A theoretical model for estimating the vacancies produced in graphene by irradiation

The award of the Nobel Prize of Physics 2010 to the scientists that isolated graphene is a clear evidence of the great interest that this system has raised among the physicists. This quasi-two-dimensional material, whose electrons behave as massless Dirac particles, presents sui generis properties that seem very promising for diverse practical applications. At the same time, the system poses new theoretical challenges for the scientists of very different branches, from Material Science to Relativistic Quantum Mechanics. A topic of great actuality in graphene researches is the search of ways to control the number and distribution of the defects in its crystal lattice, in order to achieve certain physical properties. One of these ways can be the irradiation with different kind of particles. However, the irradiation processes in two-dimensional systems have been insufficiently studied. The classic models of interaction of the radiation with solids are based on three-dimensional structures, for what they should be modified to apply them to graphene. In the present work we discuss, from the theoretical point of view, the features of the processes that happen in the two-dimensional structure of monolayer graphene under irradiation with different kinds of particles. In that context, some mathematical expressions that allow to estimate the concentration of the vacancies created during these processes are presented. We also discuss the possible use of the information obtained from the model to design structures of topological defects with certain elastic deformation fields, as well as their influence in the electronic properties. (Author)