Effect of Spin Fluctuations on Phonon-Mediated Superconductivity in the Vicinity of a Quantum Critical Point
Abstract
We consider an s-wave superconductor in the vicinity of a second-order ferromagnetic (FM) or spin-density-wave (SDW) quantum critical point (QCP), where the superconductivity and magnetism arise from separate mechanisms. The quantum critical spin fluctuations reduce the superconducting Tc. Near a FM QCP, we find that Tc falls to zero as 1/|ln kappa| in 3D and as kappa in 2D, where kappa ~ |J-Jc|nu is the inverse correlation length of the spin fluctuations, and measures the distance |J-Jc| from the quantum critical point. SDW quantum critical fluctuations, on the other hand, suppress Tc to zero as sqrt(kappa) in 2D, and suppress Tc only to a finite value in 3D, producing a cusp of the form (const + |J-Jc|nu).
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