Density-functional theory of multicomponent quantum dots

Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different types of fermions with isotropic effective masses. The density-functional method with the local density approximation is used. The increased number of internal (Kohn-Sham) states leads to a generalization of Hund’s first rule at high densities. At low densitites the formation of Wigner molecules is favored by the increased internal freedom.

Figure 1

Addition energy spectrum of a four-component quantum dot. The confinement potential changes with the number of electrons so that the average electron density in the dot center corresponds to $r_s=2a_0^{*}$. The inset shows schematically the filling of levels in the case of 10 electrons. The peaks at 4, 12, and 24 are caused by shell closings while those in between are caused by Hund’s rule.

Figure 2

The total electron densities of a quantum dot having (from left to right) 7, 8, and 9 electrons at low densities. The confinement strenght is $K=2\bullet {10}^{-4}$ atomic units. The localization in the local density approximation is made possible by the eight internal degrees of freedom of the system.

Figure 3

Addition energy for a eight component quantum dot at a low electron density (the confinement strenght is $K=2\bullet {10}^{-4}$ atomic units). The spectrum shows a weak kink at $N=7$ as a precursor of the geometrically magic structure. For comparison, addition energy spectrum of classical electrons is shown.

Figure 4

Electron density of a four-cmponent quantum dot for three different values of $r_s$: From left to right $r_s=2a_0^{*}$, $6a_0^{*}$, and $14a_0^{*}$. The localization in the multicomponent LDA is made possible by the fact that the neighboring localized electrons belong to different components as indicated by numbers in the contour plot.

Figure 5

The effect of varying effective mass on the single particle Kohn-Sham levels in a four component electron system with 24 electrons. The light components have mass $m=1m_e$ and the heavy mass is indicated in the figure.