  The topological metal states in electronic systems have been extensively
studied, but topological phonons were explored only in few examples so far.
Here, we expose for the first time that the topological nodal gimbal phonons,
type-I and type-II Weyl phonons are simultaneously present in T-carbon, a
recently realized new allotrope of carbon. At about 15.2 THz, we find that
there exist three mutually intersecting nodal loops (named as nodal gimbal
phonons) around {\Gamma} point, and two pairs of type-I Weyl phonons on the
boundary of Brillouin zone around each X point. In addition, there exist three
pairs of type-II Weyl phonons at about 14.5 THz around each L point. It is
shown that these exotic topological phonons are protected by corresponding
symmetries, and lead to topologically nontrivial surface states. Our findings
not only afford plenty of intriguing topological phonon states in a simple
material like T-carbon but also provide a new platform to study novel
properties of topological phonons, which would facilitate further both
experimental and theoretical works in future.
