Electronic structure of super-honeycomb systems: A peculiar realization of semimetal/semiconductor classes and ferromagnetism

Lateral superstructures with honeycomb symmetry are shown to be classified, with a simple criterion, into semimetals with gapless k-linear dispersions, semiconductors, and metals. In some of the classes, the symmetry enforces flat bands to exist, which implies the occurrence of ferromagnetism when the electron correlation is turned on. These provide a unique opportunity for band structure engineering.