Quantum Theory of Electron Transport Through Single-Level Quantum Dot
  A new approach in the quantum theory of few-electron nanoelectronic devices -- the S-matrix approach -- is presented in a simple example: a single-electron transistor consisting of a single-level quantum dot connected with two metallic leads through the corresponding potential barriers. The electron transport through the quantum dot due to the electron tunneling between the dot and the leads is studied. The strong Coulomb repulsion between the electrons in the dot is taken into account exactly, while the tunneling between the dot and the leads, considered as a small perturbation, is studied by means of the perturbation theory. For summing up the infinite perturbation theory series we apply the Green function technique and the Heisenberg equation of motion of the electron annihilation and creation operators. The matrix elements of the transition processes include both the direct and crossing terms, so that there is no need to use the non-crossing approximation (NCA). The explicit expression of the electron transport current is derived. 
Nguyen Van Hieu and Nguyen Bich Ha