Influence of Relativistic Effects on the Contact Formation of Transition Metals

Our analysis of the contact formation processes undergone by Au, Ag, and Cu nanojunctions reveals that the distance at which the two closest atoms on a pair of opposing electrodes jump into contact is, on average, 2 times longer for Au than either Ag or Cu. This suggests the existence of a longer-range interaction between those two atoms in the case of Au, a result of the significant relativistic energy contributions to the electronic structure of this metal, as confirmed by ab initio calculations. Once in the contact regime, the differences between Au, Ag, and Cu are subtle, and the conductance of single-atom contacts for metals of similar chemical valence is mostly determined by geometry and coordination.

Figure 1

A trace of conductance recorded during the formation of a gold contact in a STM setup at 4.2 K. As the electrodes approach each other, an initial exponential increase in conductance is followed by a jump into contact, as indicated by the vertical black arrow. Conductance values before and after contact formation are marked and labeled as $G_a$ and $G_b$, respectively. On the right-hand side, from bottom to top, different stages of the contact process are illustrated.

Figure 2

Upper panels: Density plots of jump to contact parameters extracted from more than 2000 contact formation traces for Au, Ag, and Cu (labeled correspondingly). Bottom panels: Evaluation of the results from fitting the data in the upper panels to a sum of three bivariate normal distributions.

Figure 3

Graphical summary of the fitting results used to compare the metals. Dots mark the mean value of the distribution, the size of which is proportional to the ratio of occurrence of each configuration, and the ellipse contour encloses the equivalent of 1 standard deviation for each bivariate distribution; in other words, the ellipse encloses 68% of the data.

Figure 4

(Rescaled) total energy (a), and its derivative (b), as a function of (rescaled) interatomic separation $z$ between atoms in infinite monatomic chains of nonrelativistic gold (dashed blue) and silver (dashed red), and scalar relativistic gold (solid blue) and silver (solid red). The derivative curves in (b) were obtained from a fit of the total-energy data in (a) to sixth-order polynomials. In the absence of scalar relativistic corrections, monatomic gold and silver chains exhibit almost identical force curves. Conversely, the interaction “force" between relativistic gold atoms in (b) rises, from large separations, to the maximum value for relativistic silver atoms a distance $\sim 0.7\AA$ earlier.