We study the behaviour of a charge bound on a graphene annulus under the assumption that the particle can be treated as a massless Dirac electron. The eigenstates and relative energy are found in closed analytical form. Subsequently, we consider a large annulus with radius $\rho \in [5000,10,000]a_0$ in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radiation. Moreover, a small radial force acts upon the annulus with a stretching effect. A linearly polarized electromagnetic field propagating in the orthogonal direction is added; the time evolution of the operators show that the acceleration of the electron is proportional to the rate of change of the spin of the particle.

中文翻译：

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磁化环空中的激光辅助狄拉克电子

我们假设粒子可以被视为无质量的狄拉克电子，我们研究了在石墨烯环上束缚的电荷的行为。本征态和相对能以封闭的分析形式存在。随后，我们考虑了一个半径较大的环$\rho \in [5000，10，000]{\mathrm{一种}}_0$在存在一个垂直于其平面的静磁场的情况下，狄拉克电子的本征态和本征能再次以解析形式和数值形式找到。示出了通过控制轨道角动量和磁场来设计丝状电流的可能性。在受电磁辐射控制的光电设备中，电流可能是令人感兴趣的。此外，小的径向力以拉伸作用作用在环上。增加了在正交方向上传播的线性极化电磁场；算子的时间演化表明，电子的加速度与粒子自旋的变化率成正比。