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Two-channel resonant tunneling.

We study the conductance of a tunneling junction with two resonant impurities. We show that when the distance between the impurities is of the order of the de Broglie wavelength of an electron in the contacts, the coupling of the impurity states via the continuum of states in the contacts becomes important. If two identical impurities are located in the middle of the barrier, the resonant peak in the conductance, as a function of the Fermi energy, is dramatically narrowed. The resonant peak transforms into a deep minimum if impurity states have different energies or if impurities are shifted from the middle of the barrier. With nonvanishing overlap of the impurity wave functions, the position of the minimum is shifted from the resonance. We also study two-channel resonant tunneling between the edge states in the quantum Hall geometry. We show that for perfect resonance the coupling between the edge states is nonzero only within a narrow interval of magnetic fields.