Symmetry protected topological phases characterized by isolated exceptional points

Abstract: Exceptional point (EP) associated with eigenstates coalescence in non-Hermitian systems has many exotic features. The EPs are generally sensitive to system parameters, here we report symmetry protected isolated EPs in the Brillouin zone (BZ) of a two-dimensional non-Hermitian bilayer square lattice; protected by symmetry, the isolated EPs only move, merge, and split in the BZ. The average values of Pauli matrices under the eigenstate of system Bloch Hamiltonian define a real planar vector field, the topological defects of which are isolated EPs associated with vortices. The winding number characterizes the vortices and reveals the topological properties of the non- Hermitian system. Different topological phases correspond to different EP configurations, which are unchanged unless topological phase transition occurs accompanying with the EPs merging or splitting.