Time‐dependent quantum transport theory and its applications to graphene nanoribbons

Abstract

Time‐dependent quantum transport parameters for graphene nanoribbons (GNR) are calculated by the hierarchical equation of motion (HEOM) method based on the nonequilibrium Green's function (NEGF) theory [Xie et al., J. Chem. Phys. 137, 044113 (2012)]. In this paper, a new initial‐state calculation technique is introduced and accelerated by the contour integration for large systems. Some Lorentzian fitting schemes for the self‐energy matrices are developed to effectively reduce the number of Lorentzians and maintain good fitting results. With these two developments in HEOM, we have calculated the transient quantum transport parameters in GNR. We find a new type of surface state with delta‐function‐like density of states in many semi‐infinite armchair‐type GNR. For zigzag‐type GNR, a large overshooting current and slowly decaying transient charge are observed, which is due to the sharp lead spectra and the “even–odd” effect.

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

“…The details of this scheme are given in our previous paper [16]. One example for this zigzag graphene ribbon is shown in Fig.…”

“…There are some oscillations in the middle part of the spectrum due to the interference effect between the device-lead interfaces. The steady state solution of TDDFT-NEGF is obtained from the rapid residue calculation method developed in our previous papers [16][17]. Then the TDDFT-NEGF simulation is implemented with the 4 th order Runge-Kutta scheme for solving Eqs.…”

“…From the figure we see that there exist large oscillations in the beginning, which is the over-shotting effect. This is due to the very narrow spectrum of the lead [16]: Only a small amount of electron near the Fermil level can be disspated into the GNR lead, so most of the electron wave 13 injected in the device is reflected on the device-lead boundary, which gives the oscillation current.…”

“…Recently we developed a new method to calculate the time dependent quantum transport based on the NEGF theory [13][14][15][16][17]. This method, termed as the time dependent density functional theory -nonequilibrium Green's function (TDDFT-NEGF) scheme, treats the lead spectrum exactly, which is beyond the commonly used wide band limit (WBL) approximation [8][9].…”

Emergence of Bloch oscillations in one-dimensional systems

“…To account for the time-dependence of the electric field, we use a recently developed numerical method 22 , which is based on the time-dependent non-equilibrium Green's function (TDNEGF) formalism 23,24 in combination with an auxiliary-mode expansion 25 . This approach has already been successfully applied to study time-dependent nanoelectronics [26][27][28][29][30][31][32] and it allows us to obtain the timedependent currents and occupations during and after the pulse has been applied. This information is then used to characterize the spatiotemporal evolution of the electrons in the device.…”