We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential demarcated in a large intrinsic graphene circular ribbon which is then connected to a circular lead. Considering different regions composing our system, we explicitly determine the energy spectrum solutions in terms of Hankel functions using the scattering matrix approach. The asymptotic behavior of the Hankel functions for large arguments allowed us to calculate the density of states (DOS) and show that it has an oscillatory behavior with the appearance of some resonant peaks associated with the quantum dot bound states with definite angular momenta. It was also found that the energy gap can control the amplitude and width of these resonances and affect even their location as reflected in the density of states profile.

我们研究了在存在磁通量的情况下，带隙石墨烯量子点中载流子的静电限制。圆形量子点由在大型本征石墨烯圆形带中划分出的静电栅极电势定义，然后将其连接到圆形引线。考虑组成系统的不同区域，我们使用散射矩阵方法根据汉克尔函数明确确定能谱解。Hankel函数对于大参数的渐近行为使我们能够计算态密度（DOS），并显示出它具有振荡行为，并且出现了一些共振峰，这些共振峰与具有确定角动量的量子点束缚态相关。