Midgap states and the fractional quantum Hall regime in graphene quantum dots*

Graphene quantum dots (QDs) with zigzag edges exhibit midgap single-paticle states associated with such edges. At zero magnetic field ($B$), these states form a manifold of degenerate states similar to the lowest Landau level that forms in semiconductor QDs at high $B$. It has been recently suggested\footnote{B. Wunsch {\it et al.\/}, arXiv:0707.2948v2} that the midgap-state manifold in graphene dots can support correlated many-body states similar to the rotating-electron-molecule (REM) states (also referred to as rotating Wigner crystallites) that are well known in semiconductor QDs at high $B$.\footnote{C. Yannouleas and U. Landman, Rep. Prog. Phys. {\bf 70}, 2067 (2007)} Here, we will report systematic exact-diagonalization calculations (for $N=4-10$ QD electrons) describing the REM states in graphene QDs. We anticipate that the graphene REM states exhibit for all $N$ a single polygonal ring of localized electrons, in contrast to the multiple polygonal-ring configurations known from semiconductor QDs.