Zhang Shuo, Zhang Xiaoming, He Zeqing, Jin Lei, Liu Cong, Liu Ying, Liu Guodong
State Key Laboratory of Reliability and Intelligence of Electrical Equipment, and School of Materials Science and Engineering Hebei University of Technology, Tianjin 300130, China.
Hebei Engineering Laboratory of Photoelectronic Functional Crystals, and School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China.
Nanoscale. 2023 Sep 1;15(34):14018-14024. doi: 10.1039/d3nr01606d.
The investigation of two-dimensional (2D) multiferroic and topological quantum phases is a significant topic in current condensed matter physics. In this study, we discover quantum topological phases in the multiferroic material TlNO. We observe that its ferroelectric (FE) phase displays a ferromagnetic ground state with magnetization favoring in-plane orientation. In the absence of spin-orbit coupling (SOC), a Weyl nodal loop around the Fermi level is evident, representing a 1D band crossing between spin-up and spin-down states. When spin-orbit coupling is taken into account, setting the magnetization in-plane, the Weyl nodal loop becomes gapped. Additionally, a pair of 2D Weyl nodes appear on the high-symmetry path, protected by a vertical mirror symmetry allowed by the magnetization. Remarkably, we prove that the Weyl nodes are situated at the topological phase transition between two quantum anomalous Hall (QAH) phases with opposite Chern numbers. Therefore, by adjusting the magnetization, it is possible to switch the propagation direction of chiral edge states. Furthermore, from its ferroelectric state to a paraelectric state, the time-reversal symmetry breaking nodal line is transformed into a Weyl point, achieving 100% spin polarization. Particularly, the Weyl points remain robust against SOC when the vertical mirror symmetry is preserved. Importantly, we also demonstrate that the Weyl point also represents the transition point where the QAH phase changes the sign of its Chern number. Overall, our study provides new insights into the study of multiferroic and topological phenomena in 2D materials and offers a potential avenue for controlling QAH phases.
二维（2D）多铁性和拓扑量子相的研究是当前凝聚态物理中的一个重要课题。在本研究中，我们在多铁性材料TlNO中发现了量子拓扑相。我们观察到其铁电（FE）相呈现出一个铁磁基态，磁化方向倾向于面内取向。在没有自旋轨道耦合（SOC）的情况下，费米能级附近存在一个外尔节线环，这代表了自旋向上和自旋向下状态之间的一维能带交叉。当考虑自旋轨道耦合并将磁化设置为面内时，外尔节线环出现能隙。此外，一对二维外尔点出现在高对称路径上，由磁化允许的垂直镜面对称性保护。值得注意的是，我们证明外尔点位于两个具有相反陈数的量子反常霍尔（QAH）相之间的拓扑相变处。因此，通过调整磁化强度，可以切换手性边缘态的传播方向。此外，从其铁电态转变为顺电态时，时间反演对称性破缺的节线会转变为一个外尔点，实现100%的自旋极化。特别地，当垂直镜面对称性得以保留时，外尔点对自旋轨道耦合具有鲁棒性。重要的是，我们还证明外尔点也代表了QAH相陈数符号发生变化的转变点。总体而言，我们的研究为二维材料中的多铁性和拓扑现象研究提供了新的见解，并为控制QAH相提供了一条潜在途径。
