  We perform both lattice dynamics analysis and molecular dynamics simulations
to demonstrate the existence of topologically protected phonon modes in a
two-dimensional, monolayer hexagonal boron nitride sheet. The topological
phonon modes are found to be localized at an in-plane interface that divides
the system into two regions of distinct valley Chern numbers. The dispersion of
this topological phonon mode crosses over the frequency gap [1123, 1278]
cm^{-1}, which is opened through analogy with the quantum valley Hall effect by
breaking inversion symmetry of the boron and nitride atoms in the primitive
unit cell. Consequently, vibrational energy with frequency within this gap is
topologically protected, resulting in wave propagation that exhibits minimal
backscattering, is robust with regards to structural defects such as sharp
corners, and exhibits excellent temporal stability. Our findings open up the
possibility of realizing topological phonons and mechanics in two-dimensional
nanomaterials.
