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Time-dependent electron tunnelling through a quantum dot with Coulomb interactions

Keldysh's nonequilibrium Green function is used to study the electron tunnelling through a quantum dot. Two kinds of intra-dot electron - electron (e - e) interaction are introduced: for the interaction at the same energy level n with different spins, and for the interaction between different levels n and m. General formulas of the time-varying current j(t) and the averaged current are derived when the external fields are applied to the system. In the time-independent linear response regime, our calculation demonstrates that the interval of the Coulomb oscillation peaks is mainly determined by which is always smaller than . When the external microwave (MW) fields are applied to the system, we obtain: (1) The j(t) may become negative for a certain period of time, even if the chemical potential is larger than all the time. (2) The calculated structure of the Coulomb oscillation peaks (in asymmetric MW fields) is in good agreement with the experimental results of Kouwenhoven et al. (3) For the symmetric MW field case, our theoretical results are well consistent with the experiments of Blick et al and Drexler et al.