Size-dependent enhancement of superconductivity in Al and Sn nanowires: Shape-resonance effect

A shape-dependent superconducting resonance can be expected when an energy level associated with the transverse motion in a wire passes through the Fermi surface. We show that the recently observed width-dependent increase of $T_c$ in Al and Sn nanowires is a consequence of this shape-resonance effect.

Figure 1

(Color online) The width-dependent relative gap ${\Delta }_{\sigma }∕{\Delta }_{\mathrm{bulk}}$ (a) and the relative mean density of the single-electron states in the Debye window $N_D∕[2\hslash {\omega }_{D}VN(0\left)\right]$ (b) versus ${\sigma }^{1∕2}$ for cylindrical Al nanowires with cross section $\sigma$ at zero temperature.

Figure 2

(Color online) Critical temperature $T_{c,\sigma }∕T_{c,\mathrm{bulk}}$ versus the square root of the cross section of a cylindrical Al nanowire. Symbols are the experimental results from Refs. 4, 5, 13, the solid curve is a guide to the eye and indicates the general trend of the experimental results. Inset: the same dependence but in the small-$\sigma$ region.

Figure 3

(Color online) The shape resonances in the relative transition temperature for Al and Sn cylindrical nanowires.