  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.
