Anomalous superfluid density in quantum critical superconductors

TL;DR

This study reveals that in quantum critical superconductors, the superfluid density exhibits an unusual 3/2 power-law temperature dependence, likely due to quantum fluctuation-induced renormalization near the nodes of the energy gap.

Contribution

It demonstrates a universal anomalous superfluid density behavior in various quantum critical superconductors and proposes a theoretical explanation involving Fermi velocity renormalization near gap nodes.

Findings

Superfluid density shows a 3/2 power-law temperature dependence.

The behavior is universal across different classes of quantum critical superconductors.

Quantum fluctuations near the nodes affect low-energy properties.

Abstract

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.