Electronic structure theory of weakly interacting bilayers

Abstract

We derive electronic structure models for weakly interacting bilayers such as\ngraphene-graphene and graphene-hexagonal boron nitride, based on density\nfunctional theory calculations followed by Wannier transformation of electronic\nstates. These transferable interlayer coupling models can be applied to\ninvestigate the physics of bilayers with arbitrary translations and twists. The\nfunctional form, in addition to the dependence on the distance, includes the\nangular dependence that results from higher angular momentum components in the\nWannier $p_z$ orbitals. We demonstrate the capabilities of the method by\napplying it to a rotated graphene bilayer, which produces the analytically\npredicted renormalization of the Fermi velocity, van Hove singularities in the\ndensity of states, and Moir\\'{e} pattern of the electronic localization at\nsmall twist angles. We further extend the theory to obtain the effective\ncouplings by integrating out neighboring layers. This approach is instrumental\nfor the design of van der Walls heterostructures with desirable electronic\nfeatures and transport properties and for the derivation of low-energy theories\nfor graphene stacks, including proximity effects from other layers.\n

Keywords

Affiliated Institutions

• Harvard University US

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