Novel quantum hall phenomena in arrays of quantum dots

Abstract

A theory of two-dimensional arrays of coupled quantum dots in transverse magnetic fields is described. These systems are expected to exhibit exotic Hofstadter-like spectral and transport properties at modest magnetic fields ≥1 Tesla. They are shown to support intricate spectra of normal and “counter-rotating” magnetic edge states. The edge states are predicted to give rise to positive, negative and fractional quantum Hall plateaus in ballistic arrays coupled to ideal reservoirs. The fractions differ in value and origin from the usual fractional quantum Hall effect. In non-ballistic, macroscopic systems we predict integer positive and negative quantum Hall plateaus only, as in earlier theories of electrons in periodic 2D systems. This is understood in terms of “directed localization”, a generalization of Anderson localization to disordered waveguides supporting different numbers of modes propagating in opposite directions. The sample quality requirements for observing these effects are found to be very stringent.