Single-gap Isotropic $s-$wave Superconductivity in Single Crystals AuSn₄

London, λL (T), and Campbell, λC (T), penetration depths were measured in single crystals of a topological superconductor candidate AuSn₄. At low temperatures, λL (T) is exponentially attenuated and, if fitted with the power law, λ(T) ~ Tⁿ, gives exponents $n>4$, indistinguishable from the isotropic single $s-$wave gap Bardeen-Cooper-Schrieffer (BCS) asymptotic. The superfluid density fits perfectly in the entire temperature range to the BCS theory. The superconducting transition temperature, Tc = 2.40 ± 0.05\:K, does not change after 2.5 MeV electron irradiation, indicating the validity of the Anderson theorem for isotropic $s-$wave superconductors. Campbell penetration depth before and after electron irradiation shows no hysteresis between the zero-field cooling (ZFC) and field cooling (FC) protocols, consistent with the parabolic pinning potential. Interestingly, the critical current density estimated from the original Campbell theory decreases after irradiation, implying that a more sophisticated theory involving collective effects is needed to describe vortex pinning in this system. In general, our thermodynamic measurements strongly suggest that the bulk response of the AuSn₄ crystals is fully consistent with the isotropic $s-$wave weak-coupling BCS superconductivity.