Anomalous superfluid density in quantum critical superconductors

When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these “quantum critical” superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T c often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T c is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T -linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such “nodal criticality” may have an impact on low-energy properties of quantum critical superconductors.