Interaction-Induced Spin Polarization in Quantum Dots

The electronic states of lateral many-electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb-blockade peaks are measured. A zigzag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.

Figure 1

Schematic of a single lateral quantum dot connected to two leads (Source and Drain). In a perpendicular magnetic field, Landau levels ($LL$) appear with a specific spin polarization. Landau level 0 is located at the edge of the dot, Landau level 1 in the center. Arrows show the spin configuration within each Landau level.

Figure 2

(a) Differential conductance $G$ as a function of magnetic field $B$ and gate voltage $V_G$. Six Coulomb peaks are visible showing a pronounced zigzag pattern. (b) The peak positions are transferred to an energy scale with the Coulomb energy removed. A cross pattern is found with states going down in energy with increasing field ($LL0$) and states going up in energy ($LL1$).

Figure 3

(a) Measured energetic peak distances for states in $LL0$ (triangles) and in $LL1$ (diamonds). The distances for $LL0$ show a bimodal behavior due to spin and can be fitted with the Fock-Darwin model (dashed lines, $\hslash {\omega }_0=1.83\mathrm{meV}$, $g^{*}=-0.71$). The Fock-Darwin spectrum using these parameters is shown in (b). Values for $LL1$ [diamonds in (a)] cannot be explained with the Fock-Darwin spectrum.

Figure 4

Results of the SDFT calculations: (a) chemical potentials ${\mu }_{46}$, ${\mu }_{47}$, and ${\mu }_{48}$ without Coulomb energy. As in the experiment, a cross pattern is found. (b) Energetic distances for the two Landau levels. The data qualitatively fit to the measurements. For $LL0$ a bimodal behavior is found (squares). The values for $LL1$ (diamonds) increase with increasing field and do not show a bimodality.

Figure 5

Spin configuration resulting from the SDFT calculations for a typical section of the zigzag pattern. While electrons in $LL0$ are filled in regularly with alternating spin, $LL1$ is spin polarized with electrons having spin up only.