Analytic theory of resonant magnetotransport in ballistic quantum conductors

A transparent analytic theory of resonances in quantum-wire junctions has been developed. The effects of the resonances on four-terminal resistances are evaluated exactly for realistic, smoothly tapered junctions of arbitrary symmetry, with and without defects, in the quantum Hall regime. The theory also provides a simple analytic description of resonances in symmetric untapered junctions in excellent quantitative agreement with detailed numerical computations.