Local Measurement of the Eliashberg Function of Pb Islands: Enhancement of Electron-Phonon Coupling by Quantum Well States

Inelastic tunneling spectroscopy of Pb islands on Cu(111) obtained by scanning tunneling microscopy below 1 K provides a direct access to the local Eliashberg function of the islands with high energy resolution. The Eliashberg function describes the electron-phonon interaction causing conventional superconductivity. The measured Eliashberg function strongly depends on the local thickness of the Pb nanostructures and shows a sharp maximum when quantum well states of the Pb islands come close to the Fermi energy. Ab initio calculations reveal that this is related to enhanced electron-phonon coupling at these thicknesses.

Figure 1

(a) STM topography ($800\times 800{\mathrm{nm}}^2$, 1 V, 100 pA) showing Pb islands on the stepped Cu(111) surface after depositing a total amount of 3.8 MLs. The colored surfaces indicate the local thickness whose distribution is given in (b).

Figure 2

(a) Large energy range tunneling conductance spectra (normalized and shifted) of the WL and of a 13 MLs Pb area ($R_T=8\mathrm{M}\mathrm{\Omega }$). While the conductance of the WL is constant, it exhibits a significant decrease at zero bias on the Pb island. ${\mathit{d}}^{2}I/\mathit{d}{U}^2$ spectrum (b) taken on the same position in a smaller bias interval around $E_F$ ($R_T=0.4\mathrm{M}\mathrm{\Omega }$). The scale bar indicates the energy resolution $\mathrm{\Gamma }$. (c) Average of the positive and negative bias side of the ITS spectrum in (b) (dots) in comparison with the previous result for ${\alpha }^{2}F(\omega )$ (line) [3].

Figure 3

(a) Topographic image of a wedge shaped island. The color code of the Pb areas corresponds to the thicknesses given in (b) where the QWSs obtained from the $\mathit{d}I/\mathit{d}U$ spectra ($R_T=0.1\mathrm{G}\mathrm{\Omega }$) at an arbitrary location on the Pb areas of different heights are shown. (d) Average of the positive and negative bias side of the ${\mathit{d}}^{2}I/\mathit{d}{U}^2$ spectra ($R_T=0.4\mathrm{M}\mathrm{\Omega }$) recorded at the same locations as in (b). The intensity of ${\alpha }^{2}F(\omega )$ increases considerably on the 11 MLs high Pb area as can also be seen from the ${\mathit{d}}^{2}I/\mathit{d}{U}^2$ map of the same island taken at 8 mV (c). QWSs (e), and ${\mathit{d}}^{2}I/\mathit{d}{U}^2$ spectra (f) of 17 to 22 MLs.

Figure 4

Theoretical calculation. (a) QWS in the electronic DOS. (b) Eliashberg function. The numbers indicate the corresponding values of $\lambda$.