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We present a new formulation to calculate the electric conductance ofmesoscopic conductors by utilizing the singular value decomposition, which is amathematical technique to manipulate matrices. Our formulation is useful intreating conductors with rather complicated atomic structures, for which naiverecursion formula is cumbersome. It also has an advantage in scaling up thecalculation by using parallel computation, which potentially allows us thereal-scale calculations at the atomic level. On the other hands, the effects ofelectron-electron interactions are hard to be treated within this framework,since it depends crucially on the linearity of the system. In this paper, westudy graphene nanoribbons with external leads for a simple example.

A Numerical Formulation to Calculate the Conductance of Mesoscopic Conductors Using Singular Value Decomposition