The spin fields of the ground state of the two-dimensional quantum rings with Rashba and Dresselhaus spin-orbit couplings are studied and compared with our analysis of the one-dimensional model. The topological charge of the spin field varies periodically due to the step-like change of the angular momentum with an increase of the magnetic field which is perpendicular to the ring. We also demonstrate the cases where the one-dimensional model is invalid or unreliable for a relatively wide ring, by comparing with the reliable numerical results of the two-dimensional model. As a result, the period of the topological transition can be biased from the period of the Aharonov-Bohm effect. Moreover, in a non-symmetric quantum ring where a non-magnetic impurity is located, the density and the spin textures of the single-electron ground state jointly make a dramatic change comparing with the one-dimensional model. Even higher topological charge ±2 of the spin field at single-electron level can be achieved by tuning the magnetic field, which indicates a great advantage over other systems in potential applications.

研究了带有Rashba和Dresselhaus自旋轨道耦合的二维量子环基态的自旋场，并将其与我们对一维模型的分析进行了比较。由于角动量随着垂直于环的磁场的增加而呈阶梯状变化，因此自旋场的拓扑电荷周期性地变化。通过与二维模型的可靠数值结果进行比较，我们还证明了一维模型对于相对较宽的环无效或不可靠的情况。结果，拓扑转变的周期可以与阿哈罗诺夫-波姆效应的周期有偏差。另外，在非磁性杂质所在的非对称量子环中，与一维模型相比，单电子基态的密度和自旋织构共同发生了巨大变化。通过调节磁场，甚至可以在单电子水平获得更高的自旋场拓扑电荷±2，这表明在潜在应用中，与其他系统相比，它具有很大的优势。