Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Four-Fermion Interactions

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 (PQED) and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large$-N_f$ expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the non-perturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value ${\alpha }_c(D{N}_f)$. In particular, we obtain the critical coupling constant ${\alpha }_c\approx 0.36$ for $D{N}_f=8$., where $D=2,4$ corresponds to the SU(2) and SU(4) cases, respectively, and $N_f$ 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. 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.

9 pages, 3 figures

References in corpus (5)

• The electronic properties of graphene
• Electromagnetic current correlations in reduced quantum electrodynamics
• Unitarity of theories containing fractional powers of the d'Alembertian operator
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$
• Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

Cited by in corpus (13)

• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions
• Pseudo Quantum Electrodynamics and Chern-Simons theory Coupled to Two-dimensional Electrons
• Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane
• Reduced QED with few planes and fermion gap generation
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Gross-Neveu Interaction at finite temperature
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch
• Critical properties of three-dimensional many-flavour QEDs
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• The influence of a conducting surface on the conductivity of graphene