Fast algorithm for transient current through open quantum systems

Abstract

Transient current calculation is essential to study the response time and capture the peak transient current for preventing melt down of nano-chips in nanoelectronics. Its calculation is known to be extremely time consuming with the best scaling T N 3 where N is the dimension of the device and T is the number of time steps. The dynamical response of the system is usually probed by sending a step-like pulse and monitoring its transient behavior. Here, we provide a fast algorithm to study the transient behavior due to the step-like pulse. This algorithm consists of two parts: The algorithm I reduces the computational complexity to T 0 N 3 for large systems as long as T < N ; The algorithm II employs the fast multipole technique and achieves scaling T 0 N 3 whenever T < N 2 beyond which it becomes T log 2 N for even longer time. Hence it is of order O(1) if T < N 2 . Benchmark calculation has been done on graphene nanoribbons with N = 10 4 and T = 10 8 . This new algorithm allows us to tackle many large scale transient problems including magnetic tunneling junctions and ferroelectric tunneling junctions that cannot be touched before.PACS numbers: 71.15.Mb

First-principles investigation of transient spin transfer torque in magnetic multilayer systems

“…However, the NEGF-DFT-CAP framework has never been used for planar structures with k samplings. Moreover, in order to overcome the slow convergence for the energy integral involving the Fermi distribution functions, an efficient sumover-poles decomposition, namely, the Padé approximation, was used to replace the Fermi functions in the time-dependent quantum transport studies [30][31][32][33].…”

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

“…While the WBLA makes the computation of the time-resolved transport properties very efficient, it is not a critical approximation in the NEGF approach, and descriptions beyond the WBLA are also possible to resolve numerically. For extended device descriptions, these developments include also one-dimensional wires [300,317,[336][337][338][339][340][341], organic semiconductors [342], systems on bulk surfaces or STM junctions [343,344], graphene nanoribbons [55,[345][346][347], and carbon nanotubes [348]. In general, descriptions beyond the WBLA are essential when the interaction between the leads and the device region is not simple, and they introduce further intricacies for a quantitative analysis of transient dynamics of molecular devices.…”

Charge nonconservation of molecular devices in the presence of a nonlocal potential

“…Over the past few decades, investigations on transport properties of mesoscopic systems and nanostructures have been extensively reported both on experimental advances [1][2][3][4][5][6][7][8][9][10][11][12][13] and theoretical explorations. [14][15][16][17][18][19][20][21][22][23][24][25][26][27] It is widely acknowledged that these functional devices can be constituted by ultrasmall conjugated molecules, singlelayer or multi-layer nanotubes, bulk organic molecules, etc., and plenty of interesting phenomena such as molecular field effects, 1 Coulomb blockade, 2 negative differential resistance 3 and conductance switching effects 4 have been revealed, which exhibit fundamental significance and potential microelectronic applications. In most of the works, considerable research efforts are focused on current-voltage (I-V ) characteristics as the I-V profiles provide opportunities for a deeper understanding of, e.g., the basic mechanism and structure properties, as well as promising guidance for future molecular nanoelectronics designs and manipulations.…”

“…31 It has been shown that if the Hamiltonian H includes a general nonlocal potential V (r, r ′ ), an extra term naturally appears in the continuity equation and the charge conservation will not be fulfilled. 24,25,32,33 Thus the calculations may give very incorrect results, even nonphysical results.…”