Evidence of Correlation in Spin Excitations of Few-Electron Quantum Dots

We report inelastic light scattering measurements of spin and charge excitations in nanofabricated $\mathrm{AlGaAs}/\mathrm{GaAs}$ quantum dots with few electrons. A narrow spin excitation peak is observed and assigned to the intershell triplet-to-singlet monopole mode of dots with four electrons. Configuration-interaction theory provides precise quantitative interpretations that uncover large correlation effects that are comparable to exchange Coulomb interactions.

Figure 1

Side panels: Scanning electron microscope images of the studied QDs. (a) Experimental low-temperature ($T=1.8\mathrm{K}$) polarized (parallel incident and scattered photon polarizations, in red) and depolarized (perpendicular incident and scattered light polarizations, in black) resonant inelastic light scattering spectra after conventional subtraction of the background due to laser light. Incident laser energy is 1567 meV, intensity is $I=0.08\mathrm{W}/{\mathrm{cm}}^2$, and integration time is 30 minutes. Fits of the data with three Gaussians are shown. (b) Theoretical spectra for electron number $N=4$. Gaussian distributions with a phenomenological standard deviation $\sigma =0.18\mathrm{meV}$ were used.

Figure 2

Evolution of the theoretical inelastic light scattering spectra as a function of electron occupation number $N$ within a configuration-interaction approach. Red (black) curves represent charge (spin) excitations. The blue peak is the TS monopole mode.

Figure 3

(a) Evolution of spin excitations as a function of incident laser intensity. The resonant laser energy is 1567 meV. (b) Temperature dependence of spin transitions. The laser intensity $I$ is $0.1\mathrm{W}/{\mathrm{cm}}^2$. Spectra are presented after conventional subtraction of background due to laser light.

Figure 4

Comparison between measured (right column) and calculated excitation energies of charge (red) and spin (black) channels, identified by arrows in Fig. 1: From left to right, noninteracting Fock-Darwin model (FD), self-consistent Hartree-Fock (HF), full configuration interaction (CI). Side diagrams show the most-weighted configurations in the CI linear expansion of correlated wave functions, with the corresponding weight percentage. HF calculations refer to such configurations.