Quantum nonlinear ac transport theory at low frequency

Based on the nonequilibrium Green's function (NEGF), we develop a quantum nonlinear theory to study time-dependent ac transport properties in the low frequency and nonlinear bias voltage regimes. By expanding NEGF in terms of time to the linear order in Wigner representation, we can explicitly include the time-dependent self-consistent Coulomb interaction induced by external ac bias. Hence this theory automatically satisfies two basic requirements, i.e. current conservation and gauge invariance. Within this theory, the nonlinear ac current can be evaluated at arbitrarily large bias voltages under the low frequency limit. In addition, we obtain the expression of time-dependent current under the wide band limit and derive the relation between the nonlinear electrochemical capacitance and the bias voltage, which are very useful in predicting the dynamical properties of nanoelectronic devices. This quantum theory can be directly combined with density functional theory to investigate time-dependent ac transport from first-principles calculation.