Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counterpropagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This topological surface state crosses the bandgap of the TI and lives at the interface between the topological and a trivial material, such as vacuum. Despite its balanced perfection, it is rather useless for any practical applications. Instead, it takes the breaking of time-reversal symmetry (TRS) and the appearance of an exchange gap to unlock hidden quantum states. The quantum anomalous Hall effect, which has first been observed in Cr-doped (Sb,Bi)2Te3, is an example of such a state in which two edge channels are formed at zero field, crossing the magnetic exchange gap. The breaking of TRS can be achieved by magnetic doping of the TI with transition metal or rare earth ions, modulation doping to keep the electronically active channel impurity free, or proximity coupling to a magnetically ordered layer or substrate in heterostructures or superlattices. We review the challenges these approaches are facing in the famous 3D TI (Sb,Bi)2(Se,Te)3 family and try to answer the question whether these materials can live up to the hype surrounding them.

中文翻译：

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3D 拓扑绝缘体中的磁序——一厢情愿的想法还是通往新兴量子效应的大门？

三维拓扑绝缘体 (TI) 是一种完美调谐的量子力学机制，其中反向传播和相反自旋极化的传导通道在材料表面相互平衡。这种拓扑表面状态跨越了 TI 的带隙，并存在于拓扑和普通材料（如真空）之间的界面处。尽管它的平衡完美，但它对于任何实际应用都毫无用处。相反，它需要打破时间反转对称性 (TRS) 和交换间隙的出现来解锁隐藏的量子态。量子反常霍尔效应首先在 Cr 掺杂的 (Sb,Bi)2Te3 中观察到，是这种状态的一个例子，其中在零场形成两个边缘通道，穿过磁交换间隙。TRS 的破坏可以通过用过渡金属或稀土离子对 TI 进行磁性掺杂、调制掺杂以保持电子活性通道杂质自由、或与异质结构或超晶格中的磁性有序层或衬底的邻近耦合来实现。我们回顾了这些方法在著名的 3D TI (Sb,Bi)2(Se,Te)3 家族中面临的挑战，并试图回答这些材料是否能达到围绕它们的炒作的问题。