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Dynamical Mass Generation

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Dynamical mass generation via space compactification in graphene

A. D. Alhaidari1, A. Jellal1,2,3, E. B. Choubabi3 and H. Bahlouli4,1
1 Saudi Center for Theoretical Physics, Jeddah, Saudi Arabia
2 Physics Department, College of Science, King Faisal University,PO Box 380, Al-Ahsaa 31982, Saudi Arabia
3 Theoretical Physics Group, Faculty of Sciences, Chouaib Doukkali University, PO Box 20, 24000 El Jadida, Morocco
4 Physics Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Fermions in a graphene sheet behave like massless particles. We show that by folding the sheet into a tube they acquire non-zero effective mass as they move along the tube axis. That is, changing the space topology of graphene from 2D to 1D (space compactification) changes the 2D massless problem into an effective massive 1D problem. The size of the resulting mass spectrum depends on the quantized azimuthal frequency and its line spacing is proportional to the inverse of the tube diameter.

PACS numbers: 73.63.-b; 73.23.-b; 11.80.-m
Keywords: graphene, space compactification, dimensional reduction, mass generation, graphene tube, Dirac equation, square barrier.