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

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.

arXiv comment12 pages, 7 figures. Replaced with version matching the published one

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• Superconducting phase transition in planar fermionic models with Dirac cone tilting
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Tilted Dirac superconductor at quantum criticality: Restoration of Lorentz symmetry
• First order phase transitions within Weyl type of materials at low temperatures
• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Influence of Dynamical Floquet Spectrum on the Plasmon Excitations and Exchange Energy of tilted monolayer 1T${}^{\prime }$MoS${}_2$
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• A Lorentz-violating low-energy model for the bilayer Graphene
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals