Detection of Vibration-Mode Scattering in Electronic Shot Noise

We present shot noise measurements on Au nanowires showing very pronounced vibration-mode features. In accordance to recent theoretical predictions the sign of the inelastic signal, i.e., the signal due to vibration excitations, depends on the transmission probability becoming negative below a certain transmission value. We argue that the negative contribution to noise arises from coherent two-electron processes mediated by electron-phonon scattering and the Pauli exclusion principle. These signals can provide unique information on the local phonon population and lattice temperature of the nanoscale system.

Figure 1

Measurement of inelastic signals in shot noise for Au atomic chains. (a) Circuit diagram for the measurement of conductance and noise on atomic junctions formed by the mechanically controllable break junction technique. Noise is measured by employing two sets of low-noise amplifiers in parallel, each having an amplification factor of ${10}^5$. A spectrum analyzer is used for taking the cross spectrum of the two channels, in a frequency range of 250 Hz to 100 kHz. By averaging over ${10}^4$ spectra the uncorrelated noise of the preamplifiers is suppressed. (b) Fano factor plot for many different realizations of atomic chains. The data are consistent with assuming a single conductance channel only. (c) Symmetric part of the differential conductance (left axis) and its derivative (right axis) for a Au atomic chain. The signal was measured with 2 mV modulation amplitude at 3.33 kHz; the second derivative was computed numerically. The peak at $20.0\pm 0.4\mathrm{mV}$ signals the onset of scattering by a vibration-mode. (d) Shot noise as a function of bias for the same atomic contact as in (c). The red (medium gray) curve is a fit to Eq. (1) up to 20 mV. The Fano factor $F_1=0.020\pm 0.002$ agrees with the conductance of $G=0.98G_0$ in (c). The broken red curve is an extrapolation of the fit. The green (light gray) line is a linear fit to the data above 20 mV.

Figure 2

The kink in shot noise and its sign and position for a range of values of the transmission of the contact. (a) Reduced noise $Y$, Eq. (3), plotted as a function of the variable $X$, defined in Eq. (4). The data below the phonon energy are described by a linear dependence (fitted with a solid line up to the kink, and extrapolated by a dashed line). The slope of this line gives the Fano factor. The transmission probability obtained from the conductance is shown as a label to each curve. Above the phonon energy a new linear dependence is observed. The kink is towards higher slope when the transmission probability $\tau$ is close to 1. For $\tau$ below 0.94 we observe a reduced slope. (b) The phonon energy as observed in the differential conductance plotted as a function of the position of kink in the shot noise. The line shows the expected 1:1 relation. Red and black points are for positive and negative kinks, respectively. (c) Fits of the theory, including the energy dependence of the transmission as estimated from the $dI/dV$ signals (full curves). The broken curves show the linear extrapolation of the zero-bias curve. The values for the zero-bias transmission $\tau$ and the inelastic scattering strength are (from top to bottom): $\tau =0.669$, $\lambda =0.35\Gamma$; $\tau =0.818$, $\lambda =0.20\Gamma$; $\tau =0.956$, $\lambda$ undetermined; $\tau =0.981$, $\lambda =0.11\Gamma$; $\tau =0.998$, $\lambda =0.08\Gamma$.

Figure 3

Distribution of the observed change in the Fano factor at the kink, plotted as a function of the conductance. The points are obtained for different realizations of Au atomic chains. For conductance (i.e., transmission) close to 1 we find exclusively positive values for $\delta F/F$. Below a cross-over regime near $G=0.95G_0$ only negative values are observed. The curves are obtained from the theory of Ref. 9, for fixed values of the inelastic scattering strength $\lambda$. Inset: The top part illustrates the atomic chain configuration and the vibration mode involved in the scattering. The lower part sketches an example of a two-electron process giving rise to reduction of the Fano factor: two electrons injected from the left lead at different energies tend to compete for the same outgoing state after the emission of a phonon (see text).