Electronic properties of double quantum wires in a magnetic field

Abstract: The electronic properties of double quantum wires (DQW) in presence of a per-pendicular magnetic field are investigated theoretically. Analytical solution of theproblem of electronic spectrum is obtained in the framework of the two-subbandmodel for the DQW. It is shown, that in sufficiently strong magnetic fields, thespectrum develops the partial energy gap, where only one of the two modes remainspropagating while the other becomes evanescent. As a result of the magnetic-field-induced localization of the propagating states with opposite velocities in the oppositewires, electron backscattering in the gap is strongly suppressed. The possibility ofthe effect when the DQW behaves as a ballistic conductor or an Anderson insulatordepending on whether the Fermi energy lies inside or outside the gap, is suggested.The problem of electron scattering on one, two, an an array of random elasticscatterers in the DQW is solved rigorously. It is shown that evanescent states playvery important role in the electron dynamics at energies in the partial energy gap. Inparticular, they are responsible for the giant enhancement of backscattering from apair of defects located in the opposite wires at a small distance from each other. Thiseffect produces a significant correction to the localization length in the disorderedDQW. The strong dependence of the localization length on the intra- and inter-wirespatial correlations in the potential of disorder is predicted. In the scattering ofan electron on a single impurity, the higher-order scattering processes are shown togive rise to the resonances of scattering. The resonances, i. e., quasi-bound states, areformed for both attractive and repulsive potentials of impurity. Similar resonancesappear in the spectrum of two interacting particles in the DQW.

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