Theoretical studies of topological and electron correlation effects in graphene

我研究了石墨烯和硅烯（石墨烯的表亲）的电子和拓扑特性。特别地，我分析了各种拓扑绝缘体及其拓扑相变。主要研究结果如下：基于石墨烯的狄拉克理论，研究了三角形之字形石墨烯的零能扇区。得到了三角形石墨烯的解析波函数。一个圈数为2的漩涡出现在三角形石墨烯中。石墨烯纳米磁盘阵列具有多简并完美平坦带和铁磁性。硅烯的带隙可以通过施加垂直于硅烯的外加电场来控制。硅烯在附着铁磁体时表现出量子反常霍尔效应。此外，硅烯在光照射下发生拓扑相变，在临界点处出现单狄拉克锥态。我还研究了skyrmion，它是磁铁中的拓扑结构。

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.