Ballistic resistivity in aluminum nanocontacts

We perform a representative series of semiclassical molecular dynamics simulations of aluminum nanocontact breakages, coupled to full quantum conductance calculations. This approach allows to obtain realistic conductance histograms of polyvalent species and understand the origin of their peaked structures. The results show that the conductance depends linearly on the contact minimum cross section for the geometrically favored nanocontact configurations. Valid in a broad range of conductance values, such relation suggests the definition of a transport parameter for the nanoscale, that represents the novel concept of ballistic resistivity.

Figure 1

Time evolution of the minimum cross section (black symbols) and the quantum conductance (open symbols) corresponding to two aluminum wire breakages at $T=4\mathrm{K}$, illustrating two rupture mechanisms: (a) the formation of a single-central atomic configuration before breakage, and (b) the formation of a dimer-chain contact before breakage. Insets depict several atomic configurations during nanowire stretching. Arrows and dashed vertical lines denote the corresponding conductance and minimum cross section associated with these nanoneck configurations.

Figure 2

Conductance per minimum cross-section $G_a$ as a function of the minimum cross-section $S_m$. The figure shows more than 800 points corresponding to 50 simulated aluminum nanocontact breakages. The dotted line is a guide to the eye and denotes the quantum conductance value $G_0$.

Figure 3

Calculated conductance histogram for aluminum (top) using those points shown in Fig. 2. Below this histogram, we separately show the partial conductance histograms for those configurations corresponding to effective number of atoms $N_a=1$, 2, 3, 4, 5 and 10. Gray bins denote the maximum value of the conductance $G_M\left(N_a\right)$. Vertical dashed lines denote the computed average conductances $⟨G\left(N_a\right)⟩$ for each depicted conductance distribution.

Figure 4

Conductance per atom as a function of the effective number of atom contacts $N_a$ (open circles). Average conductance $⟨G\left(N_a\right)⟩$ (black circles) and peak conductance $G_M\left(N_a\right)$ (gray squares) as a function of the effective number of atom contacts. Bars denote the standard error. Dashed line represents a linear fit to the $G_M\left(N_a\right)$ data.