Tight binding electrons on a honeycomb lattice are described by an effective Dirac theory at low energies. Lowering symmetry by an alternate ionic potential (∆) generates a single-particle gap in the spectrum. We employ the dynamical mean field theory (DMFT) technique, to study the effect of on-site electron correlation (U ) on massive Dirac fermions. For a fixed mass parameter ∆, we find that beyond a critical value Uc1(∆) massive Dirac fermions become massless. Further increasing U beyond Uc2(∆), there will be another phase transition to the Mott insulating state. Therefore the competition between the single-particle gap parameter, ∆, and the Hubbard U restores the semi-metallic nature of the parent Hamiltonian. The width of the intermediate semi-metallic regime shrinks by increasing the ionic potential. However, at small values of ∆, there is a wide interval of U values for which the system remains semi-metal.
Particle-hole continuum in Dirac sea of graphene has a unique window underneath, which provides a unique opportunity for emergence of a pole in the susceptibility of the triplet particle-hole channel in the entire Brillouin zone (BZ). Here we use random phase approximation (RPA) to study such collective mode at zero temperature, in a single layer of doped graphene. We find that due to the chiral nature of one-particle states, in undoped graphene, the wave function overlap factors do not lead to qualitative differences, while in doped graphene they will kill small momentum part of the branch of magnetic excitations by pushing it to touch the lower part of the continuum. The pole corresponding to magnetic excitations survives for for larger momenta in the BZ.(Color online) Continuum of the inter-band and intra-band particle-hole excitations is the color-filled region. The dark line is intensity plot corresponding to the magnetic excitations in (a) doped, and (b) undoped graphene.
In an earlier work we predicted the existence of a neutral triplet collective mode in undoped graphene and graphite [Phys. Rev. Lett. 89 (2002) 016402]. In this work we study a phenomenological Hamiltonian describing the interaction of tight-binding electrons on honeycomb lattice with such a dispersive neutral triplet boson. Our Hamiltonian is a generalization of the Holstein polaron problem to the case of triplet bosons with non-trivial dispersion all over the Brillouin zone. This collective mode constitutes an important excitation branch which can contribute to the decay rate of the electronic excitations. The presence of such collective mode, modifies the spectral properties of electrons in graphite and undoped graphene. In particular such collective mode, as will be shown in this paper, can account for some part of the missing decay rate in a time-domain measurement done on graphite.
Phase transition in a honeycomb lattice is studied by the means of the two dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semimetal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-site interaction are determined using renormalized Fermi velocity factor.
In this work, we obtain the black hole solutions in the dilaton [Formula: see text]-gravity (R is not considered as a constant here) and investigate their thermodynamics especially phase transition and critical behavior in the anti-de Sitter (AdS) extended phase-space. We obtain the exact Banados, Teitelboim and Zanelli (BTZ) counterpart solutions in dilaton [Formula: see text]-gravity which is the basis of our work. We also obtain the exact form of [Formula: see text] model for some solutions. In the thermodynamical analysis, we calculate the thermodynamical quantities like the temperature and entropy for these solutions and we compare them with the BTZ corresponding quantities. After that, we investigate the stability (local and global) for these obtained solutions. In the critical behavior analysis, we find that there is no evidence to show the existence of P–V criticality (like the ordinary BTZ case) in this modified gravity model except some unusual P–V behavior in the corresponding diagrams.
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