Symmetry Dependence of Vibration-Assisted Tunneling

We present spatially resolved vibronic spectroscopy of individual pentacene molecules in a double-barrier tunneling junction. It is observed that even for this effective single-level system the energy dissipation associated with electron attachment varies spatially by more than a factor of 2. This is in contrast to the usual treatment of electron-vibron coupling in the Franck-Condon picture. Our experiments unambiguously prove that the local symmetry of initial and final wave function determines the dissipation in electron transport.

Figure 1

Differential conductance spectroscopy on different insulating films. (a)–(c) $dI/dV$ curves acquired on pentacene on Xe, NaCl, and RbI, respectively. Spatial positions are indicated in (e). Dashed gray lines indicate voltages of the elastic peak and two vibronic peaks, respectively. Inset in (a) shows spectra on Xe for a larger voltage range. (d) The centroid of spectra taken along the long axis of the molecule [indicated by the line in (e)]. For Xe reorganization energies $\lambda$ are indicated for positions at the end and the center. (e) STM image on Xe ($I=0.2\mathrm{pA}$, $V=2.2\mathrm{V}$).

Figure 2

Spatial maps of elastic and vibration-assisted contributions on RbI. Data have been constructed from $63\times 31$ individual $dI/dV$ curves in a rectangle of $31.6\AA \times 15.5\AA$ above the molecule. (a) Two exemplary $dI/dV$ curves acquired at positions indicated in (e) and the corresponding fits. The slight deviation at bias voltages above the LUMO is due to the tunneling barrier increasing with voltage [18]. In addition, each of the three Gaussian peaks is shown. (b) Intensity map of the elastic peak. A molecular model is superimposed as a guide to the eye. (c),(d) Plots of the ratio of the first and second vibronic to the elastic peak. Data are shown only for spots at which the tunneling current significantly exceeds the noise level. (e) Dashed rectangle in the STM image corresponds to the mapped region. (f) Schematic illustration of elastic tunneling: when the tip is positioned above the outermost lobe of the LUMO, the tunneling matrix element is high. In contrast, when the tip is centered above the molecule, elastic tunneling contributions cancel. The matrix element for $s$-wave tunneling is low.

Figure 3

Tip-dependent data acquired on NaCl. (a)–(c) and (e)–(g) Color plots of $dI/dV$ curves of the HOMO and LUMO along the green dashed lines in (d) and (h), respectively. The black curves show the spatially resolved centroid extracted from the spectra. The open arrows roughly indicate their spatial variations reflecting changes in $\lambda$. Note that for the HOMO absolute voltage rises from top to bottom. Panels (c) and (g) are acquired with a CO-functionalized tip. (d),(h) Constant height STM images of HOMO and LUMO, respectively, acquired with a CO tip. Insets: STM images acquired with a metal tip at same voltages and corresponding density functional theory calculated orbital densities. Exemplary spots of local $s$, $p$, and $d$ character are indicated. On axis (off axis) refers to the line along (parallel to) the long molecular axis.

Figure 4

$p$-wave to $s$-wave tunneling. (a),(b) Bias-dependent constant current STM images at the indicated voltages ($I=2\mathrm{pA}$) acquired with a CO tip on NaCl. (c) Calculated $p$-wave STM image [16, 29]. Inset: density functional theory calculated orbital density. (d) Constant current STM image acquired with a metal-terminated tip ($I=2\mathrm{pA}$, $V=1.8\mathrm{V}$).