Time-dependent quantum transport : first principles simulations and applications

Abstract

Based on the time dependent density functional theory (TDDFT) for open system and the non-equilibrium Green's function (NEGF) formalism, a practical first principle method to simulate time dependent quantum transport is developed and applied to different areas. The method propagates a closed set of equations of motion of the reduced single electron density matrix(RSDM) and the auxiliary single electron density matrices(ARSDM), which describe the dissipation of the system. The method can go beyond the commonly used wide-band limit approximation and take into account electronic structures of the electrodes accurately. Non-orthogonal basis, which is commonly used in first principle simulation, is also considered properly. And in order to make larger scale simulation possible, two distributed-memory parallelization schemes, the columnwise and checkerboard decomposition schemes, are developed. They distribute the second tier ARSDM over compute nodes and the communication involved is basically the same as that in matrix vector multiplication. So the scalability of the parallelization is also as good as the corresponding schemes in the matrix vector multiplication.

The method is then applied to different areas, which include the study of time-dependent properties in integer quantum hall system and two-dimensional electronic spectroscopy in molecular junctions. Integer quantum hall system is two-dimensional metallic system under strong magnetic field. The system is described by a tight binding Hamiltonian and the magnetic field is taken into account by Peierls substitution. It is observed that the size of the square lattice would affect the magnetic field strength required to enter the quantum hall regime and localization of edge current is related to the quantum hall conductance. The development of current upon applying voltages is also studied for both two-terminal and four-terminal cases. Finally, we observe how the integer quantum hall system transit from one quantum hall plateau to another by applying a gate voltage in the device region.

For two-dimensional electronic spectroscopy (2DES), the method is first benchmarked with simple two-level and three-level model systems connected to two wide band electrodes. We observe peaks resulting from diagrams in which the system is started at excited state. These peaks are present due to the broadening introduced by the electrodes and they distinguishes 2DES of molecular junctions from 2DES of isolated molecules. When bias voltage is applied, the changes in occupation number also lead to suppression or enhancement of certain peaks. Finally, the 2D electronic spectrum of a benzene connected to gold chain electrodes is simulated at density functional tight-binding level with wide band approximation. The broadening introduced by the gold chain electrodes is pretty small and the electronic spectrum is similar to the isolated benzene. And when bias voltage is applied, we observe peak shift of the electronic spectrum due to the induced electric field in the device region.