Wannier Function Approach to Realistic Coulomb Interactions in Layered Materials and Heterostructures

We introduce an approach to derive realistic Coulomb interaction terms in free standing layered materials and vertical heterostructures from ab-initio modelling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random phase approximation, Wannier function representation of Coulomb matrix elements within some low energy Hilbert space and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab-initio calculations of the Coulomb matrix elements within an accuracy of $0.2$eV or better. We show that realistic Coulomb interactions in bilayer graphene can be manipulated on the eV scale by different dielectric and metallic environments. A comparison to electronic phase diagrams derived in [M. M. Scherer et al., Phys. Rev. B 85, 235408 (2012)] suggests that the electronic ground state of bilayer graphene is a layered antiferromagnet and remains surprisingly unaffected by these strong changes in the Coulomb interaction.