The topological states of quantum matter have recently attracted widespread attention in condensed matter physics and materials science. Materials with these novel quantum effects exhibit exotic edge states [1,2], which are protected by the topology of their bulk electronic band structure. The edge states are highly robust against impurity scattering, allowing dissipation-less transport. These topologically protected edge states could be verified by the non-zero value of topological invariants associated with the bulk band structure [3,4].

Besides, isolated valleys at the band edges provide a new degree of freedom in addition to conventional charge and spin. A non-zero topological invariant associated with the valleys could combine the transport properties of valley and topology, providing a possibility to realize the dissipation-less valleytronics. These require well-separated valleys in the Brillouin zone (BZ) so that their self-interactions are absent. Lack of inversion symmetry in materials could provide distinct momentum states in the BZ, resulting in momentum-dependent isolated valleys. Moreover, the non-triviality of these valleys could be characterized by the non-zero value of Berry curvature. The detailed study of the inherent properties of valley and topology could accelerate the search for new valleytronic materials [5].