Classical Nuclear Motion in Quantum Transport

An ab initio quantum-classical mixed scheme for the time evolution of electrode-device-electrode systems is introduced to study nuclear dynamics in quantum transport. Two model systems are discussed to illustrate the method. Our results provide the first example of current-induced molecular desorption as obtained from a full time-dependent approach and suggest the use of ac biases as a way to tailor electromigration. They also show the importance of nonadiabatic effects for ultrafast phenomena in nanodevices.

Figure 1

Left panel: Ground-state displacement $x_i$, $i=-7,\dots ,7$, at weak ($\lambda =0.1$) and strong ($\lambda =1.0$) coupling. The inset shows the LDOS (energy in units of $|V|$) on site $-6$ (dashed line) and site 0 (solid line). Right panel: current $I(t)$ (in units of ${10}^{-2}|V|$) at weak and strong coupling along the bond ($-7$, $-6$) (solid thin line), (0, 1) (solid thick line) and (6, 7) (dashed line) after the sudden switching on of a bias $U_L=0.5|V|$ in electrode $L$. The insets show a 3D plot of $\mathbf{x}(t)$ between $t=0$ and $t=480|V{|}^{-1}$ (in the top panel the range of $\mathbf{x}$ is between $-3.2$ and $-4$, while in the bottom panel the range is between $-19.4$ and $-20$).

Figure 2

$I_{L,R}(t)$ (in units of $|V|$) at the left (solid line) and right (dashed line) interface for a sudden switching $U_L=0.25|V|$ [green (light gray) line], $0.5|V|$ [red (thin dark gray) line], and $1.0|V|$ [blue (thick black) line]. Inset (a): Time-dependent density $n_3$ of nucleus 3 (by symmetry $n_2=n_3$ at any time). Inset (b): $x_3(t)$ (solid line) and $y_3(t)$ (dashed line) of nucleus 3 (by symmetry $x_2=x_3$ and $y_2=-y_3$ at any time). Time scale and color coding in insets (a) and (b) are the same as in the main figure. A schematic of the device D2 and the adiabatic result (labeled curve) are also shown.

Figure 3

Left panel: $I_{L,R}(t)$ (in units of $|V|$) at the left (solid line) and right (dashed line) interface for $U_L=1.0|V|$, $\omega =0.05|V|$. In the inset, $x_2(t)=x_3(t)$ (thick solid line) $y_2(t)$ (thin solid line), and $y_3(t)$ (dashed line). The time scale is the same as in the main panel. Right panel: same as left, but with $\omega =0.10|V|$. Left and right insets have the same vertical scale.