First-principles investigation of transient dynamics of molecular devices

Abstract

Based on the nonequilibrium Green's function (NEGF) and time-dependent density-functional theory (TDDFT), we propose a formalism to study the time-dependent transport behavior of molecular devices from first principles. While this approach is equivalent to the time-dependent wave-function approach within TDDFT, it has the advantage that the scattering states and bound states are treated on equal footing. Furthermore, it is much easier to implement our approach numerically. Different from the time-dependent wave-function [ψ(t,E)] approach, our formalism is in the time space [G r (t,t )], making this method superior in the time-dependent transport problem with many subbands in the transverse direction. For the purpose of numerical implementation on molecular devices, a computational tractable numerical scheme is discussed in detail. We have applied our formalism to calculate the transient current of two molecular devices Al-1,4-dimethylbenzene-Al and Al-benzene-Al from first principles. In the calculation, we have gone beyond the wideband limit and used the adiabatic local density approximation that was used within TDDFT. It is known that when the wideband limit is abandoned, the boundary condition of the transport problem is non-Markovian, resulting in a memory term in the effective Hamiltonian of the scattering region. To overcome the computational complexity due to the memory term, we have employed a fast algorithm to speed up the calculation and reduced the CPU time from the scaling N 3 to N 2 log 2 2 (N ) for the steplike pulse, where N is the number of time steps in the time evolution of the Green's function. To ensure the accuracy of our method, we have done a benchmark transient calculation on an atomic junction using a time-dependent wave-function approach within TDDFT in momentum space, which agrees very well with the result from our method.

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

“…At present stage, quantitative agreement between theoretical first principles calculations and experiment results can be reached when the system is in the steady state regime under external DC bias [12][13][14][15]. Besides the DC steady state problem, the question of how fast a molecular device can turn on and off is also an important issue, which attracts a lot research attention recently [16][17][18][19][20][21]. This kind of question can be answered by studying the dynamic response of molecular devices by sending a step like pulse from the electrodes.…”

“…One is based on the NEGF-TDDFT method proposed in Ref. [18] which is an order N 2 (log 2 N) 2 algorithm and other one is our proposed formalism in this paper termed as NEGF-DFT-CAP. Here we take one dimensional Al-C 1 -Al atomic chain (where both leads are one-dimensional Al chain) as a toy molecular device and apply a step-like pulse to test numerical implementation of our formalism.…”

“…In addition, there are many quasi-poles near the energy axis making the integration very difficult to converge. On the other hand, the theoretical prediction of the transient dynamics of molecular devices from first principles can be addressed by numerically solving scattering wave function or non-equilibrium Green's function (NEGF) combined with time dependent density functional theory (TDDFT) [17][18][19]. These methods again are very time-consuming for transient current calculation although the scaling has been reduced to N 2 (log 2 N) 2 .…”

Transient spin current under a thermal switch

“…Due to the simultaneous variation of the temperature, it is not clear about whether there is an intrinsic enhancement of spin currents in the transient regime or not. Although electrically-induced transient phenomena are well investigated for charge currents [13][14][15][16][17] and spin currents [9,18,19], little is known about thermally-induced transient spin currents.…”

Fast algorithm for transient current through open quantum systems

“…The major obstacle of theoretical investigation on the first principles transient current is its computational complexity. Many attempts were made trying to speed up the calculation 3,4,[10][11][12][13][14] . Despite of these efforts, the best algorithm to calculate the transient current from first principles going beyond WBL limit scales like T N 3 using complex absorbing potential (CAP) 15 where T and N are number of time steps and size of the system respectively.…”