Nonlocal electrodynamics and the penetration depth of superconducting Sr_2RuO_4

The thermal quasiparticles in a clean type-II superconductor with line nodes give rise to a quadratic low-temperature change of the penetration depth, Δλ∼ 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_2RuO_4 using a high-precision tight-binding model. We compare the calculations to recent penetration depth measurements in high purity single crystals of Sr_2RuO_4 [J. F. Landaeta et al., arXiv:2312.05129]. When assuming the order parameter to have B_1g 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.