Fluctuation conductivity of disordered superconductors in magnetic fields

We calculate fluctuation corrections to the longitudinal conductivity of disordered superconductors subject to an external magnetic field. We derive analytic expressions that are valid in the entire metallic part of the temperature–magnetic field phase diagram as long as the effect of the magnetic field on the spin degrees of freedom of the electrons may be neglected. Our calculations are based on a kinetic equation approach. For the special case of superconducting films and wires in parallel magnetic fields, we perform a detailed comparison with results that were previously obtained with diagrammatic perturbation theory in the imaginary-time formalism. As an application, we study the fluctuation conductivity of films in tilted magnetic fields with a special focus on the low-temperature regime. We present a detailed discussion of the phenomenon of the nonmonotonic magnetoresistance and find that it displays a pronounced dependence on the tilting angle.

Figure 1

A sketch of the system under study. A superconducting film of thickness $d$ is penetrated by a magnetic field of magnitude $B$ at an angle $\theta$.

Figure 2

Phase diagram of the film in a tilted magnetic field at zero temperature. The diagram is parametrized by parameters $h$ and $z$, illustrated by lines of constant $h$ (solid line) and constant $z$ (dashed line). SC denotes the region of superconductivity. Regions I and II refer to the asymptotic regions in which we evaluate the corrections to conductivity. They are separated by the line $h=2/(1+z)$. The sharp angular dependence of the negative correction to conductivity discussed below is a result of the pinching of region II near $B_{c\parallel }$.

Figure 3

The correction to conductivity of a disordered film at very low temperatures ($T=0.005T_{c0}$, $d/{\xi }_0=0.3$). The transition is approached by tuning the magnitude of the magnetic field at a fixed angle $\theta$. When one tilts the angle starting from the perpendicular magnetic field case, the dominant effect is a reduction of the negative correction to conductivity. When tilting further towards parallel fields, a second effect sets in, namely, a sudden decrease of the thermal contribution. This effect becomes visible mainly for small $h$.