Introducing directionality to Anderson localization: The transport properties of quantum railroads

Abstract

We present a study of the transport properties of a general class of quantum mechanical wave guides: quantum railroads (QRR). These wave guides are characterized by having adiabatic modes that carry current along the wave guide in opposite directions; for example N forward modes and M reverse modes. Anderson localization and the integer quantum Hall effect are characteristic of the disordered N = M and M = 0 cases, respectively. We consider the general case of arbitrary N and M, and show that it can be understood in terms of directed localization. Thus, we unify the theories of Anderson localization and the integer quantum Hall effect and demonstrate how they fit into a broader conceptual framework. We find that in any QRR there are always [Formula: see text] perfectly transmitted effective adiabatic modes with the remainder being subject to multiple scattering and interference effects characteristic of the N = M case.