Time-dependent density functional theory quantum transport simulation in non-orthogonal basis

Abstract

Real-time, local basis-set implementation of time-dependent density functional theory for excited state dynamics simulations A model study of quantum dot polarizability calculations using time-dependent density functional methods Basing on the earlier works on the hierarchical equations of motion for quantum transport, we present in this paper a first principles scheme for time-dependent quantum transport by combining timedependent density functional theory (TDDFT) and Keldysh's non-equilibrium Green's function formalism. This scheme is beyond the wide band limit approximation and is directly applicable to the case of non-orthogonal basis without the need of basis transformation. The overlap between the basis in the lead and the device region is treated properly by including it in the self-energy and it can be shown that this approach is equivalent to a lead-device orthogonalization. This scheme has been implemented at both TDDFT and density functional tight-binding level. Simulation results are presented to demonstrate our method and comparison with wide band limit approximation is made. Finally, the sparsity of the matrices and computational complexity of this method are analyzed.

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

“…From the lead spectrum of the carbon chain (see Fig. 3(b) in Reference [17]) we see that it is very flat near the Fermi level, thus the carbon-atom-chain behaves like a wide-band-limit (WBL) lead near the Fermi energy [17]. Compared to the sharp spectrum of the zigzag GNR lead (see Fig.…”

“…One way to solve this problem is to modify the TDDFT-NEGF theory for the non-orthogonal bases, which is shown in our recent paper [17]. Another way is to orthogonalize the original basis with some basis transformation.…”

“…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.…”

“…The initial state of Eqs. (19)- (21) is calculated by the residue calculation method as stated in literatures [16,17]. 4.…”

“…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].…”