Stacking and band structure of van der Waals bonded graphane multilayers

We use density functional theoryand the van der Waals density functional (vdW-DF) methodto determine the binding separation in bilayer and bulk graphaneand study the corresponding electronic band structure.The calculated binding separation (distance between center-of-mass planes)and binding energy are 4.5-5.0 \uc5 (4.5-4.8 \uc5) 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 calculationsfor 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 signalsa potential of vdW-induced band-gap engineering in other material