Superconducting Penetration Depth Through a Van Hove Singularity: Sr${}_2$RuO${}_4$ Under Uniaxial Stress

Abstract

In the unconventional superconductor Sr${}_2$RuO${}_4$, uniaxial stress along the $[100]$ direction tunes the Fermi level through a Van Hove singularity (VHS) in the density of states, causing a strong enhancement of the superconducting critical temperature $T_{\text{c}}$. Here, we report measurements of the London penetration depth $\hat{I}»$ as this tuning is performed. We find that the zero-temperature superfluid density, here defined as $\hat{I}»(0{)}^{-2}$, increases by $\sim$15%, with a peak that coincides with the peak in $T_{\text{c}}$. We also find that the low temperature form of $\hat{I}»(T)$ is quadratic over the entire strain range. Using scanning tunneling microscopy, we find that the gap increases from $\hat{I}{”}_0\approx 350\hat{I}¼$eV in unstressed Sr${}_2$RuO${}_4$ to $\hat{I}{”}_0\approx 600\hat{I}¼$eV in a sample strained to near the peak in $T_c$. With a nodal order parameter, an increase in the superconducting gap could bring about an increase in the superfluid density through reduced sensitivity to defects and through reduced non-local effects in the Meissner screening. Our data indicate that tuning to the VHS increases the gap throughout the Brillouin zone, and that non-local effects are likely more important than reduced scattering.