  When a second-order magnetic phase transition is tuned to zero temperature by
a non-thermal 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 exhibit, unlike the expected $T$-linear dependence, an anomalous
3/2 power-law temperature dependence over a wide temperature range. We propose
that this non-integer power-law can be explained if a strong renormalization of
effective Fermi velocity due to quantum fluctuations occurs only for momenta
$\bm{k}$ close to the nodes in the superconducting energy gap $\Delta(\bm{k})$.
We suggest that such `nodal criticality' may have an impact on low-energy
properties of quantum critical superconductors.
