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Ritus Method and SUSY-QM: Theoretical Frameworks to Study the Electromagnetic Interactions in Graphene

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Book cover GraphITA 2011

Part of the book series: Carbon Nanostructures ((CARBON))

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Abstract

We study the Dirac fermion propagator in (2 + 1) dimensions in the background of external magnetic fields in a quantum electrodynamics framework. In graphene, the massless limit of our findings is of direct relevance. We present the Ritus formalism to obtain the fermion propagator in the general case. We show how, for some class of external static magnetic fields, the graphene hamiltonian can be cast into a hamiltonian with quantum mechanical supersymmetric properties, leading us to an exactly solvable model. As an example of these two formalisms we work out the canonical case of a uniform constant magnetic field.

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Acknowledgements

We acknowledge support from CIC-UMSNH under grant 4.22. GM acknowledges support from DGAPA-UNAM grant under project PAPIIT IN118610. AR acknowledges support from SNI and CONACYT grants under project 82230.

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Avenida Universidad 3000, Ciudad Universitaria, 04510, México, Distrito Federal, México

    G. Murguía

  2. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, 58040, Morelia, Michoacán, México

    A. Raya

Authors
  1. G. Murguía
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  2. A. Raya
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Corresponding authors

Correspondence to G. Murguía or A. Raya .

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Editors and Affiliations

  1. , Dipartimento di Fisica, FISICA Università dell’Aquila (ITALY), Via Vetoio 10, Coppito-L'Aquila, 67100, Italy

    Luca Ottaviano

  2. CNR - IMM Sezione di Bologna, via Gobetti 101, Bologna, 40129, Italy

    Vittorio Morandi

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Murguía, G., Raya, A. (2012). Ritus Method and SUSY-QM: Theoretical Frameworks to Study the Electromagnetic Interactions in Graphene. In: Ottaviano, L., Morandi, V. (eds) GraphITA 2011. Carbon Nanostructures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20644-3_17

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