Perturbative expansion of currents in scanning tunnelling microscopy and vibration-mediated resonant charge transfer

Abstract

The transient current in the existence of external electric field can be calculated by the non-equilibrium Green’s function (NEGF) method and wide-band limit (WBL) approximation can be used to simplify the expression. A perturbative expansion of the current is derived in frequency domain and the lower-order integrated current is then analysed in detail. The scanning tunnelling microscopy (STM) integrated with carrier-envelope phase (CEP) stable pulses has enabled the control of ultrafast electronic motion such as tunnelling and excitation. Experiments find that the effective tunnelling current, i.e., the integrated current, can be controlled by tuning the CEP in a single-pulse configuration, and a phase shift exists between the maxima of the tunnelling current and field. Our frequency-domain perturbative expansion of the integrated current reveals that this phenomenon is mainly caused by the third order response. A real-time time-dependent density functional based tight-binding for open systems (RT-TDDFTB-OS) simulation on a gold-tip-gold-substrate STM structure with 128 atoms then confirms the existence of the phase shift. Perturbative RT-TDDFTB-OS simulations on a four-atom hydrogen chain system validate mutually the conclusion made from frequency domain. The well-known current rectification in STM is en passant found to originate in the even order responses. In a pump-probe configuration where two pulses have the same profile except the central time, the effective current is found to be periodically decaying with respect to the pump-probe delay. The perturbative expansion has been applied to a two-level model open system, which produced an analytical expression for the second order integrated current. The result is a convolution of pulses and line-width-related function of the system, therefore it is oscillating with the frequency between the pulse and energy gap between the two levels. Various limits of the second order integrated current are inspected. The occupation of two levels after two pulses is also derived without dissipation, which is in accordance with the integrated current in zero line width limit. This implies the excitation of electrons can be controlled by the pump-probe delay and measured by the effective current. The vibration-mediated resonant charge separation across the donor-acceptor interface in an organic photovoltaic device has also been studied. A concise two-level electronic system coupled to a molecular vibrational mode is pro- posed and solved using Lindblad master equation. It was found that the charge transfer is enhanced considerably when the vibrational energy is resonant to the energy gap between the interface. This process is ultrafast, completing within 100 fs. An open-system Ehrenfest dynamics simulation of the model system is then performed with qualitatively correct results being obtained. The Ehrenfest dynamics is less computationally intensive, and can be applied to the simulation of atomistic organic photovoltaic systems.