Quantum dynamics of small Josephson junctions: an application to superconductivity in granular films

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 <1> between the superconductors. In Chapters I and IT 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 21t 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 m and N 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 ftlms 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, Rq=h/4e2 , quantum tunnelling of the phase between neighboring islands drives the film normal. This value of the universal resistance· agrees quantitatively with the experiment

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Fisher, Matthew Paul Alejandro

Contributors dc:contributor

• Leggett, Anthony J.

• quantum dynamics
• small Josephson functions
• superconductors

Statement dc:rights

• 1986 Matthew Paul Alejandro Fisher

Language dc:language

en

Identifier

978711

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/25250