Generalized uncertainty principle in graphene

@article{Iorio2019GeneralizedUP,
  title={Generalized uncertainty principle in graphene},
  author={Alfredo Iorio and Pablo Pais},
  journal={Journal of Physics: Conference Series},
  year={2019},
  volume={1275}
}
  • A. IorioP. Pais
  • Published 31 January 2019
  • Physics
  • Journal of Physics: Conference Series
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, [xi,xj] ≠ 0, and on their possible physical realization. 

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References

SHOWING 1-10 OF 28 REFERENCES

Generalized Dirac structure beyond the linear regime in graphene

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with

Electronic properties of graphene

Graphene is the first example of truly two‐dimensional crystals – it's just one layer of carbon atoms. It turns out that graphene is a gapless semiconductor with unique electronic properties

Two-dimensional gas of massless Dirac fermions in graphene

This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.

Revisiting the gauge fields of strained graphene

We show that when graphene is only subject to strain, the spin connection gauge field that arises plays no measurable role, but when intrinsic curvature is present and strain is small, spin

Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that

The solutions of many issues, of the ongoing eorts to make deformed graphene a tabletop quantum eld theory in curved spacetimes, are presented. A detailed explanation of the special features of