First order phase transitions within Weyl type of materials at low temperatures

Abstract

We analyze the possible dynamical chiral symmetry breaking patterns taking place within Weyl type of materials. Here, these systems are modeled by the (2+1)-dimensional Gross-Neveu model with a tilt in the Dirac cone. The optimized perturbation theory (OPT) is employed in order to evaluate the effective potential at finite temperatures and chemical potentials beyond the traditional large-$N$ limit. The nonperturbative finite-$N$ corrections generated by the OPT method and its associated variational procedure show that a first-order phase transition boundary, missed at large $N$, exists in the regime of low temperatures and large chemical potentials. This result, which represents our main finding, implies that one should hit a region of mixed phases when exploring the low-temperature range. The associated first order transition line, which starts at $T=0$, terminates at a tricritical point such that the transitions taking place at high $T$ are of the second kind. In particular, we discuss how the tilt in the Dirac cone affects the position of the tricritical point as well as the values of critical temperature and coexistence chemical potential among other quantities. Some experimental implications and predictions are also briefly discussed.

13 pages, 8 figures. Replaced with version matching the published one in the Phys. Rev. B

References in corpus (19)

• Interactions and phase transitions on graphene's honeycomb lattice
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Is graphene in vacuum an insulator?
• Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Lattice field theory simulations of graphene
• Theory of integer quantum Hall effect in graphene
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Lorentz violation in Dirac and Weyl semimetals
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• Magnetization of Planar Four-Fermion Systems
• Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Tilted Dirac cone effects and chiral symmetry breaking in a planar four-fermion model
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Superconducting phase transition in planar fermionic models with Dirac cone tilting
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model

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