Global critical temperature in disordered superconductors with weak multifractality

• Published in: Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2015-11, Vol.92 (17), Article 174526
• Main Authors: Mayoh, James, García-García, Antonio M.
• Format: Article
• Language: English
• Subjects: Aluminum; Critical temperature; Energy gap; Inhomogeneity; Mathematical analysis; Order parameters; Superconductors; Transition temperature (superconductivity)
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.92.174526

There is growing evidence that a key feature of sufficiently disordered superconductors is the spatial inhomogeneity of the order parameter. However, not much is known analytically about the impact of the inhomogeneity on the global critical temperature that signals the onset of resistance in the superconductor. Here we address this problem in the experimentally relevant case of disordered conventional superconductors characterized by weak multifractality such as quasi-two-dimensional thin films. We compute analytically the superconducting energy gap, the temperature at which it vanishes, and the energy dependence and spatial distribution of the order parameter. The latter is found to be log normal. The global critical temperature, computed by percolation techniques, is much smaller than the temperature at which the energy gap vanishes. We show that disorder might enhance superconductivity but only for very weakly coupled superconductors, such as Al, and for relatively weak phase fluctuations. These results are consistent with experiments where enhancement of the critical temperature is observed in Al thin films but not in more strongly coupled materials.