• A code implementing the auxiliary mode approach for time-dependent quantum transport in open systems is presented. The code is demonstrated using three examples of nano-scale devices applying different levels of complexity in the mean-field description of the electronic structure. The auxiliary mode approach to time-dependent open quantum system calculations is implemented and refined to yield a feasible computational approach to simulate nanostructures far from equilibrium. It is done by a careful diagonalization of the electrode level-width function, and provides an efficient approach which can simulate large, open systems at the level of time-dependent density functional theory. The approach, as given in this work, is implemented in the new open-source code Zandpack. The framework is applied to three systems perturbed by the same THz electromagnetic field pulse-form: 1) A Hubbard model for hydrogen on graphene is used to calculate spin-currents, mutual information, spin-transitions, and a pump-probe setup. 2) An armchair graphene nanoribbon (AGNR) probed by a metal tip showing electrons excited from the valence band of the AGNR into the tip via electron-electron interactions. 3) A gold break-junction is modeled with various gap distances, and displays behavior that is more different from the adiabatic case as the gap widens. In the examples 2 and 3, we develop and use a general linearization scheme for time-dependent open system calculations, which utilizes the DFTB+ or SIESTA codes. Program Title: Zandpack CPC Library link to program files: (to be added by Technical Editor) Developer’s repository link: https://github.com/AleksBL Licensing provisions: MPL-2.0 Programming language: Python Nature of problem: Simulating the evolution of electrons in a device region connected to electrodes that are experiencing a time-dependent and strong bias, while at the same time describing the evolving device electrons accurately at the mean-field level. The electronic structure of the electrodes must also be described accurately in terms of the energy-dependence of its level-width function. This on a practical level requires fitting a set of known functions to a sum of Lorentzians. This fit then fixes the parameters of a coupled system of ODEs, in which the electronic density and Hamiltonian appears. Lastly, this system of ODEs has to be solved numerically. Solution method: A user-friendly routine for fitting the electrode level-width functions is implemented. It can either take input from TBtrans or custom user input and convert it to a sum of Lorentzians. We employ the auxiliary mode expansion (AME) method following Popescu and Croy New J. Phys. 18, 093944 (2016) with a modified version of the diagonalization technique, combined with an effective account for the electrode level-width functions. The code can obtain the initial steady state, and propagate this initial steady state after application of a user-defined voltage bias-pulse applied to the electrodes using an explicit Runge-Kutta solver. Throughout this propagation, a user-defined density-dependence is needed, e.g. by interfacing to an external LCAO-DFT code. Such an interface is available for SIESTA and DFTB+, but can also be written by the user. Additional comments including restrictions and unusual features: The AME method does not have any restrictions on how fast oscillations can be, meaning it is valid for slow (e.g. THz fields) as well as fast (e.g. optical fields) perturbations. Simulations with normal-superconducting-normal type setups are also possible. In the current implementation, phonons cannot be included in the calculation, but the method does in theory allow for such Y. Zhang, C. Y. Yam, G. Chen, J. Chem. Phys. 138 (16) (2013).
Lorentzen et al. (Sun,) studied this question.