Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

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 αc≈0.36 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.