  Recent experimental synthesis of two-dimensional (2D) heterostructures opens
a door to new opportunities in tailoring the electronic properties for novel 2D
devices. Here, we show that a wide range of lateral 2D heterostructures could
have a prominent advantage over the traditional three-dimensional (3D)
heterostructures, because their band alignments are insensitive to the
interfacial conditions. They should be at the Schottky-Mott limits for
semiconductor-metal junctions and at the Anderson limits for semiconductor
junctions, respectively. This fundamental difference from the 3D
heterostructures is rooted in the fact that, in the asymptotic limit of large
distance, the effect of the interfacial dipole vanishes for 2D systems. Due to
the slow decay of the dipole field and the dependence on the vacuum thickness,
however, studies based on first-principles calculations often failed to reach
such a conclusion. Taking graphene/hexagonal-BN and MoS2/WS2 lateral
heterostructures as the respective prototypes, we show that the converged
junction width can be order of magnitude longer than that for 3D junctions. The
present results provide vital guidance to high-quality transport devices
wherever a lateral 2D heterostructure is involved.
