First-principles investigation of transient current in molecular devices by using complex absorbing potentials

Based on the nonequilibrium Green's function (NEGF) coupled with density function theory (DFT), namely, NEGF-DFT quantum transport theory, we propose an efficient formalism to calculate the transient current of molecular devices under a step-like pulse from first principles. By combining NEGF-DFT with the complex absorbing potential (CAP), the computational complexity of our formalism (NEGF-DFT-CAP) is proportional to $O\left(N\right)$ where $N$ is the number of time steps in the time-dependent transient current calculation. Compared with the state-of-the-art algorithm of first-principles time-dependent calculation that scales with at least $N^2$, this order $N$ technique drastically reduces the computational burden making it possible to tackle realistic molecular devices. We have presented a detailed discussion on how to implement this scheme numerically from first principles. To check the accuracy of our method, we carry out the benchmark calculation compared with NEGF-DFT formalism and they agree well with each other. As an application of this method, we investigate the transient current of a molecular device Al–C${}_3$–Al from first principles.

Figure 1

Schematic plot of a two terminal molecular device. The device consists of a central molecular part (green solid cube) and two semi-infinite leads, which will extend to the $\pm \infty$. The black solid lines represent the complex absorbing potential added to both lead regions. The region enclosed by the red dashed line is the central region; the purple dashed-dot line encloses the central region plus complex absorbing potential region in the leads.

Figure 2

Schematic diagram of a molecular device Al–C${}_3$–Al. The device consists of a three carbon atoms chain coupled to the perfect aluminium atomic electrodes which extends to the reservoirs at $\pm \infty$, where the current is collected.

Figure 3

The time-dependent transient current $I\left(t\right)$ versus time with $V=0.0005$ a.u. for one-dimensional atomic Al–C${}_1$–Al chain. Blue solid line and red dashed line are time-transient-dependent current calculated by using NEGF-DFT method and NEGF-DFT-CAP method; black solid line is the DC current at the steady state limit.

Figure 4

The comparison of the transmission coefficient of a carbon chain sandwiched between Al(100) leads. The numerical results calculated by using CAP method with 30 unit cells in the lead region (blue solid line) is compared with the exact method (red dashed line).

Figure 5

The time-dependent transient current $I\left(t\right)$ versus time with different bias voltages for a Al–C${}_3$–Al molecular device. The blue and black solid lines correspond to the time-dependent transient current and DC current at a steady state for $V=0.0025$ a.u., respectively. The red solid and black dashed lines are the time-dependent transient current and DC current at steady state for $V=0.01$ a.u., respectively.