Energy band gaps in periodic bent graphene

• The periodic smooth bending is unable to open the band gap of graphene.
• The band gap can be larger than 100 meV in stepped graphene.
• Band gap can only be opened in a certain range of tilt angle in stepped graphene.
• Localized states greatly influence the band gap opening.

Based on the first-principles calculations, we studied the energy bandgaps of the two kinds of periodic bent graphenes: smooth-bent graphene and stepped graphene. In the smooth-bent graphene, the sinusoidal type of graphene superlattice is a gapless semiconductor as the flattened graphene. The periodic smooth bending is unable to open the bandgap of graphene. Although the bandgap can be larger than 100 meV in stepped graphene, it is sensitively dependent on the details of structure. Band gap can only be opened in a certain range of tilt angle. The localized states greatly influence the bandgap opening in stepped graphene.