Zener tunneling and localization in small conducting rings

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We study the single-particle properties of an electron in a small one-dimensional conducting ring subject to a large uniform electric field which is generated by a linearly ramped magnetic flux. The adiabatic eigenstates of this system form a complete set of minibands which are separated by gaps determined by the static scattering potential in the ring. At high fields the Zener tunneling transitions between these minibands promote the particles to higher energy states. In spite of the absence of inelastic scattering in this model, D. Lenstra and W. van Haeringen [Phys. Rev. Lett. 57, 1623 (1986)] found a resistive behavior of the electrons which they attributed to the process of phase randomization generated by Zener tunneling between the minibands. We have studied several model systems to investigate the roles of phase randomization and of the energy dependence of the Zener tunneling amplitudes. None of the models studied showed resistive behavior. We find that the process of phase randomization alone (constant Zener tunneling amplitudes) leads to an exponential localization of the electrons in energy space. The addition of energy-dependent Zener tunneling amplitudes weakens the localization. Our main conclusion is that the process of phase randomization leads to localization of the electrons in energy space and not to resistive behavior. © 1988 The American Physical Society.

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Physical Review B

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