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

Abstract

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 with 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-principles calculations with two-band kp 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 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 half-valley-metal state. In addition, we find that in the so obtained half-valley-metal state, the conduction valley demonstrates Dirac cone-like linear energy dispersion. Interestingly, with the increase of the correlation effect, the system becomes insulating again with all valleys follow same optical selection rule. We confirm that in this specific case, the valence bands, which consist of single spin, possess non-zero Chern number and consequently intrinsic quantum anomalous valley Hall effect emerges. Our findings open an appealing route toward functional 2D materials design of valleytronics.