Ground state determination and band gaps of bilayers of graphenylenes and octafunctionalized-biphenylenes

Device fabrication often requires materials that are either reliably conducting, reliably semiconducting, or reliably nonconducting. Bilayer graphene (BLG) changes from a superconductor to a semiconductor depending on it's stacking, but because it is difficult to control its stacking, it is not a reliable material for device fabrication. Using DFTB+, this work demonstrates that bilayers of graphenylene, net-C, and net-W can be reliably used for device fabrication without knowing the details of their stackings. Bilayers of graphenylene and net-C are semiconducting for all sheer displacements, net-W is conducting for all sheer displacements, while that Type II, like BLG, is conducting or semiconducting depending on the sheer displacement. The method used gives bond lengths, unit cell dimensions, and band dispersion of single-layer graphene that are consistent with previously reported values, it correctly predicts that AB stacking is the ground state of BLG and gives an interlayer separation that is consistent with previous studies. The bond lengths and lattice constants of the other carbon allotropes are consistent with previously published values. \textcolor{blue}{In order to calculate the band structures the bilayer systems,} DFTB+ was first used to determined the interlayer separations of the 2-D carbon allotropes under shear displacement.