Doubling theorem for Fermi points, degenerate points, and exceptional points in 2D non-Hermitian systems

Fermion doubling theorem, which is known as Nielsen-Ninomiya theorem, states that once a Weyl node with a non-zero topological charge is present in the 3D Brillouin zone, the node must be accompanied by at least one Weyl node to neutralize the total topological charge in the entire Brillouin zone. In 2D non-Hermitian systems, Fermi points, degeneracy points, and exceptional points can be protected by non-zero topological invariants in the absence of symmetries. We show that these three types of protected points obey the doubling theorem in the 2D Brillouin Zone in this talk.