Topological nodal phases in non-Hermitian systems with parity-time and parity-particle-hole symmetries

Exceptional points emerge from band touching in non-Hermitian systems. We study band degeneracy in non-Hermitian systems with parity-time and parity-particle-hole symmetries. When parity-time or parity-particle-hole symmetry is present, it is shown that exceptional lines and surfaces can appear in two-dimensional and three-dimensional non-Hermitian systems, respectively. We also investigate topological properties of the nodal band structures. We demonstrate the non-Hermitian topological nodal phases by using lattice models of a topological semimetal and a superconductor.