On the local aspect of valleytronics

Valley magnetic moments play a crucial role in valleytronics in 2D hexagonal materials. Traditionally, based on studies of quantum states in homogeneous bulks, it is widely believed that only materials with broken structural inversion symmetry can exhibit nonvanishing valley magnetic moments. Such constraint excludes from relevant applications those with inversion symmetry, as specifically exemplified by gapless monolayer graphene despite its technological advantage in routine growth and production. This work revisits valley-derived magnetic moments in a broad context covering inhomogeneous structures as well. It generalizes the notion of valley magnetic moment for a state from an integrated total quantity to the local field called "local valley magnetic moment" with space-varying distribution. In suitable inversion-symmetric structures with inhomogeneity, e.g., zigzag nanoribbons of gapless monolayer graphene, it is shown that the local moment of a state can be nonvanishing with sizable magnitude, while the corresponding total moment is subject to the broken symmetry constraint. Moreover, it is demonstrated that such local moment can interact with space-dependent electric and magnetic fields manifesting pronounced field effects and making possible a local valley control with external fields. Overall, a path to "local valleytronics" is illustrated which exploits local valley magnetic moments for device applications, relaxes the broken symmetry constraint on materials, and expands flexibility in the implementation of valleytronics.