通过在拓扑绝缘体中引入、操作铁磁有序能产生许多新颖的物理现象，如k空间的非平庸拓扑相变，因此凝聚态物理领域对磁性拓扑绝缘体的研究是一个重要的研究课题。在磁性拓扑绝缘体中，由于时间反演对称性的破缺，拓扑绝缘体的表面态将会打开一个交换带隙，产生一定的贝里曲率，因此系统具有内廪的反常霍尔效应。在这个带隙中出现了非零的陈（省身）数量子态，即C=±1，系统的边缘将会存在一个手性的拓扑边缘态，并受到拓扑保护。目前制备磁性拓扑绝缘体的手段主要有两个，第一是通过磁性掺杂，第二是通过磁近邻效应。前者已经成功地实现了量子反常霍尔效应，但由于实现的温度极低（低于300mK），因此人们尝试通过把拓扑绝缘体和高温铁磁体耦合在拓扑绝缘体的表面诱导出铁磁有序。除了铁磁体，何庆林研究员在早期的研究中指出还能通过耦合反铁磁体的方式来产生铁磁有序。相对于铁磁体，反铁磁体具有极小的净磁化，因此既不产生漏磁场也不影响拓扑绝缘体磁性的表征和探测，降低器件之间的耦合，提高器件密度。

近期，北京大学量子材料科学中心的何庆林研究员及其合作者在实验上观察到拓扑绝缘体薄膜的拓扑相变。通过使用反铁磁体，拓扑绝缘体的表面态能够分别被磁化并受到独立控制。如图a，c所示，当上下表面磁化（M_T和M_B）具有相同的符号并大于表面杂化带隙m_0时（Case i和iii），系统的陈数为C =±1，具有手性边缘态，也就是量子反常霍尔效应。另一方面，在磁矩翻转的瞬间，由于上下表面磁矩翻转在这个材料系统中不同步，因此也能形成性的拓扑相。当M_T > 0 和M_B < 0 时，由于时间反演对称性和反对称性同时被打破（Case iv），边缘态会打开一个带隙，系统变成一个常规绝缘体，系统的陈数变为零（图d）。有趣的是，在磁矩翻转的时候还能产生另一个拓扑相（Case ii）。当M_T = M_B 以及|M_T,B| < m_0时，系统的陈数也为零，但由于反对称性的恢复，系统具有一对反向传播的边缘态（图b），即螺旋式边缘态。以上四种拓扑相及拓扑相变能够通过一个反铁磁体-拓扑绝缘体-反铁磁体三层结构样品的输运性质来探测到，并通过计算非平衡格林函数来模拟。如图e所示，当样品具有螺旋式边缘态时，由于导电沟道的增加，系统的磁阻在相应的磁场区域会突然变小（Case ii）；当系统变为一个常规绝缘体时，由于导电沟道的减少，系统的磁阻也相应地增加（Case iv）。由于这两种情况的不对称性，实验上也能观察到不对称的磁阻信号，如图e所示。这一理论计算和实验数据相符。

该工作于2018年8月29日发表于知名学术期刊《物理评论快报》上。论文链接：https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.096802.

该项工作由量子中心的何庆林研究员、美国加州大学洛杉矶分校的王康隆教授团队、美国国家技术标准研究院的Alexander J. Grutter博士和Brian J. Kirby博士、香港科技大学的K. T. Law教授团队、美国加州大学欧文分校的夏晶教授团队、北京工业大学的韩晓东教授团队、美国加州大学河滨分校的Roger K. Lake教授等合作完成。其中，何庆林研究员、Gen Yin博士、Luyan Yu为文章第一作者，何庆林教授和王康隆教授为文章共同通讯作者。该项工作得到了国家自然科学基金面上项目（项目号 11874070）、国家重点研发计划 （项目号 2018YFA0305601）以及中组部“青年千人”计划的支持。

图：a-d，拓扑绝缘体薄膜上下表面具有不同自旋结构时的能带结构（黑色）。反铁磁体提供一个类抛物线的能带结构（灰色）。e，当拓扑绝缘体上下表面的磁矩不同时翻转时，能产生特殊的纵向和横向电阻输运特性。 Figure: a-d, The black solid lines show the energy spectrum of a TI thin film with different top-bottom spin configurations. The grey lines indicate the parabolic bands from the AFM layers. e, The evolution of the longitudinal resistance Rxx and the Hall resistance Rxy during the unsynchronized magnetic switching.

Physical Review Letters reports Prof Qing Lin He et al.’s study on topological transition in topological insulator

Currently there is immense interest in the manipulation of ferromagnetic phases in topological insulators (TIs) through either doping with magnetic elements or proximity coupling to a strong ferromagnetic system. This interest is driven by the novel physics which is a consequence of the non-trivial topology in k space. Breaking time-reversal symmetry in these systems with magnetic dopants opens an exchange band gap, inducing a finite Berry curvature and leading to an intrinsic anomalous Hall effect (AHE). Inside this exchange gap, non-zero Chern numbers (C) of ±1 arise, protecting a chiral edge mode. Other than doping, proximity coupling to ferromagnets is another common method to introduce ferromagnetic order in TIs. Besides ferromagnets, antiferromagnets (AFMs) have been recently shown by Prof Qing Lin He et al. to enhance the magnetic order of a Cr doped TI thin film through interfacial exchange coupling. AFMs have vanishingly small net magnetization and consequently neither produce stray fields nor affect the characterization of the TI layer. Therefore the magnetic order is robust against the external magnetic field or moderate current perturbations, minimizing the crosstalk between devices and improving the scalability.

Recently, Prof Qing Lin He in ICQM – Peking University and his collaborators reported an experimental observation of the topological transition in thin-film topological insulator. By using antiferromagnetism, the surface magnetizations in both surfaces of the TI can be independently controlled. As shown in Figs. a and c, when the top and bottom surface magnetizations, M_T and M_B, have the same sign and are larger than the hybridization gap m_0 (Cases i and iii), Chern number of the system is C =±1, and chiral edge modes are therefore introduced. The magnetic TI thin film Hamiltonian can describe a quantum-anomalous-Hall (QAH) phase with C =±1 counting the number of topologically protected edge modes. On the other hand, during the reversal of the magnetization, unsynchronized switching may occur, inducing intermediate magnetic configurations without edge modes. When M_T > 0 and M_B < 0, the edge modes are gapped out due to the breaking of both time-reversal symmetry and inversion symmetry (Case iv), and an insulating phase is therefore obtained (Fig. d). Interestingly, during the reversal of the magnetization, an intermediate magnetic configuration can occur as shown by Case (ii). In this case, the C = 0 Chern number can possess counter-propagating edge modes induced by a restored inversion symmetry when both M_T = M_B and |M_T,B| < m_0 are satisfied in a transient spin configuration. The energy spectrum of this special case is depicted in Fig. b. It is important to note that the different M_T,B configurations can be detected by measuring the longitudinal (Rxx) and the Hall resistance (Rxy) as demonstrated in Fig. e, in which, Rxx and Rxy of the magnetic thin film and the AFM layers are calculated numerically using nonequilibrium Green's function techniques. Importantly, when M_T = M_B and |M_T,B| < m_0, two counter-propagating helical edge modes arise due to the restored inversion symmetry of the sandwich structure, and Rxx is therefore reduced (Case ii). On the other hand, when M_T and _MB have opposite signs, the edge channels are absent and Rxx is increased (Case iv). Due to the intrinsic asymmetry of M_T and M_B, we obtain antisymmetric magneto-resistance (Rxx) spikes during magnetization reversals as demonstrated in Fig. e. It is remarkable that the experimentally measured Rxx and Rxy can be well explained by the numerical simulations.

The above work was published on Physical Review Letters on Aug 29, 2018. The link to this paper is: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.096802.

This work was studied by Prof Qing Lin He in ICQM, the group led by Prof Kang L Wang in UCLA, Dr. Alexander J. Grutter and Dr. Brian J. Kirby in NIST, the group led by Prof K. T. Law in HKUST, the group led by Prof Jing Xia in UC-Irvine, the group led by Prof Xiaodong Han in Beijing University of Technology, and Prof Roger K. Lake in UC-Riverside. Prof Qing Lin He, Dr. Gen Yin, and Luyan Yu are the first authors of the paper, while Prof Qing Lin He and Prof Kang L. Wang are the corresponding authors. This work is supported in part by the National Natural Science Foundation of China (Grant No. 11874070), the National Key R&D Program of China (Grant No. 2018YFA0305601), and National Thousand-Young Talents Program in China.