Single-gap Isotropic s-wave Superconductivity in Single Crystals AuSn_4

London, λ_L (T), and Campbell, λ_C (T), penetration depths were measured in single crystals of a topological superconductor candidate AuSn_4. At low temperatures, λ_L (T) is exponentially attenuated and, if fitted with the power law, λ(T) ∼ T^n, 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, T_c = 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 AuSn_4 crystals is fully consistent with the isotropic s-wave weak-coupling BCS superconductivity.