Among the tools for band-structure

Among the tools for band-structure engineering in van der Waals heterostructures are the relative alignment between the neighboring crystals, surface reconstruction, charge transfer, and proximity effects (when one material can borrow the property of another by contact via quantum tunneling or by Coulomb interactions). Thus, a moiré structure for graphene on hexagonal boron nitride (hBN) leads to the formation of secondary Dirac points (5 9), commensurate-incommensurate transition in the same system leads to surface reconstruction (10) and gap opening in the electron spectrum (8), and spin-orbit interaction can be enhanced in graphene by neighboring transition metal dichalcogenides (TMDCs) (11, 12). Here we provide a review of 2D materials, analyzing the physics that can be observed in such crystals. We discuss how these properties are put to use in new heterostructure devices. Transition metal dichalcogenides Transition metal dichalcogenides, with the formula MX2 (where M is a transition metal and X is a chalcogen), offer a broad range of electronic properties, from insulating or semiconducting (e.g., Ti, Hf, Zr, Mo, and W dichalcogenides) to metallic or semimetallic (V, Nb, and Ta dichalcogenides). The different electronic behavior arises from the progressive filling of the nonbonding d bands by the transition metal electrons. The evolution of the electronic density of states (DOS) is shown in Fig. 1 [adapted from (13 17)] for the most stable phase of each of the dichalcogenides. All TMDCs have a hexagonal structure, with each monolayer comprising three stacked layers (X-M-X). The two most common polytypes of the monolayers are trigonal prismatic (e.g., MoS2 and WS2) and octahedral (e.g., TiS2); these terms refer to the coordination of the transition metal atom. Inversion symmetry is broken in the former, giving rise to piezoelectricity and having important consequences for the electronic structure. In addition, many of the tellurides, TcS2, ReS2, and