p-shell hybridization and Hund's-rule mitigation: Engineering Hilbert spaces in artificial atoms

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The magnetic-field dependence of many-body states in quantum dots can be tailored by controlling the mixing of various angular momenta. In lateral quantum dots -- defined electrostatically in a two-dimensional electron gas -- this mixing can be accomplished by introducing anisotropies in the confinement potential, thereby explicitly breaking rotational symmetry. Mixing can be severe enough to violate Hund's rules, even at zero magnetic field. We illustrate the principle through calculations of states and spectra of four-electron droplets (p-shell) with long-range Coulomb repulsions and confined in anisotropic potentials. Our results show that the Hilbert space in these nanostructures can be engineered to the particular application domain.