Fluctuation spectroscopy 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 $\ensuremath{\delta}{\ensuremath{\sigma}}_{xx}^{(\mathrm{tot})}(T,H)$ and to get asymptotic expressions in all its qualitatively different domains. This surface becomes in particular nontrivial at low temperatures, where it is trough-shaped with $\ensuremath{\delta}{\ensuremath{\sigma}}_{xx}^{(\mathrm{tot})}(T,H)<0$. In this region, close to the quantum-phase transition, $\ensuremath{\delta}{\ensuremath{\sigma}}_{xx}^{(\mathrm{tot})}(T,H=\mathrm{const})$ is nonmonotonic, 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 ${H}_{\mathrm{c}2}(0)$ and $T=0$ where fluctuation Cooper pairs rotate with cyclotron frequency ${\ensuremath{\omega}}_{c}\ensuremath{\sim}{\ensuremath{\Delta}}_{\mathrm{BCS}}^{\ensuremath{-}1}$ and Larmor radius $\ensuremath{\sim}$${\ensuremath{\xi}}_{\mathrm{BCS}}$, forming some kind of quantum liquid with long coherence length ${\ensuremath{\xi}}_{\mathit{QF}}\ensuremath{\gg}{\ensuremath{\xi}}_{\mathrm{BCS}}$ and slow relaxation (${\ensuremath{\tau}}_{\mathit{QF}}\ensuremath{\gg}\ensuremath{\hbar}{\ensuremath{\Delta}}_{\mathrm{BCS}}^{\ensuremath{-}1}$).