Topology in the Physics of Atomic Layers

Abstract

The topological aspects in the physics of atomic layers, particularly the valley physics, are briefly reviewed. First, the Berry curvature of band structure is introduced as a basic concept for the k-space topology. The stability of Dirac cones and the valley splitting of Landau levels in gapped graphene are explained topologically. The valley Hall effect in gapped graphene is discussed as a remarkable topological transport phenomenon. The spin-valley correspondence is also mentioned in 2H-MoS₂ monolayer with no inversion symmetry.