Stacking and band structure of van der Waals bonded graphane multilayers

We use density functional theory and the van der Waals density functional (vdW-DF) method to determine the binding separation in bilayer and bulk graphane and study the corresponding electronic band structure. The calculated binding separation (distance between center-of-mass planes) and binding energy are 4.5-5.0 Å (4.5-4.8 Å) and 75-102 meV/cell (93-127 meV/cell) in the bilayer (bulk), depending on the choice of vdW-DF version. We obtain the corresponding band diagrams using ordinary GGA calculations for the geometries specified by our vdW-DF results. We find significant band-gap modifications by up to -1.2 eV (+4.0 eV) in various regions of the Brillouin zone, produced by the bilayer (bulk) formation. The possibility of such large modifications signals a potential of vdW-induced band-gap engineering in other material