Generalized uncertainty principle in graphene

Abstract

We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac Hamiltonians one obtains are those compatible with specific generalizations of the uncertainty principle. We also briefly comment on the compatibility of the latter with noncommuting positions, $[x_i,x_j]\ne 0$, and on their possible physical realization.

arXiv comment11 pages, 1 figure. Work Prepared for the Proceedings of DICE 2018 Workshop held at Toscana, Italy

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• Testing Short Distance Anisotropy in Space
• A Lorentz-violating low-energy model for the bilayer Graphene
• Thermodynamics of spacetime from minimal area