这两天，研读了一些霍尔效应的文献，特别是C. X. Liu, S. C. Zhang, X. L. Qi, The Quantum Anomalous Hall Effect: Theory and Experiment. Annual Review of Condensed Matter Physics, 7: 301-321 (2016).一文，要点摘录如下：

    Two necessary conditions for Quantum anomalous Hall (QAH) effect of (a) inverted band structures and (b) ferromagnetic insulators have been suggested for seeking realistic materials. For the first condition, one may consider materials with electronic band structure in the inverted regime or close to the transition point when there is no magnetization. Only for these materials, it is possible for the exchange coupling to drive the system into the inverted regime. This indicates that we should consider time reversal invariant topological insulators, of which the band structure is already inverted, or other narrow gap (or zero gap) semiconductors. The second condition is not easy to satisfy because ferromagnetism usually coexists with metallic behaviors, and ferromagnetic insulators are rare. There are several ferromagnetic insulators, such as EuO and GdN. However, inverted band structure is difficult to realize in these materials because of the large band gap.

    The QAH effect has potential applications in future electronic devices. A key signature of the QAH state is the chiral edge state, which can carry electric current without dissipation, because all electrons have the same direction of current, and backscattering is impossible. Dissipationless transport is always very important because Joule heating becomes a more and more significant problem when the size of electronic devices is reduced. It has been shown that chiral edge states can also carry spin polarization, thus enabling the potential applications in spintronics. Another mechanism to realize dissipationless transport is, of course, using superconductors. Currently, both the QAH state and superconductivity require very low temperatures, which limits their practical application. However, one may suspect that it is in general easier to realize a room-temperature QAH state than to realize a room-temperature superconductor, because magnetism can easily occur at room temperature in many materials. More experimental and theoretical efforts in seeking QAH materials are certainly required for finding the route toward a room temperature QAH effect.

    该文建议"室温""窄禁带铁磁半导体"是实现"量子反常霍尔效应"应用的物质基础。