Resonant Vibrations, Peak Broadening, and Noise in Single Molecule Contacts: The Nature of the First Conductance Peak

We carry out experiments on single-molecule junctions at low temperatures, using the mechanically controlled break junction technique. Analyzing the results obtained with various molecules, the nature of the first peak in the differential conductance spectra is elucidated. We observe an electronic transition with a vibronic fine structure, if the first peak occurs at small voltages. This regime can accurately be described by the resonant tunneling model. At higher voltages, additional smearing is observed and no fine structure can be resolved. A detailed analysis of the noise signal indicates that the onset of current is associated with strong fluctuations as a precursor of current flow. The data indicate that a complex fluctuation-driven transport mechanism takes over in this regime.

Figure 1

(a) $dI/dV$ measurement at the first electronic peak for a small blockade region. Several single excitations can be recognized, for positive voltages the distance is $\approx 5.2\mathrm{mV}$, for negative $\approx 8.3\mathrm{mV}$. The onset of current shows the same asymmetry, taking place at $-43.2\mathrm{mV}$ and at $+28.0\mathrm{mV}$. (b) Schematic representation of two leads with chemical potentials ${\mu }_l$ and ${\mu }_r$ coupled asymmetrically (${\Gamma }_1<{\Gamma }_2$) to a molecular level, which is accompanied by a vibrational state $\hslash \omega$. (c) Resulting current-voltage characteristic. The onset of current and peak distance is lower for positive voltages, when the left electrode is weaklier coupled (in case of LUMO transport).

Figure 2

$dI/dV$ characteristics obtained from a nonequilibrium Green’s function calculation for a resonant level model [7, 13, 14]. The model comprises an electronic state 39 meV above the Fermi energy and ten vibrational modes with frequencies ${\omega }_n$ that are coupled to this state with a uniform coupling strength such that the reorganization energy amounts to 22 meV for both plots. In the calculation, the vibrational modes are assumed to be in their thermal equilibrium state determined by the junction’s temperature $T=1\mathrm{K}$. The level-width functions ${\Gamma }_1=9\mu \mathrm{eV}$ and ${\Gamma }_2=13\mu \mathrm{eV}$ have been chosen to model the current and voltage drop retrieved from Fig. 1a.

Figure 3

$dI/dV$ measurements at the onset of current for a small blockade region (left curve) and after pulling at the electrodes in three subsequent steps. With increasing onset voltage the vibrational features smear out step by step.

Figure 4

$IV$ measurements that show high fluctuations at the onset of current when lowering the scanning speed from $75\mathrm{mV}/\mathrm{s}$ (inset) by a factor of 5.

Figure 5

(a) Spectral noise density $S_{II}$ at three different frequencies and $dI/dV$ curve (red or gray) at the first conductance peak. At the onset of current the noise is enhanced by several orders of magnitude. (b) Noise spectra at the onset of current (red or gray) and beyond the conductance peak (black) show different frequency dependence ($f^{-2}$ vs $f^{-1}$) above 1 kHz.