Impurity-Induced Magnetization of Graphene

We present a model of impurity-induced magnetization of graphene assuming that the main source of graphene magnetization is related to impurity states with a localized spin. The analysis of solutions of the Schrödinger equation for electrons near the Dirac point has been performed using the model of massless fermions. For a single impurity, the solution of Schrödinger’s equation is a linear combination of Bessel functions. We found resonance energy levels of the non-magnetic impurity. The magnetic moment of impurity with a localized spin was accounted for the calculation of graphene magnetization using the Green’s function formalism. The spatial distribution of induced magnetization for a single impurity is obtained. The energy of resonance states was also calculated as a function of interaction. This energy is depending on the impurity potential and the coupling constant of interaction.

Free energy and entropy for an impurity in a periodic background in one dimension

In this paper, we continue our study of periodic lattices formed by delta functions and their derivatives in (1+1) dimensions. Such systems are interesting as allowing for investigation of complicated problems in quite simple terms. Specifically, we consider the free energy of a single impurity in the background of such lattice. After developing the necessary technical tools, we consider as an example a specific case and found that the free energy shows a non monotone behavior as function of the temperature.