Resistivity of Inhomogeneous Superconducting Wires
Abstract
We study the contribution of quantum phase fluctuations in the superconducting order parameter to the low--temperature resistivity $\rho(T)$ of a dirty and inhomogeneous superconducting wire. In particular, we account for random spatial fluctuations of arbitrary size in the wire thickness. For a typical wire thickness above the critical value for superconductor--insulator transition, phase--slips processes can be treated perturbatively. We use a memory formalism approach, which underlines the role played by weak violation of conservation laws in the mechanism for generating finite resistivity. Our calculations yield an expression for $\rho(T)$ which exhibits a smooth crossover from a homogeneous to a ``granular'' limit upon increase of $T$, controlled by a ``granularity parameter'' $D$ characterizing the size of thickness fluctuations. For extremely small $D$, we recover the power--law dependence $\rho(T)\sim T^\alpha$ obtained by unbinding of quantum phase--slips. However in the strongly inhomogeneous limit, the exponent $\alpha$ is modified and the prefactor is {\em exponentially enhanced}. We examine the dependence of the exponent $\alpha$ on an external magnetic field applied parallel to the wire. Finally, we show that the power--law dependence at low $T$ is consistent with a series of experimental data obtained in a variety of long and narrow samples. The values of $\alpha$ extracted from the data, and the corresponding field dependence, are consistent with known parameters of the corresponding samples.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2007
- DOI:
- 10.48550/arXiv.0712.3241
- arXiv:
- arXiv:0712.3241
- Bibcode:
- 2007arXiv0712.3241V
- Keywords:
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- Condensed Matter - Superconductivity;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 10 pages, 3 colored figures