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Spontaneous Symmetry Breaking in Metal Adsorbed Graphene Sheets

Graphene has received a great deal of attention and this has more recently extended to boron nitride sheets (BNS) with a similar structure. Both have hexagonal lattices and it is only the alternation of atoms in boron nitride, which changes the symmetry structure. This difference can for example be seen in the mean field equations, which for the corners of the Brillouin Zone are Dirac equations. For the case of graphene (equal atoms) we have the equation for massless particles, while for Boron Nitride has a finite gap and is more near a Dirac equation with mass near this gap.. Carbon structures in general and in particular also graphene can adsorb electron donors, such as alkaline atoms or molecules with a dipole moment. Typically these atoms and the dipoles can only attach in the sense to donate electron density. Some results for small sheet like structures are available.