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We used photoluminescence spectra of single electron quasi-two-dimensional InP/GaInP 2 islands having Wigner-Seitz radius ~4 to measure the magnetic-field dispersion of the lowest s , p , and d single-particle states in the range 0-10 T. The measured dispersion revealed up to a nine-fold reduction of the cyclotron frequency, indicating the formation of nano-superconducting anyon or magneto-electron ( e  m ) states, in which the corresponding number of magnetic-flux-quanta vortexes and fractional charge were self-generated. We observed a linear increase in the number of vortexes versus the island size, which corresponded to a critical vortex radius equal to the Bohr radius and closed-packed topological vortex arrangements. Our observation explains the microscopic mechanism of vortex attachment in composite fermion theory of the fractional quantum Hall effect, allows its description in terms of self-localization of e  m s and represents progress towards the goal of engineering anyon properties for fault-tolerant topological quantum gates.

Fractional Charge States in the Magneto-Photoluminescence Spectra of Single-Electron InP/GaInP2 Quantum Dots