Introducing Directionality to Anderson Localization: The Transport Properties of Quantum Railroads

TL;DR

This paper investigates the transport properties of Quantum Railroads, revealing a new phenomenon called directed localization, where the difference in mode directions determines transmission characteristics.

Contribution

It introduces the concept of directed localization in quantum waveguides with asymmetric modes, extending understanding beyond Anderson localization and quantum Hall effects.

Findings

|N-M| modes are perfectly transmitted in QRRs

Remaining modes experience multiple scattering and interference

Directed localization depends on the difference in forward and reverse modes

Abstract

We present a study of the transport properties of a general class of quantum mechanical waveguides: Quantum Railroads (QRR). These waveguides are characterised by having a different number of adiabatic modes which carry current in one direction along the waveguide to the opposite direction; for example N forward modes and M reverse modes. Just as Anderson localization is a characteristic of the disordered N=M case and the quantum Hall effect a characteristic of the M=0 case we find that a mixed effect, DIRECTED localization, is a characteristic of QRR's. We find that in any QRR there are always |N-M| perfectly transmitted effective adiabatic modes with the remainder being subject to multiple scattering and interference effects characteristic of the N=M case.