Anomalous Scaling of the Penetration Depth in Nodal Superconductors

TL;DR

This paper investigates how quantum critical fluctuations influence the temperature dependence of penetration depth in nodal superconductors, revealing non-universal logarithmic corrections linked to symmetry reductions and comparing findings with experimental data.

Contribution

It provides a renormalization group analysis showing how symmetry-breaking quantum critical fluctuations cause non-universal corrections to penetration depth scaling in 2D nodal superconductors.

Findings

Logarithmic corrections depend on velocity anisotropy ratio.

YBa2Cu3O6.95 is near a vertical nematic QCP.

CeCoIn5 is near a diagonal nematic QCP.

Abstract

Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group calculation for the problem of two dimensional superconductors with point nodes, we show that quantum critical fluctuations associated with point group symmetry reduction result in non-universal logarithmic corrections to the $T$-dependence of the PD. The resulting apparent power law depends on the bare velocity anisotropy ratio. We then compare our results to data sets from two distinct nodal superconductors: YBa$_2$Cu$_3$O$_{6.95}$ and CeCoIn$_5$. Considering all symmetry-lowering possibilities of the point group of interest, $C_{4v}$, we find our results to be remarkably consistent with YBa$_2$Cu$_3$O$_{6.95}$ being near vertical nematic QCP, and CeCoIn$_5$ being near diagonal nematic QCP. Our results motivate search for diagonal nematic fluctuations in CeCoIn$_5$.