  Three-dimensional topological Weyl semimetals can generally support a
zero-dimensional Weyl point characterized by a quantized Chern number or a
one-dimensional Weyl nodal ring (or line) characterized by a quantized Berry
phase in the momentum space. Here, in a dissipative system with particle gain
and loss, we discover a new type of topological ring, dubbed Weyl exceptional
ring consisting of exceptional points at which two eigenstates coalesce. Such a
Weyl exceptional ring is characterized by both a quantized Chern number and a
quantized Berry phase, which are defined via the Riemann surface. We propose an
experimental scheme to realize and measure the Weyl exceptional ring in a
dissipative cold atomic gas trapped in an optical lattice.
