标题： 三维拓扑反常霍尔效应在外尔半金属中 显示英文标题

标题： Three-dimensional quantum anomalous Hall effect in Weyl semimetals

摘要： 量子反常霍尔效应（QAHE）是一种量子现象，在无磁场的情况下，二维系统表现出量子化的霍尔电阻$h/e^2$，其中$h$是普朗克常数，$e$是电子电荷。 在本工作中，我们将这种新颖的相扩展到三维，并因此提出一种具有更丰富和更通用输运行为的三维 QAHE。 我们首先通过量子化的陈数确认这种三维 QAHE，然后建立其体-边界对应关系，最后通过独特的输运特性重新验证它。 值得注意的是，我们发现三维 QAHE 在一个空间方向上承载两个手性表面态，而在另一个方向上承载一对手性棱边态，且棱边态的位置对费米能级非常敏感。 这两种类型的边界态通过垂直的手性表面态进一步连接，其手性也依赖于费米能级。 因此，根据输运方向，当费米能级穿过电荷中性点时，其霍尔电阻可以量子化为$0$、$h/e^2$或$\pm h/e^2$。 这种三维 QAHE 不仅填补了霍尔效应家族中的空白，而且在内存计算等器件应用中具有重要的潜力。 显示英文摘要

摘要： The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron charge. In this work, we extend this novel phase to three dimensions and thus propose a three-dimensional QAHE exhibiting richer and more versatile transport behaviors. We first confirm this three-dimensional QAHE through the quantized Chern number, then establish its bulk-boundary correspondence, and finally reaffirm it via the distinctive transport properties. Remarkably, we find that the three-dimensional QAHE hosts two chiral surface states along one spatial direction while a pair of chiral hinge states along another direction, and the location of the hinge states depends sensitively on the Fermi energy. These two types of boundary states are further connected through a perpendicular chiral surface states, whose chirality is also Fermi energy dependent. Consequently, depending on the transport direction, its Hall resistance can quantize to $0$, $h/e^2$, or $\pm h/e^2$ when the Fermi energy is tuned across the charge neutral point. This three-dimensional QAHE not only fill the gap in the Hall effect family but also holds significant potentials in device applications such as in-memory computing.