Quantum Flatland and Monolayer Graphene from a Viewpoint of Geometric Algebra

• Authors: A. Dargys
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

73.43.Cd; 81.05.U-; 03.65.Pm

Discipline

• 81.05.U-: Carbon/carbon-based materials(for carbon-based superconductors, see 74.70.Wz)
• 73.43.Cd: Theory and modeling
• 03.65.Pm: Relativistic wave equations

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 4
• Pages: 732-739

Dates

published

2013-10

received

2013-05-11

Contributors

author

A. Dargys

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

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Identifiers

DOI

10.12693/APhysPolA.124.732