Two-point Green functions of free Dirac fermions in single-layer graphene ribbons with zigzag and armchair edges

Abstract

Green function technique is a very efficient theoretical tool for the study of dynamical quantum processes in many-body systems. For the study of dynamical quantum processes in graphene ribbons it is necessary to know two-point Green functions of free Dirac fermions in these materials. The purpose of present work is to establish explicit expressions of two-point Green functions of free Dirac fermions in single-layer graphene ribbons with zigzag and armchair edges. By exactly solving the system of Dirac equations with appropriate boundary conditions on the edges of graphene ribbons we derive formulae determining wave functions of free Dirac fermions in above-mentioned materials. Then the quantum fields of free Dirac fermions are introduced, and explicit expressions of two-point Green functions of free Dirac fermions in single-layer graphene ribbons with zigzag and armchair edges are established.