Wigner crystallization of quadratically dispersing electrons in graphene

✍ Scribed by Kombiah Iyakutti; Velappa Jayaraman Surya; Ratnavelu Rajeswarapalanichamy; Yoshiyuki Kawazoe

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 1014 KB
• Volume: 112
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.23172

✦ Synopsis

Abstract

The graphene surface with the unpaired π electrons presents an ideal two‐dimensional electron system. Although the effective massless Dirac fermions are important, they are not the only carriers that describe the quantum transport in graphene. Above zero energy, the current carrying carriers in graphene are the usual electrons. This electron density may vary depending on the surface defects and π–σ interaction, and this may lead to a possible Wigner crystallization on the surface of graphene. Calculations for nonmagnetic, ferromagnetic, and antiferromagnetic Wigner crystals are carried out based on the Koster–Kohn variational principle for direct calculation of Wannier functions. The effect of positive background due to the carbon ions is suitably treated. From our results, we find that Wigner crystallization is possible in grapheme, if we consider the electrons on the surface, which obey quadratic dispersion relation. The electron crystal with ferromagnetic phase and face centered square lattice structure has the lowest energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012