Chiral symmetry breaking in the pseudo-quantum electrodynamics with non-Abelian four-fermion interactions

TL;DR

This paper investigates chiral symmetry breaking in 2+1D Dirac materials considering electromagnetic and non-Abelian four-fermion interactions, revealing how system parameters influence symmetry breaking thresholds.

Contribution

It introduces a combined PQED and non-Abelian four-fermion interaction model, deriving critical parameters for chiral symmetry breaking using Schwinger-Dyson equations.

Findings

Critical fermion flavor number increases with N_c

Critical fine structure constant decreases with N_c

System becomes more prone to symmetry breaking at higher N_c

Abstract

In the context of 2+1 dimensional Dirac materials, we consider electromagnetic interactions alongside a type of spin-dependent Hubbard interaction. The former is described by PQED theory, while the latter corresponds to an effective theory represented by the $SU(N_c)$ Thirring model. Employing Hubbard-Stratonovich transformation and large N expansion in the model yields a non-local $SU(N_c)$ Yang-Mills action. Subsequently, we solve Schwinger-Dyson equations to obtain the self-energy function of the fermion propagator, from which we determine the critical fermion flavor number $N^c_f$ and critical fine structure constant $\alpha_c$ indicative of chiral symmetry breaking. Our findings suggest that as the non-Abelian color number $N_c$ increases, the minimum value of the critical fermion flavor number monotonically increases, while the maximum value of the critical fine structure constant decreases accordingly, rendering the system more susceptible to chiral symmetry breaking.