  Layer-layer coupling plays a critical role in defining the physical
properties of few-layer graphene (FLG). With respect to vibrations, the
interlayer coupling is predicted to create a set of N-1 finite frequency,
out-of-plane interlayer modes in N-layer graphene. Unlike the widely studied
in-plane vibrations, the properties of these layer-breathing modes (LBMs) are
defined by the layer-layer interactions. Here we report direct observation of
the distinct LBMs for graphene of thicknesses from 2 to 20 layers through
electronically resonant overtone Raman bands observed in the range of 80 - 300
cm-1. The Raman bands exhibit multi-peak features that are unique for graphene
samples of each layer thickness up to 20 layers. The frequencies of the set of
layer breathing modes for all samples can be described within a simple model of
nearest plane coupling.
