Few-electron ground states of charge-tunable self-assembled quantum dots

The few-electron ground states of self-assembled InAs quantum dots are investigated using high-resolution capacitance spectroscopy in magnetic fields up to 23 T. The level structure reveals distinct shells which are labeled as $s$-, $p$-, and $d$-like according to their symmetry. Our measurements enable us to resolve the single-electron charging not only of the lowest $\mathrm{}\left(s\right)\mathrm{}$ state with two electrons but also of the second lowest $\mathrm{}\left(p\right)\mathrm{}$ state with four electrons as pronounced maxima in the capacitance spectra. Furthermore, two peaks at higher energy can be attributed to charging of the $d$ shell with the first two electrons. We discuss the energy spectrum in terms of spatial quantization energy, Coulomb blockade, and many-particle effects. At around $B=15\mathrm{}$ T we observe a magnetic-field-induced intermixing of the $p$ and $d$ shell. Additional fine structure in the capacitance spectra is observed and discussed both in terms of nearest-neighbor Coulomb interactions and monolayer fluctuations of the dot size.