Boundary conditions, the critical conductance distribution, and one-parameter scaling

Abstract

We study the influence of boundary conditions transverse to the transport direction for disordered mesoscopic conductors both at the Anderson metal-insulator transition and in the metallic regime. We show that the boundary conditions strongly influence the conductance distribution exactly at the metal-insulator transition and we discuss implications for the standard picture of one-parameter scaling. We show in particular that the scaling function that describes the change of conductance with system size depends on the boundary conditions from the metallic regime up to the metal-insulator transition. An experiment is proposed that might test the correctness of the one-parameter scaling theory.