Tilted Dirac cone effects and chiral symmetry breaking in a planar four-fermion model

TL;DR

This paper investigates how tilting the Dirac cone influences chiral symmetry breaking in a 2+1D four-fermion model, with implications for materials like graphene and Weyl semimetals under magnetic fields.

Contribution

It introduces a comprehensive analysis of tilt effects on chiral symmetry breaking in a planar four-fermion model, incorporating chemical potential, temperature, and magnetic field influences.

Findings

Tilt modifies the phase structure and critical parameters for symmetry breaking.

External magnetic fields induce anomalous Hall effects in the model.

Results have potential applications in understanding graphene and Weyl semimetals.

Abstract

We analyze the chiral symmetry breaking in a planar four-fermion model with non-null chemical potential, temperature and including the effect of the tilt of the Dirac cone. The system is modeled with a $(2 + 1)$-dimensional Gross-Neveu-like interaction model in the context of the generalized Weyl Hamiltonian and its phase structure is studied in the mean-field and large-$N$ approximations. Possible applications of the results obtained, e.g., in connection to graphene, are discussed. We also discuss the effect of an external magnetic field applied to the system, which can give rise to the appearance of the anomalous Hall effect and that is expected to arise in connection with two-dimensional Weyl and Dirac semimetals.