Theoretical study on symmetries and properties of three-dimensional valleytronic systems

Materials with spin-split valleys showing direct bandgaps, such as transition metal dichalcogenides, have been attracting interest in the context of valleytronics. All such materials known so far are two-dimensional. In this talk, we show a list of space groups to realize three-dimensional materials with such a valley degree of freedom. For this purpose, we made some criteria for space groups allowing valleys with good properties for valleytronics, and we find that there are only a few space groups that satisfy all of these criteria. Moreover, we propose a model which possesses inequivalent six valleys, and reveal its properties in the context of valleytronics, such as spin-valley coupling, nonzero Berry curvature, and some ways of controlling these valleys.