Majorana Anyon Composites in Magneto-Photoluminescence Spectra of Natural Quantum Hall Puddles

In magneto-photoluminescence (magneto-PL) spectra of quasi two-dimensional islands (quantum dots) having seven electrons and Wigner-Seitz radius r(s)similar to 1.5, we revealed a suppression of magnetic field (B) dispersion, paramagnetic shifts, and jumps of the energy of the emission components for filling factors nu > 1 (B < 10 T). Additionally, we observed B-hysteresis of the jumps and a dependence of all these anomalous features on r(s). Using a theoretical description of the magneto-PL spectra and an analysis of the electronic structure of these dots based on the single-particle Fock-Darwin spectrum and many-particle configuration-interaction calculations, we show that these observations can be described by the r(s)-dependent formation of the anyon (magneto-electron) composites (ACs) involving single-particle states having non-zero angular momentum and that the anyon states observed involve Majorana modes (MMs), including zero-B modes having an equal number of vortexes and anti-vortexes, which can be considered as Majorana anyons. We show that the paramagnetic shift corresponds to a destruction of the equilibrium self-formed nu similar to 5/2 AC by the external magnetic field and that the jumps and their hysteresis can be described in terms of Majorana qubit states controlled by B and r(s). Our results show a critical role of quantum confinement in the formation of magneto-electrons and implies the liquid-crystal nature of fractional quantum Hall effect states, the Majorana anyon origin of the states having even nu, i.e., composite fermions, which provide new opportunities for topological quantum computing.