Nucleation and Enhancement of Superconductivity under Tip-Induced Strain Fields

A metallic point contact formed on a non-superconducting or weakly superconducting material often nucleates or enhances superconductivity confined under the contact. However, no unified theoretical description of the phenomenon exists. We show that the spatially inhomogeneous, predominantly uniaxial nature of the stress field under a point contact is fundamental for such tip-induced and tip-enhanced superconductivity (TISC/TESC). We also show that the coupling of such a stress field to the electronic structure can be estimated through an experimentally measurable uniaxial coupling scale $C^{\mathrm{exp}}$. Combining Hertzian contact mechanics with a Ginzburg-Landau variational analysis, we derive a criterion for the nucleation of TISC/TESC and determine $C^{\mathrm{exp}}$ for twenty-one materials. For topological semimetals with ungapped band crossings, the framework explains observed critical temperatures with no free parameters and for all others, $C^{\mathrm{exp}}$ provides a direct experimental determination of the uniaxial strain sensitivity and a target scale for microscopic theories.The work predicts TISC in elemental Sb and Y with $T_c \approx 2.8$\,K and $T_c \approx 12$\,K respectively.