We report measurements of the in-plane London penetration depth λ in single crystals of the α-PdBi2 superconductor -the α-phase counterpart of the putative topological superconductor β-PdBi2, down to 0.35 K using a high-resolution tunnel-diode-based technique. Both λ and superfluid density ρs exhibit an exponential behavior for T ≤ 0.35Tc, with ∆(0)/kBTc ∼2.0, ∆C/γTc∼2.0 and λ(0)∼140 nm, showing that α-PdBi2 is a moderately-coupling, fully-gapped superconductor. The values of ∆(0) and ∆C/γTc are consistent with each other via strong-coupling corrections.

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