Fermion Doubling Theorems in Two-Dimensional Non-Hermitian Systems for Fermi Points and Exceptional Points

The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come pairs three-dimensional semimetals. Here, we present an extension of the to non-Hermitian lattice Hamiltonians. We focus on two-dimensional systems without any symmetry constraints, which can host two different types point nodes, namely, (i) Fermi and (ii) exceptional points. show these protected nodes obey theorems, require pairs. To prove points, introduce generalized winding number invariant, call discriminant number. Importantly, this invariant is applicable Hamiltonian with arbitrary order, moreover also be used characterize non-defective degeneracy Furthermore, surface system violate implies unusual bulk physics.