Molecular dynamics study of the thermopower of Ag, Au, and Pt nanocontacts

Using molecular dynamics simulations of many junction stretching processes combined with tight-binding-based electronic structure and transport calculations, we analyze the thermopower of silver (Ag), gold (Au), and platinum (Pt) atomic contacts. In all cases we observe that the thermopower vanishes on average within the standard deviation and that its fluctuations increase for a decreasing minimum cross section of the junctions. However, we find a suppression of the fluctuations of the thermopower for the $s$-valent metals Ag and Au, when the conductance originates from a single, perfectly transmitting channel. Essential features of the experimental results for Au, Ag, and copper (Cu) of Ludoph and van Ruitenbeek [Phys. Rev. B 59, 12290 (1999)], as yet unaddressed by atomistic studies, can hence be explained by considering the atomic and electronic structure at the disordered narrowest constriction of the contacts. For the multivalent metal Pt our calculations predict the fluctuations of the thermopower to be larger by one order of magnitude as compared to Ag and Au, and suppressions of the fluctuations as a function of the conductance are absent. Main features of our results are explained in terms of an extended single-level model.

Figure 1

Formation of an Ag dimer contact. The upper, middle, and lower panels show, respectively, the tensile force, the thermopower, and the conductance as a function of the electrode displacement. For the conductance also the decomposition into conduction eigenchannels $G_0{\tau }_n$ is displayed. Horizontal dashed lines indicate the zero level of the thermopower or a conductance of $1G_0$, while the vertical dotted lines mark the main plastic reorganizations of the contact. Above and below the graphs snapshots of the contact geometry during the stretching process are shown, and the length of the central wire is given for zero electrode displacement.

Figure 2

The same as Fig. 1, but for the formation of an Au dimer contact.

Figure 3

The same as Fig. 1, but for the formation of a Pt dimer contact.

Figure 4

Scatter plots of the thermopower as a function of the conductance for (a) Ag, (b) Au, and (c) Pt. The main panels show all computed data points, while the insets display the average of the thermopower together with its standard deviation. Panels (d)–(f) are the corresponding density plots. For the insets of plots (a)–(c) and the density plots (d)–(f), the bin size of the conductance is $0.1G_0$. Those of the thermopower amount to $0.075$ $\mu$V/K for (d) and (e), and 0.75 $\mu$V/K for (f).

Figure 5

Standard deviation ${\sigma }_S$ of the thermopower as a function of the conductance for (a) Ag, (b) Au, and (c) Pt. Shown in the background is the conductance histogram for each metal, and the number of counts is indicated on the right $y$ axis. In each case the bin size of the conductance is $0.1G_0$.

Figure 6

The same as Fig. 1 for another Ag contact forming a dimer before rupture.

Figure 7

The same as Fig. 1, but for a Au contact forming a chain of four atoms before rupture.

Figure 8

The same as Fig. 1, but for a Pt contact forming a chain of six atoms before rupture.

Figure 9

Average eigenchannel transmission probabilities ${〈{\tau }_n〉}_G$ as a function of the conductance for (a) Ag, (b) Au, and (c) Pt, as determined from the atomistic simulations presented in the manuscript. Error bars show the standard deviation and the dashed horizontal lines indicate unit average transmission. See also Refs. 31 and 32 for further explanations.

Figure 10

Behavior of the eigenchannel transmission probabilities ${\tau }_n$ and the standard deviation of the thermopower ${\sigma }_S$ as a function of the conductance for (a) and (c) a monovalent metal, and (b) and (d) a multivalent metal. For (c) and (d) we used $\gamma =0.6$ eV and $0.1$ eV, respectively, and the bin size was set to $\Delta G=0.04G_0$ in the main panels. In the insets of panel (c) we have chosen a smaller bin size of $\Delta G=0.002G_0$ to resolve the selected region more clearly and show the function ${\sigma }_S=\alpha \sqrt{n-G/G_0}/n$ for $G\lesssim n{G}_0$ and $n=1,2$ as a red line, assuming $\alpha =1.44$ $\mu$V/K.