Non-universal Transverse Electron Mean Free Path through Few-layer Graphene.

In contrast to the in-plane transport electron mean-free path in graphene, the transverse mean-free path has received little attention and is often assumed to follow the 'universal' mean-free path (MFP) curve broadly adopted in surface and interface science. Here we directly measure transverse electron scattering through graphene from 0 to 25 eV above the vacuum level both in reflection using Low Energy Electron Microscopy and in transmission using electron-Volt Transmission Electron Microscopy. From this data, we obtain quantitative MFPs for both elastic and inelastic scattering. Even at the lowest energies, the total MFP is just a few graphene layers and the elastic MFP oscillates with graphene layer number, both refuting the 'universal' curve. A full theoretical calculation taking the graphene band structure into consideration agrees well with experiment, while the key experimental results are already reproduced by a simple optical toy model.