Fluctuoscopy of Disordered Two-Dimensional Superconductors

Abstract

We revise the long studied problem of fluctuation conductivity (FC) in disordered two-dimensional superconductors placed in a perpendicular magnetic field by finally deriving the complete solution in the temperature-magnetic field phase diagram. The obtained expressions allow both to perform straightforward (numerical) calculation of the FC surface $\delta\sigma_{xx}^{(\mathrm{tot})}(T,H)$ and to get asymptotic expressions in all its qualitatively different domains. This surface becomes in particular non-trivial at low temperatures, where it is trough-shaped with $% \delta\sigma_{xx}^{(\mathrm{tot})}(T,H)<0$. In this region, close to the quantum phase transition, $\delta\sigma_{xx}^{(\mathrm{tot})}(T,H=\mathrm{const})$ is non-monotonic, in agreement with experimental findings. We reanalyzed and present comparisons to several experimental measurements. Based on our results we derive a qualitative picture of superconducting fluctuations close to $H_{\mathrm{c2}}(0) $ and T=0 where fluctuation Cooper pairs rotate with cyclotron frequency $\omega_{c}\sim\Delta_{\mathrm{BCS}}^{-1}$ and Larmor radius $\sim \xi_{\mathrm{BCS}}$, forming some kind of quantum liquid with long coherence length $\xi_{\mathrm{QF}}\gg\xi_{\mathrm{BCS}}$ and slow relaxation ($\tau_{\mathrm{QF}}\gg\hbar\Delta_{\mathrm{BCS}}^{-1}$).