通過在拓撲絕緣體中引入、操作鐵磁有序能産生許多新穎的物理現象，如k空間的非平庸拓撲相變，因此凝聚态物理領域對磁性拓撲絕緣體的研究是一個重要的研究課題。在磁性拓撲絕緣體中，由于時間反演對稱性的破缺，拓撲絕緣體的表面态将會打開一個交換帶隙，産生一定的貝裡曲率，因此系統具有内廪的反常霍爾效應。在這個帶隙中出現了非零的陳（省身）數量子态，即C=±1，系統的邊緣将會存在一個手性的拓撲邊緣态，并受到拓撲保護。目前制備磁性拓撲絕緣體的手段主要有兩個，第一是通過磁性摻雜，第二是通過磁近鄰效應。前者已經成功地實現了量子反常霍爾效應，但由于實現的溫度極低（低于300mK），因此人們嘗試通過把拓撲絕緣體和高溫鐵磁體耦合在拓撲絕緣體的表面誘導出鐵磁有序。除了鐵磁體，何慶林研究員在早期的研究中指出還能通過耦合反鐵磁體的方式來産生鐵磁有序。相對于鐵磁體，反鐵磁體具有極小的淨磁化，因此既不産生漏磁場也不影響拓撲絕緣體磁性的表征和探測，降低器件之間的耦合，提高器件密度。

近期，beat365量子材料科學中心的何慶林研究員及其合作者在實驗上觀察到拓撲絕緣體薄膜的拓撲相變。通過使用反鐵磁體，拓撲絕緣體的表面态能夠分别被磁化并受到獨立控制。如圖a，c所示，當上下表面磁化（M_T和M_B）具有相同的符号并大于表面雜化帶隙m_0時（Case i和iii），系統的陳數為C =±1，具有手性邊緣态，也就是量子反常霍爾效應。另一方面，在磁矩翻轉的瞬間，由于上下表面磁矩翻轉在這個材料系統中不同步，因此也能形成性的拓撲相。當M_T > 0 和M_B < 0 時，由于時間反演對稱性和反對稱性同時被打破（Case iv），邊緣态會打開一個帶隙，系統變成一個常規絕緣體，系統的陳數變為零（圖d）。有趣的是，在磁矩翻轉的時候還能産生另一個拓撲相（Case ii）。當M_T = M_B 以及|M_T,B| < m_0時，系統的陳數也為零，但由于反對稱性的恢複，系統具有一對反向傳播的邊緣态（圖b），即螺旋式邊緣态。以上四種拓撲相及拓撲相變能夠通過一個反鐵磁體-拓撲絕緣體-反鐵磁體三層結構樣品的輸運性質來探測到，并通過計算非平衡格林函數來模拟。如圖e所示，當樣品具有螺旋式邊緣态時，由于導電溝道的增加，系統的磁阻在相應的磁場區域會突然變小（Case ii）；當系統變為一個常規絕緣體時，由于導電溝道的減少，系統的磁阻也相應地增加（Case iv）。由于這兩種情況的不對稱性，實驗上也能觀察到不對稱的磁阻信号，如圖e所示。這一理論計算和實驗數據相符。

該工作于2018年8月29日發表于知名學術期刊《物理評論快報》上。論文鍊接：https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.096802.

該項工作由量子中心的何慶林研究員、美國加州大學洛杉矶分校的王康隆教授團隊、美國國家技術标準研究院的Alexander J. Grutter博士和Brian J. Kirby博士、香港科技大學的K. T. Law教授團隊、美國加州大學歐文分校的夏晶教授團隊、北京工業大學的韓曉東教授團隊、美國加州大學河濱分校的Roger K. Lake教授等合作完成。其中，何慶林研究員、Gen Yin博士、Luyan Yu為文章第一作者，何慶林教授和王康隆教授為文章共同通訊作者。該項工作得到了國家自然科學基金面上項目（項目号 11874070）、國家重點研發計劃 （項目号 2018YFA0305601）以及中組部“青年千人”計劃的支持。

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.