Two dimensional (2D) crystals are attracting interest in materials science as they can be the building blocks of more complex three dimensional (3D) hetero-structures with properties tailored to suit specific demands. On the other side, emerging facts and concepts about 2D materials can give new insight into the electronic properties of materials that have been widely investigated and applied, such as graphite. It is therefore an important issue, in both basic research and applications, to investigate if and how these peculiar properties of 2D crystals are reflected in 3D derived systems.
In this work, we present state of the art density functional theory (DFT) calculations [1] of the electronic band structure of graphene (1 to 3 layers) and graphite, focusing on the unoccupied energy levels up to 40 eV above the Fermi level. Particular attention is given to those one-electron states of graphene, below and above the continuum threshold, whose wavefunctions are less localized on the plane showing an extended tail into the vacuum: the so-called image potential states and the recently discovered scattering resonances [2,3].
We observe that the discrete states of graphene, below and above the vacuum level, are very sensitive to (and strongly interact with) the environment surrounding the plane. When different layers are assembled, these states hybridize, giving rise to more complex states, which evolve with increasing the number of layers. Such an evolution leads to highly dispersive states vs the one-electron out-of-plane wave-vector in graphite (,) that are caught in Low energy electron diffraction and in electron emission experiments.
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- V.U. Nazarov, E.E. Krasovskii, V.M. Silkin, Phys. Rev. B 87, 041405(R) (2013).
- E. Kogan and V. U. Nazarov, Phys. Rev. B 85, 115418 (2012).
Optical properties of nanostructures , Spectroscopy , Carbon & graphene nanostructures
