Concepts of the half-valley-metal and quantum anomalous valley Hall effect

Valley, the energy extrema in the electronic band structure at momentum space, is regarded as a new degree of freedom of electrons, in addition to charge and spin. The studies focused on valley degree of freedom now form an emerging field of condensed-matter physics, i.e., valleytronics, whose development is exactly following that of spintronics, which focuses on the spin degree of freedom. Here, in analogy to half-metals in spintronics where one spin channel is conducting, whereas the other is insulating, we propose the concept of half-valley metal, in which conduction electrons are intrinsically 100% valley polarized, as well as 100% spin polarized even when spin-orbit interactions are considered. Combining first-principle calculations with a two-band k.p model, the physical mechanism to form the half-valley metal is illuminated. Taking the ferrovalley H-FeCl2 monolayer with strong exchange interaction as an example, we find that the strong electron correlation effect can induce the ferrovalley to half-valley-metal transition. Due to the valley-dependent optical selection rules, such a system could be transparent to, e.g., left-circularly polarized light, yet the right-circularly polarized light will be reflected, which can in turn be used as a crucial method to detect the half-valley-metal state. Interestingly, with the increase of the correlation effect, the system becomes insulating again with all valleys following the same optical selection rule. We confirm that in this specific case, the valence bands, which consist of single spin, possess nonzero Chern number and consequently an intrinsic quantum anomalous valley Hall effect emerges. Our findings open an appealing route toward functional 2D materials design of valleytronics.