  For first-order topological semimetals, non-Hermitian perturbations can drive
the Weyl nodes into Weyl exceptional rings having multiple topological
structures and no Hermitian counterparts. Recently, it was discovered that
higher-order Weyl semimetals, as a novel class of higher-order topological
phases, can uniquely exhibit coexisting surface and hinge Fermi arcs. However,
non-Hermitian higher-order topological semimetals have not yet been explored.
Here, we identify a new type of topological semimetals, i.e, a higher-order
topological semimetal with Weyl exceptional rings. In such a semimetal, these
rings are characterized by both a spectral winding number and a Chern number.
Moreover, the higher-order Weyl-exceptional-ring semimetal supports both
surface and hinge Fermi-arc states, which are bounded by the projection of the
Weyl exceptional rings onto the surface and hinge, respectively. Noticeably,
the dissipative terms can cause the coupling of two exceptional rings with
opposite topological charges, so as to induce topological phase transitions.
Our studies open new avenues for exploring novel higher-order topological
semimetals in non-Hermitian systems.
