Fate of the Hebel-Slichter peak in superconductors with strong antiferromagnetic fluctuations

We show that magnetic fluctuations can destroy the Hebel-Slichter peak in conventional superconductors. The Hebel-Slichter peak has previously been expected to survive even in the presence of strong electronic interactions. However, we show that antiferromagnetic fluctuations suppress the peak at q=0 in the imaginary part of the magnetic susceptibility χ′′+−(q,ω), which causes the Hebel-Slichter peak. This is of general interest as in many materials superconductivity is found near a magnetically ordered phase, and the absence of a Hebel-Slichter peak is taken as evidence of unconventional superconductivity in these systems. For example, no Hebel-Slichter peak is observed in the κ−(BEDT−TTF)2X organic superconductors but heat capacity measurements have been taken to indicate s-wave superconductivity. Similarly, experiments indicate nodeless superconductivity in many iron pnictide superconductors which exhibit no peak in the relaxation rate. If antiferromagnetic fluctuations destroy the putative Hebel-Slichter peak in organic superconductors, then the peak should be restored by applying a pressure, which is known to suppress antiferromagnetic correlations in these materials.