Excitonic Energy Shell Structure of Self-Assembled InGaAs/GaAs Quantum Dots

Performing optical spectroscopy of highly homogeneous quantum dot arrays in ultrahigh magnetic fields, an unprecedently well resolved Fock-Darwin spectrum is observed. The existence of up to four degenerate electronic shells is demonstrated where the magnetic field lifts the initial degeneracies, which reappear when levels with different angular momenta come into resonance. The resulting level shifting and crossing pattern also show evidence of many-body effects such as the mixing of configurations and exciton condensation at the resonances.

Figure 1

(a) Energy shell structure of electrons and holes for noninteracting two-dimensional harmonic oscillators (b) Emission spectra of the QD ensemble as a function of increasing annealing temperature (30 s anneals). Nominal excitation power density $\sim 200\mathrm{W}/{\mathrm{cm}}^2$ (c) Surface plot describing evolution of PL (second derivative) spectrum as a function of magnetic field. Black, red, and yellow represent low, medium, and high emission intensity, respectively. Excitation power density is $\sim 400\mathrm{W}/{\mathrm{cm}}^2$. All experiments performed at $\mathrm{T}=4.2\mathrm{K}$

Figure 2

(a) Calculated excitonic FD spectrum for electron and hole mass, confinement energy of $0.05{\mathrm{m}}_0$, $0.25{\mathrm{m}}_0$, 33.0 meV, and 6.6 meV, respectively. The value of $E_0$ was set at 1.269 for comparison with (b) calculated joint density of states from microscopic 8-band $k*p$ model.

Figure 3

Calculated emission energy (chemical potential) of a quantum dot as a function of magnetic field and population of Fock-Darwin levels. (a) Difference between the evolution of five electrons versus five excitons configurations in the vicinity of crossing of FD levels. (b) Evolution of $N_X=1\dots 12$ chemical potential for interacting (colored solid lines) and noninteracting (gray dashed lines) excitons. Solid circles indicate experimental peak positions, shifted in energy to have coincident $0T$ $s$-shell energy. Parameters used are as for Fig. 2a for both single-particle and many-body calculation.