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By means of first-principles calculations and modeling analysis, we havepredicted that the traditional 2D-graphene hosts the topological phononicWeyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum.The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 atthe BZ corners \emph{K} and \emph{K}', and PW3 locating along the$\Gamma$-\emph{K} line), one type-II PW4 locating along the $\Gamma$-\emph{M}line, and one PNL surrounding the centered $\Gamma$ point in the $q_{x,y}$plane. The calculations further reveal that Berry curvatures are vanishinglyzero throughout the whole BZ, except for the positions of these four pairs ofWeyl-like phonons, at which the non-zero singular Berry curvatures appear withthe Berry phase of $\pi$ or -$\pi$, confirming its topological non-trivialnature. The topologically protected non-trivial phononic edge states have beenalso evidenced along both the zigzag-edged and armchair-edged boundaries. Theseresults would pave the ways for further studies of topological phononicproperties of graphene, such as phononic destructive interference with asuppression of backscattering and intrinsic phononic quantum Hall-like effects.

Topological Weyl-like Phonons and Nodal Line Phonons in Graphene