HgMnTe量子阱中自旋轨道耦合诱导的拓扑相变

Topological Phase Transition Driven by Spin-Orbit Coupling in HgMnTe Quantum Wells

摘要: 在能带反转的HgTe量子阱中，体态内存在着受拓扑保护的无能隙的螺旋边界态为特征的量子自旋霍尔效应。在HgTe量子阱中掺入磁性原子(例如锰)后，磁性HgMnTe量子阱将会出现量子反常霍尔效应。本文我们讨论了由体反演不对称产生的自旋轨道耦合作用在HgMnTe量子阱中诱导的拓扑相变。首先，通过解析计算自旋陈数，我们发现当自旋轨道耦合强度超过某个临界值的时候，在HgTe量子阱中，发生了从拓扑绝缘体到普通绝缘体的拓扑相变。在交换场和自旋轨道耦合的共同作用下，通过数值计算自旋陈数，我们画出了在不同参数下的拓扑相图。我们发现，当锰掺杂引起的交换场系数GEGH < 0时，拓扑相图中出现了三个区域：普通绝缘体，拓扑绝缘体以及量子反常霍尔效应。当GEGH > 0时，出现了新的体态能隙闭合区域。然而随着自旋轨道耦合作用的增加，将会在该能隙闭合区域重新打开一个能隙。

Abstract: In the inverted band HgTe quantum wells (QWs), there are quantum spin Hall effects characterized by topological protected gapless helical edge states within the bulk energy gap. By doping magnetic atoms (such as Mn) in HgTe layer, quantum anomalous Hall effects (QAH) may occur in magnetic HgMnTe QWs. In this paper, we investigate the effect of spin-orbit coupling induced by bulk inversion asymmetry on HgMnTe QWs with respect to topological phase transition. Firstly, by the method of analytic calculation of spin Chern number in HgTe QWs, a topological phase transition from topological insulators (TI) to normal insulators (NI) is presented in HgTe QWs when the strength of spin-orbit coupling exceeds a critical value. On the combined effect of spin-orbit coupling and exchange filed, by numerical calculating spin Chern number, we plot the topological phase diagram with various parameters. When the coefficients GE and GH depicting the exchange field satisfy GEGH < 0, three regions appear on the phase diagram, i.e., NI, TI and QAH. When GEGH > 0, a new region of gap closing appears and a nonzero spin-orbit coupling will open a gap in this region.