Theoretical studies of topological and electron correlation effects in graphene

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I studied electronic and topological properties of graphene and silicene (graphene's cousin).In particular, I analyzed various topological insulators and their topological phase transitions. Main results read as follows: The zero-energy sector of the triangular zigzag graphene is investigated based on the Dirac theory of graphene.Analytic wave functions of triangular graphene are obtained. A vortex with the winding number 2 emerges in triangular graphene. Graphene nanodisk arrays have multi-degenerate perfect flat bands and are ferromagnet. The band gap of silicene can be controlled by external electric field applied perpendicular to silicene. Silicene shows the quantum anomalous-Hall effect when ferromagnet is attached. Furthermore, silicene undergoes a topological phase transition by photo-irradiation, where single-Dirac cone states appear at the critical point.I also studied the skyrmion, which is a topological structure in magnet.