Green's function in form of Bloch eigenmodes in tight binding representation

Abstract

Two dimensional structures, such as graphene ribbons, are important for the future nanoelectronics. The conductances of such complex nanostructures are determined by their transmission probabilities. Usually the transmission is calculated by Green's function technique and scattering matrix approach. Both methods are pertinent to each other via Fish-Lee relationship. Alternatively, a representation transformation can reduce the difficulties for expressing Green's functions. In this work we used Bloch eigenmodes to construct Green's functions and developed the method to be suitable for structures composed of finite length of ribbons and demonstrated the use of this method to analytic expressions in one dimensional structure. In terms of Bloch eigenmodes the Ando's scattering matrices are restored. We also proved the equivalence of Green's function and scattering matrix methods in multi-ribbon structures. In the end a numerical example of superlattice is presented to verify the approach developed in this work.