Theoretical Description of Shell Filling in Cylindrical Quantum Dots

A theoretical quantitative description is given for non-periodic oscillations observed in a current vs. gate voltage characteristics of cylindrical quantum dots. Energy eigenvalues and chemical potentials for a system of N confined electrons (N=1,...,13) are calculated by the unrestricted Hartree-Fock method with a confinement potential proportional to the gate voltage. The positions of the observed peaks of the current are reproduced with a very good accuracy. The non-periodicity of the characteristic is explained as a result of the shell filling, which is a signature of the quantum Coulomb blockade.