Quantum railroads: Introducing directionality to Anderson localization

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Abstract
We present a theory of electron transport in novel disordered waveguides that support different numbers N and M of modes propagating in opposite directions, i.e., ‘‘quantum railroads’’ (QRR). Anderson localization and the integer quantum Hall effect are special cases of our theory. More generally, our analytic results based on scattering matrix theory and our numerical simulations show that disorder results in directed localization in QRR’s. The limiting transmittance of a macroscopic QRR is T=‖N-M‖ in the majority direction but T’=0 in the minority direction.