Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

Van Sérgio Alves, Reginaldo O. C. Junior, E. C. Marino, and Leandro O. Nascimento
Phys. Rev. D 96, 034005 – Published 7 August 2017

Abstract

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the pseudo quantum electrodynamics, and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large-Nf expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the nonperturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value αc(DNf). In particular, we obtain the critical coupling constant αc0.36 for DNf=8., where D=2, 4 corresponds to the SU(2) and SU(4) cases, respectively, and Nf is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. Nevertheless, the number of renormalized masses is not changed by the four-fermion interaction within our approximation. For two-dimensional materials, in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice.

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  • Received 4 April 2017

DOI:https://doi.org/10.1103/PhysRevD.96.034005

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Van Sérgio Alves1, Reginaldo O. C. Junior2, E. C. Marino2, and Leandro O. Nascimento3,4

  • 1Faculdade de Física, Universidade Federal do Pará, Avenida Augusto Correa 01, Belém, Pará 66075-110, Brazil
  • 2Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
  • 3International Institute of Physics, Campus Universitário Lagoa Nova, C.P. 1613, Natal, Rio Grande do Norte 59078-970, Brazil
  • 4Faculdade de Ciências Naturais, Universidade Federal do Pará, C.P. Breves, Pará 68800-000, Brazil

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Issue

Vol. 96, Iss. 3 — 1 August 2017

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