Electron Interaction in a Quantum Dot with Hard Wall Confinement Potential

Abstract

We have investigated the electron interaction energy in a circular quantum dot with hard confinement potential, using a renormalized perturbation series (RPS) approach which interpolates between the perturbation solutions in the weak interaction regime and the asymptotic solutions in the strong interaction regime. The RPS is based on the scaling property of the Hamiltonian, and the numerical procedure is not complicated even when the number of electrons in the dot is not very small. The accuracy of the RPS calculation has been tested with two electrons in a dot, where the RPS ground state energy agrees with the exact numerical solution within 1% relative error. We have performed the RPS calculation for three and four electrons in the dot, from which the Coulomb charging energy is derived. The results suggest the potential application of pillar-shaped quantum dots for single-electron tunneling transistors operating at higher temperatures.