  We observed distinct interlayer shear mode Raman spectra for trilayer
graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode
phonon branches in trilayer graphene. We found that ABA trilayers exhibit
pronounced Raman response from the high-frequency shear branch, without any
noticeable response from the low-frequency branch. In contrast, ABC trilayers
exhibit no response from the high-frequency shear branch, but significant Raman
response from the low-frequency branch. Such complementary behaviors of Raman
shear modes can be explained by the distinct symmetry of the two trilayer
allotropes. The strong stacking-order dependence was not found in the
layer-breathing modes, and thus represents a unique characteristic of the shear
modes.
