Tip-induced superconductivity enhancement in single-crystalline PdSb by point-contact spectroscopy

We report our mechanical point-contact spectroscopy (MPCS) study on single-crystalline superconductor PdSb with ${T}_{c}\ensuremath{\sim}$ 1.32 K and ${\ensuremath{\mu}}_{0}{H}_{c2}(0)\ensuremath{\sim}$ 900 Oe, whose ${T}_{c}$ changes very slightly against hydrostatic pressure below 2.5 GPa. For MPCS with a soft Au tip, the Andreev reflection signals suggest the same superconducting temperature ${T}_{c}$ as in the pristine PdSb crystal and the conductance curves show a fully gapped behavior, yielding a superconducting gap value of ${\mathrm{\ensuremath{\Delta}}}_{0}=$ 0.23 meV with $2{\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}{T}_{c}\ensuremath{\sim}$ 4.25 in the strong-coupling regime. However, for MPCS with a hard W tip, an enhanced superconducting ${T}_{c}$ can be observed with a concomitant increase in the superconducting gap $\mathrm{\ensuremath{\Delta}}$ in a linear relation of 0.109 meV/kelvin, whereas $2{\mathrm{\ensuremath{\Delta}}}_{0}/{k}_{\mathrm{B}}{T}_{c}$ decreases from 4.25 to 3.5 in a negative correlation with ${T}_{c}$. From first-principles calculations, we observe a Lifshitz transition related to Pd-$4{d}_{{z}^{2}}$ orbitals under uniaxial pressure, which is absent under hydrostatic pressure. Such Lifshitz transition results in an enhanced density of states near the Fermi level $n({E}_{F})$, which is in line with the enhanced ${T}_{c}$. In addition, a soft phonon mode at $H$ is hardened under uniaxial pressure, suggesting a reduced coupling strength in this case. Such local strain effect provides a natural explanation for our MPCS results on PdSb.