圆盘形石墨烯量子点电子能态的尺寸效应

Size Effect of Electronic States in Graphene Quantum Disk

通过数值求解电子的狄拉克方程研究了半径为R的圆盘形石墨烯量子点的电子能谱,获得了扶手型和锯齿型两种边界的石墨烯量子盘在有、无外加磁场下电子的能级随量子盘半径的变化关系.研究发现,无外加磁场时,电子能级随着量子盘半径的增大而降低,半径越小,降低得越快;在有磁场时,扶手型量子盘出现了简并的最低朗道能级,且半径越大,简并度越高;在有磁场时,锯齿型量子盘随着半径的增大量子数m为正值的能态减少,m为负值的能态增多,即能谱图中出现了能谱往左边倾斜的现象.

In this paper, we studied the disk radius R graphene quantum dots of electronic spec- troscopy by solving the Dirac equation of electron. We obtained two shapes of armrest and saw boundary of graphene quantum disk electronic energy level in the situation of whether with ap- plied magnetic field or not,along with the change of radius of the quantum disk, respectively. The result of the research showed that the energy level of electron is inversely proportional to the radius of the quantum disk with no additional magnetic field. However, with the condition of additional magnetic field,the armchair quantum disk shows the least Landau energy level in degeneracy and it is proportional to radius. The energy level with positive value of quantum number m of the zigzag quantum disk is proportional to radius and with negative value is inverse proportional to radius, which means the energy spectrum has sloped to the left.