我们采用狄拉克-韦尔 (Dirac-Weyl) 模型, 计算出二维石墨烯基磁量子环和磁量子点分别在垂直非均匀磁场下的低态能谱, 并讨论包括两组旋量分量的低态能谱跟磁场的依赖关系。从直接对角计算法所获得的数值结果表明, 在非均匀磁场下, 磁量子点和磁量子环的能谱中的最低朗道能级(N-=0)皆为高度简并, 且数值恒等为零。在其邻近较高的朗道能级, 磁量子环出现了由磁场诱导的轨道角动量间的跃迁, 而磁量子点则没有。最后本文指出, 除了最低朗道能级(N-=0)外, 两组旋量分量的能谱完全一样, 只是其朗道能级所标记的两组量子数不同而已。

Using the Dirac-Weyl model, we present the magnetic-field dependence of low-lying spectra of two-dimensional graphene-based magnetic dot and ring, including both spinor components, creating from perpendicular inhomogeneous magnetic fields. Numerical results obtained from direct diagonalization show that, under inhomogeneous magnetic fields, the lowest Landau level (N-=0) is highly degenerate at zero energy, and for the other higher neighboring Landau levels, there exist angular momentum transitions induced by magnetic fields for the magnetic ring but not for the magnetic dot. Furthermore, the low-lying spectra for both spinor components, except for N-=0, are exactly the same only with the states labeled by different sets of quantum numbers.