Width and Magnetic Field Dependence of Transition Temperature in Ultranarrow Superconducting Wires

Abstract

We calculate the transition temperature in ultranarrow superconducting wires as a function of wire width, resistance and applied magnetic field. We compare the results of first-order perturbation theory and the non-perturbative resummation technique developed by Oreg and Finkel'stein. The latter technique is found to be superior as it is valid even in the strong disorder limit. In both cases the predicted additional suppression of the transition temperature due to the reduced dimensionality is strongly dependent upon the boundary conditions used. When we use the correct (zero-gradient) boundary conditions, we find that theory and experiment are consistent, although more experimental data is required to verify this systematically. We calculate the magnetic field dependence of the transition temperature for different wire widths and resistances in the hope that this will be measured in future experiments. The predicted results have a rich structure - in particular we find a dimensional crossover which can be tuned by varying either the width of the wire or its resistance per square.

12 pages, 1 table, 7 figures. The changes made to the paper are ones of emphasis. The comparison between theory and experiment has been altered, and detailed comparisons of various approximations have been omitted, although the results are summarised in the paper. Much more emphasis has been placed on the new predictions of the effect of an applied magnetic field on transition temperature in wires (Figs. 5-7)

References in corpus (4)

• Quantum suppression of superconductivity in ultrathin nanowires
• Suppression of $\bbox{T_c}$ in superconducting amorphous wires
• The Upper Critical Field in Disordered Two-Dimensional Superconductors
• Effect of Magnetic Impurities on Suppression of the Transition Temperature in Disordered Superconductors

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