Unconventional pressure dependence of the superfluid density in the nodeless topological superconductor $\alpha$-PdBi${}_2$

We investigated the superconducting properties of the topological superconductor $\alpha$–PdBi${}_2$ at ambient and external pressures up to 1.77~GPa using muon spin rotation ($\mu$SR) experiments. The ambient pressure measurements evince a fully gapped $s$-wave superconducting state in the bulk of the specimen. AC magnetic susceptibility and $\mu$SR measurements manifest a continuous suppression of $T_{\mathrm{c}}$ with increasing pressure. In parallel, we observed a significant decrease of superfluid density by $\sim$20% upon application of external pressure. Remarkably, the superfluid density follows linear relation with $T_{\mathrm{c}}$ which was found before in some unconventional topological superconductors and hole doped cuprates. This finding signals a possible crossover from BEC to BCS in $\alpha$–PdBi${}_2$.