Abstract: We have performed a first-principles density functional theory investigation of the penetration of helium atoms through a graphene monolayer with defects. The relaxation of the graphene layer caused by the incoming helium atoms does not have a strong influence on the height of the energy barriers for penetration. For defective graphene layers, the penetration barriers decrease exponentially with the size of the defects but they are still sufficiently high that very large defects are needed to make the graphene sheet permeable for small atoms and molecules. This makes graphene a very promising material for the construction of nanocages and nanomembranes.

Abstract: The effect of trigonal warping on the transmission of electrons tunneling through potential barriers in graphene is investigated. We present calculations of the transmission coefficient for single and double barriers as a function of energy, incidence angle and barrier heights. The results show remarkable valley-dependent directional effects for barriers oriented parallel to the armchair or parallel to the zigzag direction. These results indicate that electrostatic gates can be used as valley filters in graphene-based devices.

Abstract: We study theoretically the simultaneous effect of regular and random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing in the system due to the disorder. We find that the total disordering of the vortex lattice can occur either in one step or in two steps. For instance, in the limit of weak pinning, a square lattice of pinned vortices is destroyed in two steps. First, elastic chains of depinned vortices appear in the film; but the vortex lattice as a whole remains still pinned by the underlying square array of regular pinning sites. These chains are composed into fractal-like structures. In a second step, domains of totally depinned vortices are generated and the vortex lattice depins from regular array.

Abstract: A perpendicular electric field applied to multilayers of graphene modifies the electronic structure near the K point and may induce an energy gap in the electronic spectrum. This gap is tunable by the gate voltage and its size depends on the number of layers. We use a tight-binding approach to calculate the band structure and include a self-consistent calculation in order to obtain the density of charge carriers. Results are presented for systems consisting of three and four layers of graphene. The effect of the circular asymmetry of the band structure on the gap is critically examined.