In studying the wide scope of transport phenomena in molecular, nano- to mesoscopic systems where the size is small, quantum mechanics and quantum statistics dominates the physics of the whole systems. This is the field of quantum transport in which the contribution of electrons from a few to 10 thousands atoms are considered, leading to accurate description of varies novel phenomena. While both experimental measurements and theoretical formalisms were developed, the application of theoretical methods are strictly limited to small and simple system owning to the key factor of heavy computational cost in terms of speed and memory.
Dynamical response of transient current over a system provides many important information of nanodevices. In case of a nanodevice that functions as an '1' or '0' in a computer chip, the speed of the device is determined by the response time in the current upon an incident step-like bias. Transient current through molecular devices can be studied with high accuracy by first principle method and yet the practicality is strictly limited by the computational cost even with the state-of-art ~200TN^3 algorithm in the literature. Here, we proposes a new detailed methodology based on non-equilibrium Greens function (NEGF) with complex absorbing potential (CAP) under a step-like pulse, with highly optimized algorithm built on fully parallel architectures. Exact value of the integrations will be obtained using Residue theorem and Pade spectrum decompositions (PSD). To validate the new algorithms, a tested system based on the well-known intrinsic 2D material--graphene nanoribbons will be chosen. The Hamiltonian of the system is constricted by Tight-binding (TB) method. Complete transient response over period can potentially be obtained using the virtually same computational times as one time point, independent of the number of time steps, particularly suitable for large-scale implementation.
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