Application of hierarchical equations of motion (HEOM) to time dependent quantum transport at zero and finite temperatures

Abstract

Going beyond the limitations of our earlier works [X. Zheng, F. Wang, C.Y. Yam, Y. Mo, G.H. Chen, Phys. Rev. B 75, 195127 (2007); X. Zheng, G.H. Chen, Y. Mo, S.K. Koo, H. Tian, C.Y. Yam, Y.J. Yan, J. Chem. Phys. 133, 114101 (2010)], we propose, in this manuscript, a new alternative approach to simulate time-dependent quantum transport phenomenon from first-principles. This new practical approach, still retaining the formal exactness of HEOM framework, does not rely on any intractable parametrization scheme and the pole structure of Fermi distribution function, thus, can seamlessly incorporated into first-principles simulation and treat transient response of an open electronic systems to an external bias voltage at both zero and finite temperatures on the equal footing. The salient feature of this approach is surveyed, and its time complexity is analysed. As a proof-of-principle of this approach, simulation of the transient current of one dimensional tight-binding chain, driven by some direct external voltages, is demonstrated.