Quantum railroads and directed localization at the juncture of quantum Hall systems

TL;DR

This paper explains recent experimental observations of electron transfer in quantum Hall systems through the concept of directed localization in quantum railroads, unifying quantum Hall effect and Anderson localization.

Contribution

It introduces the concept of directed localization in quantum railroads and links it to recent experimental results, providing a unified theoretical framework.

Findings

Experimental evidence of quantum railroad behavior

Unification of quantum Hall effect and Anderson localization

Proposed tests for further validation

Abstract

The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called "quantum railroads" (QRR). Here we explain the surprising results of recent measurements by Kang et al. [Nature 403, 59 (2000)] of electron transfer between edges of two-dimensional electron systems and identify experimental evidence of QRR's in the general, but until now entirely theoretical, DL regime that unifies the QHE and AL. We propose direct experimental tests of our theory.