Nonlocal electrodynamics and the penetration depth of superconducting Sr$_2$RuO$_4$

TL;DR

This paper extends the understanding of how nonlocal electrodynamics influence the penetration depth in superconducting Sr$_2$RuO$_4$, comparing theoretical models with experimental data to explore gap structures.

Contribution

It generalizes the quadratic low-temperature change of penetration depth to multiple nodes and compares theoretical predictions with high-precision measurements in Sr$_2$RuO$_4$.

Findings

Both simple $d_{x^2-y^2}$-wave and complex gap structures fit the experimental data.

The study confirms the relevance of nonlocal effects in the penetration depth.

Multiple gap structures with higher harmonics and accidental nodes are consistent with observations.

Abstract

The thermal quasiparticles in a clean type-II superconductor with line nodes give rise to a quadratic low-temperature change of the penetration depth, $\Delta \lambda \sim T^2$, as first shown by Kosztin and Leggett [I. Kosztin and A. J. Leggett, Phys. Rev. Lett. 79, 135 (1997)]. Here, we generalize this result to multiple nodes and compare it to numerically exact evaluations of the temperature-dependent penetration depth in Sr$_2$RuO$_4$ using a high-precision tight-binding model. We compare the calculations to recent penetration depth measurements in high purity single crystals of Sr$_2$RuO$_4$ [J. F. Landaeta et al., arXiv:2312.05129]. When assuming the order parameter to have $\mathrm{B}_{1\mathrm{g}}$ symmetry, we find that both a simple $d_{x^2-y^2}$-wave and complicated gap structures with contributions from higher harmonics and accidental nodes can accommodate the experimental data.