Quantum Flatland and Monolayer Graphene from a Viewpoint of Geometric Algebra |

A. Dargys
Center for Physical Sciences and Technology, Semiconductor Physics Institute, A. Goštauto 11, LT-01108 Vilnius, Lithuania |

Received: May 11, 2013 |

Full Text PDF |

Quantum mechanical properties of the graphene are, as a rule, treated within the Hilbert space formalism. However a different approach is possible using the geometric algebra, where quantum mechanics is done in a real space rather than in the abstract Hilbert space. In this article the geometric algebra is applied to a simple quantum system, a single valley of monolayer graphene, to show the advantages and drawbacks of geometric algebra over the Hilbert space approach. In particular, 3D and 2D Euclidean space algebras Cl_{3,0} and Cl_{2,0} are applied to analyze relativistic properties of the graphene. It is shown that only three-dimensional Cl_{3,0} rather than two-dimensional Cl_{2,0} algebra is compatible with a relativistic flatland. |

DOI: 10.12693/APhysPolA.124.732 PACS numbers: 73.43.Cd, 81.05.U-, 03.65.Pm |