Effect of fluctuations on the NMR relaxation beyond the Abrikosov vortex state

The effect of fluctuations on the nuclear magnetic resonance (NMR) relaxation rate W=T1-1 is studied in a complete phase diagram of a two-dimensional superconductor above the upper critical field line Hc2(T). In the region of relatively high temperatures and low magnetic fields, the relaxation rate W is determined by two competing effects. The first one is its decrease in the result of suppression of the quasiparticle density of states (DOS) due to formation of fluctuation Cooper pairs (FCPs). The second one is a specific, purely quantum relaxation process of the Maki-Thompson (MT) type, which for low field leads to an increase of the relaxation rate. The latter describes particular fluctuation processes involving self-pairing of a single electron on self-intersecting trajectories of a size up to phase-breaking length ? which becomes possible due to an electron spin-flip scattering event at a nucleus. As a result, different scenarios with either growth or decrease of the NMR relaxation rate are possible upon approaching the normal-metal-type-II superconductor transition. The character of fluctuations changes along the line Hc2(T) from the thermal long-wavelength type in weak magnetic fields to the clusters of rotating FCPs in fields comparable to Hc2(0). We find that below the well-defined temperature T0*?0.6Tc0, the MT process becomes ineffective even in the absence of intrinsic pair breaking. The small scale of the FCP rotations ?xy in such high fields impedes formation of long (?) self-intersecting trajectories, causing the corresponding relaxation mechanism to lose its efficiency. This reduces the effect of superconducting fluctuations in the domain of high fields and low temperatures to just the suppression of quasiparticle DOS, analogous to the Abrikosov vortex phase below the Hc2(T) line.