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We investigate the way that the degenerate manifold of midgap edge states inquasicircular graphene quantum dots with zig-zag boundaries supports, underfree-magnetic-field conditions, strongly correlated many-body behavioranalogous to the fractional quantum Hall effect (FQHE), familiar from the caseof semiconductor heterostructures in high magnetic fields. Systematicexact-diagonalization (EXD) numerical studies are presented for the first timefor 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta inthe range of N(N-1)/2 <= L <= 150. We present a derivation of arotating-electron-molecule (REM) type wave function based on the methodologyintroduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315(2002)] in the context of the FQHE in two-dimensional semiconductor quantumdots. The EXD wave functions are compared with FQHE trial functions of theLaughlin and the derived REM types. It is found that a variational extension ofthe REM offers a better description for all fractional fillings compared withthat of the Laughlin functions (including total energies and overlaps), a factthat reflects the strong azimuthal localization of the edge electrons. Incontrast with the multiring arrangements of electrons in circular semiconductorquantum dots, the graphene REMs exhibit in all instances a single (0,N)polygonal-ring molecular (crystalline) structure, with all the electronslocalized on the edge. Disruptions in the zig-zag boundary condition along thecircular edge act effectively as impurities that pin the electron molecule,yielding single-particle densities with broken rotational symmetry that portraydirectly the azimuthal localization of the edge electrons.

Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field