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Transport through a quantum dot pillar

We have performed a calculation on the quantum transport through a quantum dot pillar with hard-wall confinement, taking into account the Coulomb interaction in the dot as well as the exact sample geometry. We have investigated the case of electrons in the dot. The many-particle eigensolutions in the dot, the tunnelling rate associated to each many-particle eigenstate in the dot, the tunnelling current and the corresponding conductance in both the nonlinear and the linear response regimes are calculated rigorously. Besides other interesting results beyond the orthodox theory, we found that for an experimentally accessible sample, the influence of the Coulomb interaction on certain matrix elements is small and can be neglected. Such an approximation will simplify the numerical study of other physical properties of the quantum dot.