  Topological heavy-fermion systems in three dimensions are usually classified
as topological insulators or semimetals. Here, we theoretically predict a
different type of heavy-fermion system (dubbed exceptional heavy-fermion
semimetal) by studying a three-dimensional periodic Anderson model consisting
of strongly correlated localized $f$ electrons and itinerant conduction $c$
electrons in a zincblende lattice. Due to the breaking of inversion symmetry,
the quasiparticle lifetimes at different sublattices are distinct, leading to
the emergence of Weyl exceptional rings in the complex pole of the Green's
function at finite temperatures; such rings lead to the appearance of bounded
Fermi surfaces (bulk Fermi disks). As temperatures rise, two pairs of Weyl
exceptional rings merge into two exceptional rings with one bounded bulk Fermi
surface (bulk Fermi tube), which are experimentally measurable by
angle-resolved photoemission spectroscopy. Finally, we use the dynamical mean
field theory to calculate the spectral functions which illustrate the emergence
of bulk Fermi tubes. Our work thus opens the door for studying exceptional
heavy-fermion semimetal phases in three dimensions.
