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.

• Received 17 August 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.4389