Abstract
We show that the appearance of ‘accidental’ degeneracies (degeneracies which persist beyond the harmonic potential) in the single-particle spectrum of quantum dots in a magnetic field can be understood by analyzing the evolution of the structure of the classical orbits of the system as a function of magnetic field. We demonstrate that these degeneracies are associated with closed orbits, which occur at particular magic ratios of the cyclotron energy to the confinement energy in the harmonic case. The spectrum of degenerate energies forms an interesting self-similar structure with an associated complete ‘devil's staircase’. Since the degeneracies are not lifted by deviations from parabolicity of the radial confinement potential of the dot, the devil's staircase structure that we predict should be detectable experimentally using available techniques.
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