Quantum Dynamics of Small Josephson Junctions: An Application to Superconductivity in Granular Films
Fisher, Matthew Paul Alejandro
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https://hdl.handle.net/2142/77393
Description
Title
Quantum Dynamics of Small Josephson Junctions: An Application to Superconductivity in Granular Films
Author(s)
Fisher, Matthew Paul Alejandro
Issue Date
1986
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
This thesis is devoted to a study of the quantum dynamics of small Josephson junctions. Of interest are those features of the junction's behavior which depend explicitly on the quantum mechanical nature of the phase difference (phi) between the superconductors.
In Chapters I and II several calculations are described which focus on the junction's DC resistance. A fully quantum mechanical Hamiltonian is employed which incorporates the dissipative effects due to the unpaired electrons by coupling to a bath of harmonic oscillators. It is shown that the model exhibits a novel zero temperature phase transition as a function of the strength of the dissipation. In the low dissipation regime the phase is free to tunnel quantum mechanically and the junction's resistance is finite; in response to an external current, tunnelling induces successive 2(pi) phase slips leading to a finite voltage state. In contrast, in the high dissipation regime, tunnelling is suppressed and the junction behaves as a superconductor carrying current with no resistive losses.
In Chapters III and IV these results are applied in an attempt to explain the recent observation that in ultra-thin Sn films there is apparently a universal normal state sheet resistance above which superconductivity cannot be established. The films are modelled as a random array of superconducting islands linked together by small Josephson junctions. By combining this picture with the calculations for the single junction behavior, a natural explanation for the observed data is presented. Specifically, it is demonstrated that when the sheet resistance is larger than the quantum of resistance, R(,Q) = h/4e('2), quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance agrees quantitatively with the experiment.
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