On a simple scheme for computing the electronic energy levels of a finite system from those of the corresponding infinite system

Computing the electronic energy levels of a finite system or nanostructure is more difficult than computing those of an infinite system or bulk material. In the literature, a technique for simplifying this computation has been proposed, wherein energy levels of a finite system are derived from those of the corresponding infinite system. So far, this method has been validated only for finite length one-dimensional systems and for higher-dimensional systems at k = 0. We establish that this technique, hereafter referred to as the confined Bloch wave (CBW) method, is valid for higher-dimensional symmorphic systems over the entire Brillouin zone, provided some symmetry requirements are satisfied. For this purpose we use a lateral surface superlattice as a model for the infinite system and a stripe or ribbon patterned in this superlattice as a model for the nanostructure. Finally, we compute the subbands of zigzag ribbons of one type patterned in artificial graphene and show that the CBW method predicts all the important subbands in these ribbons, and provides additional insight into the nature of their wavefunctions.