Effect of Fluctuations on the NMR Relaxation Beyond the Abrikosov Vortex State

TL;DR

This paper investigates how fluctuations influence NMR relaxation rates in 2D superconductors near the transition, revealing competing effects of fluctuation Cooper pairs and quantum processes, with results varying across different magnetic field and temperature regimes.

Contribution

It provides a comprehensive analysis of fluctuation effects on NMR relaxation beyond the Abrikosov vortex state, highlighting the changing nature of fluctuations along the $H_{c2}$ line and identifying a temperature threshold where the Maki-Thompson process becomes ineffective.

Findings

Relaxation rate decreases due to fluctuation Cooper pairs at high temperatures and low fields.

Quantum Maki-Thompson process can increase relaxation rate in low fields.

Below $T^*_0 \\approx 0.6T_{c0}$, the MT process is suppressed, reducing fluctuation effects.

Abstract

The effect of fluctuations on the nuclear magnetic resonance (NMR) relaxation rate, $W$, is studied in a complete phase diagram of a 2D superconductor above the upper critical field line $H_{c2}(T)$ . 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 result of suppression of quasi-particle density of states (DOS) due to formation of fluctuation Cooper pairs (FCP). 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 $l_{\phi }$ 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 $H_{c2}$ from the thermal long-wavelength type in weak magnetic fields to the clusters of rotating FCP in fields comparable to $H_{c2}$. We find that below the well-defined temperature $T^*_0\approx 0.6T_{c0}$, the MT process becomes ineffective even in absence of intrinsic pair-breaking. The small scale of FCP rotations ($\xi_{xy}$) in so high fields impedes formation of long (<$l_{\phi }$) 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 quasi-particle DOS, analogously to the Abrikosov vortex phase below the $H_{c2}$ line.