topology by means of a tilt vector that twists along a nodal loop.
We also consider the dispersion of the quasiparticles excitations in nodal superconductors in presence of weak disorder. Similarly to the semimetals, the complex self-energy correction to the Green function of quasiparticles due to disorder gives rise to the non-Hermitian BdG Hamiltonian describing the quasiparticle spectrum with exceptional points and lines.