  In parallel to electronic systems, the concept of topology has been extended
to phonons, which has led to the birth of topological phonons. Very recently,
nodal point phonons, nodal line phonons, and nodal surface phonons have been
proposed, and a handful of candidate materials have been predicted in
solid-state materials. In this work, based on symmetry analysis and
first-principles calculations, we propose that hourglass Weyl nodal line (HWNL)
phonons and Dirac nodal line (DNL) phonons coexist in the phonon dispersion of
a single material, KCuS, with a $Pnma$-type structure. The HWNLs and DNLs are
relatively flat in frequency and well separated from other phonon bands. The
corresponding topological phonon surface states appear only in the [100] and
[001] surfaces, unlike those of typical phononic nodal-line materials. The
reason for this phenomenon is explained based on Zak phase calculations. Our
work, for the first time, proves that phononic nodal lines with different types
of degeneracies can be achieved in one single material. Thus, KCuS can be
viewed as a good platform to investigate the entanglement between HWNL phonons
and DNL phonons.
