Magic number ground states of quantum dots in a magnetic field

Abstract

The electron-electron interaction in quantum dots leads to interesting effects which are highly elusive. For example, the magnetization of dots containing very small numbers of electrons is predicted to oscillate with magnetic field. The reason is that the ground states prefers to be at certain magic values of the total angular momentum which are field-dependent and the oscillations mirror jumps from one magic angular momentum value to another. This behaviour is a direct consequence of the Pauli principle which enables the electrons to reduce their energy optimally only at the magic angular momenta. An expression for the magic angular momenta in the spin-polarized case is given and electron probability distributions are computed to illustrate the physical difference between magic and nonmagic states. In the limit of large angular momentum the ground state appears to be the molecular analogue of a Wigner crystal.