Microscopic current dynamics in nanoscale junctions

So far, transport properties of nanoscale contacts have been studied mostly within the static scattering approach. The electron dynamics and the transient behavior of current flow, however, remain poorly understood. We present a numerical study of microscopic current flow dynamics in nanoscale quantum point contacts. We employ an approach that combines a microcanonical picture of transport with time-dependent density-functional theory. We carry out atomic and jellium model calculations to show that the time evolution of the current flow exhibits several noteworthy features, such as nonlaminarity and edge flow. We attribute these features to the interaction of the electron fluid with the ionic lattice, to the existence of pressure gradients in the fluid, and to the transient dynamical formation of surface charges at the nanocontact-electrode interfaces. Our results suggest that quantum transport systems exhibit hydrodynamical characteristics, which resemble those of a classical liquid.

Figure 1

(Color online) Sketch of the nanojunction geometry that is studied in the paper. At $t<0$, a bias in the form of $V\left(z\right)=V_0[H(z-z_a)-H(-z-z_a)]$ is applied to the junction (the central constriction is at $z=0$) such that the regions $\mid z\mid >z_a$ bear a potential offset from the central constriction, where $H\left(z\right)$ is the Heaviside step function.

Figure 2

(Color online) Current flux for a series of times in a nanoscale quantum point contact system in the jellium model. The applied bias at $t<0$ is $\Delta V=0.2\mathrm{V}$. The field lines in each panel depict the direction and amplitude of the current density vectors, while the colors give extra electron (red) or hole (blue) density: (a) $t=0.4\mathrm{fs}$, (b) $t=0.8\mathrm{fs}$, and (c) $t=1.6\mathrm{fs}$. In (a), the semicircle marks the contour along which the radial component of the current density is calculated (see text and Fig. 3).

Figure 3

(Color online) Time series of the radial amplitude of the current densities along a semicircle of radius $3\mathrm{\AA }$ centered on the nanojunction, as a function of angle along the contour.

Figure 4

(Color online) Time sequence of electron current streamlines in the atomic junction described in Sec. 2. (a)–(d) correspond to $t=0.2$, 0.25, 0.3, and $0.35\mathrm{fs}$, respectively. The dots denote atomic sites that correspond to the (001) facets of the gold fcc lattice. The applied bias at $t<0$ is $\Delta V=0.2\mathrm{V}$.

Figure 5

(a) Planar averaged charge density from $t=0$ to $t=0.6\mathrm{fs}$ for a jellium junction. The change in the peaks indicates the dynamic process in which excess charge builds up at the surfaces. The sign of the surface charges indicates that electron charges accumulate on the right and hole charges on the left. [(b) and (c)] Excess charge in the vicinity of the contact at $t=0$ and $t=0.6\mathrm{fs}$. The thick solid lines indicate excess electrons, while thick dashed lines indicate excess holes. The thin dashed lines mark the edges of the jellium electrodes and the contact.