Layer k -projection and unfolding electronic bands at interfaces

The k-projection method provides an approach to separate the contributions from different constituents in heterostructure systems, and can act as an aid to connect the results of experiments and calculations. We show that the technique can be used to “unfold” the calculated electronic bands of interfaces and supercells, and provide local band structure by integrating the projected states over specified regions of space, a step that can be implemented efficiently using fast Fourier transforms. We apply the method to investigate the effects of interfaces in heterostructures consisting of a graphene bilayer on H-saturated SiC(0001), BAs monolayer on the ferromagnetic semiconductor CrI3, silicene on Ag(111), and to the Bi2 Se3 surface. Our results reveal that the band structure of the graphene bilayer around the Dirac point is strongly dependent on the termination of SiC(0001): on the C face, the graphene is n doped and a gap of ∼ 0.13 eV is opened, whereas on the Si face, the graphene is essential unchanged and neutral. We show that for BAs/CrI3, the magnetic proximity effect can effectively induce a spin splitting up to about 50 meV in BAs. For silicene/Ag(111), our calculations reproduce the angle-resolved photoemission spectroscopy results, including linearly dispersing bands at the edge of the first Brillouin zone of Ag(111); although these states result from the interaction between the silicene overlayer and the substrate, we demonstrate that they are not Dirac states.