Spatially Dependent Inelastic Tunneling in a Single Metallofullerene

We have measured the elastic and inelastic tunneling properties of isolated $\mathrm{Gd}@{\mathrm{C}}_{82}$ molecules on Ag(001) using cryogenic scanning tunneling spectroscopy. We find that the dominant inelastic channel is spatially well localized to a particular region of the molecule. Ab initio pseudopotential density-functional theory calculations indicate that this channel arises from a vibrational cage mode. We further show that the observed inelastic tunneling localization is explained by strong localization in the molecular electron-phonon coupling to this mode.

Figure 1

Constant current topographs ($65\AA \times 65\AA$) of two $\mathrm{Gd}@{\mathrm{C}}_{82}$ molecules alongside a ${\mathrm{C}}_{60}$ reference molecule taken at (a) 0.1 V, 1 nA and (b) 2.0 V, 1 nA.

Figure 2

$dI/dV$ spectra taken at different points on a single $\mathrm{Gd}@{\mathrm{C}}_{82}$ molecule (points shown in inset). Inset shows a constant current topograph ($35\AA \times 35\AA$) of $\mathrm{Gd}@{\mathrm{C}}_{82}$ overlaid with the best fit ${\mathrm{C}}_{82}$ cage orientation. (1)–(6) Energy-resolved spectral maps ($35\AA \times 35\AA$) of molecular resonances seen at (1) $-0.85\mathrm{V}$, (2) 0.10 V, (3) 0.65 V, (4) 1.00 V, (5) 1.32 V, and (6) 1.66 V, respectively. Tip stabilization parameters: $V=2.0\mathrm{V}$ and $I=0.3\mathrm{nA}$. The pink spectrum (marked $+3.5\AA$) and spectral maps (1) and (2) were acquired after bringing the tip 3.5 Å closer to the molecule.

Figure 3

(a) $d^{2}I/{dV}^2$ spectra taken at a single point in the upper part of the $\mathrm{Gd}@{\mathrm{C}}_{82}$ molecule shown in Fig. 2 (black line) and on the bare Ag(001) surface (red line). (b) Spatial map ($35\AA \times 35\AA$) of the $d^{2}I/{dV}^2$ inelastic signal at 60 mV. (c) Spatial map of the $d^{2}I/{dV}^2$ reference signal at 80 mV.

Figure 4

(a) Theoretical vibrational spectrum for an isolated ${\mathrm{C}}_{82}$ molecule charged with four electrons is shown as black vertical lines. Red vertical lines show the electron-phonon coupling between each phonon mode and the ${\mathrm{C}}_{82}$ electronic state at $E_{\mathrm{F}}$. The dotted curve is the experimental inelastic tunneling signal. (b) Simulated inelastic tunneling map for the dominant phonon mode at 52 mV (c) Spatial map of the magnitude of the bare atomic displacements of the dominant phonon mode (broadened by 1.0 Å). The color scales used in Figs. 3, 4 are identical and represent standard deviations of the measured or computed on-molecule signal above the off-molecule background.