Taylor series of Landauer conductance

Abstract

In this paper, we propose a method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in mesoscopic systems. The method is based on the recursive scattering matrix method (RSMM) that permits us to find the scattering matrix of a system from the scattering matrices of its subsystems. Following ideas of automatic differentiation, we determine expressions for the sum, product, inverse, and diagonalization of a matrix Taylor expansion, and use them into the RSMM to find Taylor series of scattering matrices. The method is validated by obtaining the transmission function of atomic chains with site defects and graphene nanoconstrictions. Finally, an analysis of convergence radius and error estimations of these Taylor expansions is presented.