Shot noise in tunneling transport through molecules and quantum dots

We consider electrical transport through single molecules coupled to metal electrodes via tunneling barriers. Approximating the molecule by the Anderson impurity model as the simplest model which includes Coulomb charging effects, we extend the ``orthodox'' theory to expand current and shot noise systematically order by order in the tunnel couplings. In particular, we show that a combined measurement of current and shot noise reveals detailed information of the system even in the weak-coupling limit, such as the ratio of the tunnel-coupling strengths of the molecule to the left and right electrode, and the presence of the Coulomb charging energy. Our analysis holds for single-level quantum dots as well.