Universal features of electron-phonon interactions in atomic wires

The effect of electron-phonon interactions in the conductance through metallic atomic wires is theoretically analyzed. The proposed model allows to consider an atomic size region electrically and mechanically coupled to bulk electrodes. We show that under rather general conditions, the features due to electron-phonon coupling are described by universal functions of the system transmission coefficients. It is predicted that the reduction of the conductance due to electron-phonon coupling, which is observed close to perfect transmission, should evolve into an enhancement at low transmission. This crossover can be understood in a transparent way as arising from the competition between elastic and inelastic processes.

Figure 1

Schematic representation of an atomic wire suspended between metallic electrodes. For the theoretical description, the system is decomposed into $L$ (left), $R$ (right), and $C$ (central) regions. The labels 1 and $N$ denote the outermost sites of the wire.

Figure 2

Features due to EPH coupling in the conductance for the ideal chain geometry containing three and four atoms. The insets in the right upper and middle panels show the scaling of the total conductance step $\Delta G$ and its width $W$ with the number of atoms $N$. The correlation of these features with the phonon spectrum is illustrated by the included average phonon density of states within the chain in the lower panels. $G_0$ denotes the quantum of conductance $2e^2∕h$.

Figure 3

(Color online) Comparison between the full model calculations and the experimental measurements for the conductance of Au atomic chains. The experimental data correspond to a typical curve from the experiments described in Ref. 6, while the theoretical curve has been obtained for the case $N=3$ using the set of parameters discussed in the text.

Figure 4

Schematic representation of a minimal model accounting for the transition between negative and positive conductance step as a function of the transmission based in the mapping proposed in Ref. 20. A single phonon mode between two sites is considered. The two channels correspond to the absence or to the presence of an excited phonon. The arrows indicate all possible paths for an incident electron: elastic and inelastic transmission and reflection.

Figure 5

(Color online) Evolution of the conductance steps as a function of the transmission for an atomic chain with $N=3$ and 4. The symbols correspond to the full calculation while the full lines were obtained using Eqs. (6, 7).