Diffraction, phase breaking, and Hall anomalies in quantum dots

We present a theory of the Hall effect in a quantum dot coupled to Hall and current leads by narrow constrictions. A magnetic-diffraction effect is described which results in a series of deep minima in the Hall resistance persisting temperatures T>1 K, robustness that is unique among mesoscopic quantum interference phenomena. At higher T, phase-breaking casues an anomalous ‘‘last’’ Hall plateau at ${\mathit{R}}_{\mathit{H}}$=h/4${\mathit{e}}^2$ and, at higher B, a plateau near the single-mode quantum Hall value ${\mathit{R}}_{\mathit{H}}$=h/2${\mathit{e}}^2$. We explain the surprising behavior of the Hall resonances observed by Ford et al. (preceding paper) in quantum-wire junctions.