Turning graphene into a lab for noncommutativity

Alfredo Iorio (Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, Prague 8, Czech Republic) ; Boris Ivetić (Wöhlergasse 6, Vienna, Austria) ; Pablo Pais (Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile; Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, Prague 8, Czech Republic)

It was recently shown that, taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, (X,P), that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting X, for which [Xi,Xj]=iθij and we find that θij=2ϵij, with ℓ the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene.

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      "surname": "Iorio", 
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      "surname": "Iveti\u0107", 
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          "country": "Austria", 
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      "title": "Turning graphene into a lab for noncommutativity"
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      "source": "Elsevier", 
      "value": "It was recently shown that, taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, <math><mo>(</mo><mover><mrow><mi>X</mi></mrow><mrow><mo>\u2192</mo></mrow></mover><mo>,</mo><mover><mrow><mi>P</mi></mrow><mrow><mo>\u2192</mo></mrow></mover><mo>)</mo></math>, that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting <math><mover><mrow><mi>X</mi></mrow><mrow><mo>\u2192</mo></mrow></mover></math>, for which <math><mo>[</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>,</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msup><mo>]</mo><mo>=</mo><mi>i</mi><mspace width=\"0.2em\"></mspace><msup><mrow><mi>\u03b8</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup></math> and we find that <math><msup><mrow><mi>\u03b8</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup><mo>=</mo><msup><mrow><mi>\u2113</mi></mrow><mrow><mn>2</mn></mrow></msup><mspace width=\"0.2em\"></mspace><msup><mrow><mi>\u03f5</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup></math>, with \u2113 the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene."
    }
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  "imprints": [
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      "date": "2024-04-04", 
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Published on:
04 April 2024
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 849 C (2024)

Article ID: 138630
DOI:
https://doi.org/10.1016/j.physletb.2024.138630
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: