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We show that quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in an energy gap by studying tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as de Haas-van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the oscillations shown in this paper corresponds to the area of the first Brillouin zone and its phase is zero. The origin of these quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. These oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in dHvA oscillations. These oscillations can be observed experimentally in systems with a large supercell such as a graphene antidot lattice or ultracold atoms in an optical lattice at an external magnetic field of a few Tesla when the area of the supercell is 104 times larger than that of graphene. [ABSTRACT FROM AUTHOR]

We study the zero-temperature ground-state (GS) phase diagram of a spin-half J 1-J2 XY model on thehoneycomb lattice with nearest-neighbor exchange coupling J2 > 0 and frustrating next-nearest-neighborexchange coupling J2 = κJ1 > 0, where both bonds are of the isotropic XY type, using the coupled clustermethod. Results are presented for the GS energy per spin, magnetic order parameter, and staggered dimervalence-bond crystalline (SDVBC) susceptibility, for values of the frustration parameter in the range 0 ≤ κ ≤ 1. In this range, we find phases exhibiting, respectively, Néel xy planar [N(p)], Néel z-aligned [N(z)], SDVBC,and Néel-II xy planar [N-II(p)] orderings. The Neel-II states, which break the lattice rotational symmetry, areones in which the spins of nearest-neighbor pairs along one of the three equivalent honeycomb directions areparallel, while those in the other two directions are antiparallel. The N(p) state, which is stable for the classicalversion of the model in the range 0 ≤ κ ≤ 1/6 , is found to form the GS phase out to a first quantum critical point atkci = 0.216(5), beyond which the stable GS phase has N(z) order over the range κC1 < κ < κC2 = 0.355(5). Forvalues κ > kC2, we find a strong competition to form the GS phase between states with N-II(p) and SDVBC formsof order. Our best estimate, however, is that the stable GS phase over the range κC2 < κ < kC3 ≈ 0.52(3) is a mixedstate with both SDVBC and N-II(p) forms of order; and for values κ > kC3 is the N-II(p) state, which is stable atthe classical level only at the highly degenerate point κ = ½ Over the range 0 ≤ κ ≤ 1, we find no evidence forany of the spiral phases that are present classically for all values κ > 1/6, nor for any quantum spin-liquid state. [ABSTRACT FROM AUTHOR]

Two-dimensional graphenelike BC3 honeycomb structures, which have been grown on the NbB2(0001) surface, possess intriguing properties that offer new opportunities for applications in nanoelectronics, mechanical materials, and superconductivity. The bonding configuration of BC3 on the substrate has not yet been determined, however. We report ab initio thermodynamics calculations and analysis that lead to a prediction about the most stable bonding configuration of a monolayer BC3 on NbB2, namely the C-top configuration in which carbon is bonded directly on the top of the niobium atoms. We also find that the BC3 monolayer on NbB2 is thermodynamically stable, accounting for the experimental observation that the BC3 sheet can be grown on NbB2 by carbon substitution and surface segregation of carbon impurities. We further provide detailed information about the atomic structures and electronic properties of the BC3-bonded NbB2 surface. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting a localized surface plasmon, and study the quantum properties of the collective plasmons resulting from the near-field dipolar interaction between the nanoparticles. We analytically investigate the dispersion, the effective Hamiltonian, and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarization points close to the normal to the plane, the spectrum presents Dirac cones, similar to those present in the electronic band structure of graphene. We derive the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent Dirac-like massless bosonic excitations that present similar effects to electrons in graphene, such as a nontrivial Berry phase and the absence of backscattering off smooth inhomogeneities. We further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon dispersion by modifying the polarization of the localized surface plasmons, paving the way for a fully tunable plasmonic analogue of graphene. [ABSTRACT FROM AUTHOR]

We study the ground-state phase diagram of the frustrated quantum J1 -J2 Heisenberg antiferromagnet on the honeycomb lattice using a mean-field approach in terms of the Schwinger boson representation of the spin operators. We present results for the ground-state energy, local magnetization, energy gap, and spin-spin correlations. The system shows magnetic long-range order for 0 ⩽ J2/J1 ≲ 0.2075 (Néel) and 0.398 ≲ J2/J1 ⩽ 0.5 (spiral). In the intermediate region, we find two magnetically disordered phases: a gapped spin liquid phase, which shows short-range Néel correlations (0.2075 ≲ J2/J1 ≲ 0.3732), and a lattice nematic phase (0.3732 ≲ J2/J1 ≲ 0.398), which is magnetically disordered but breaks lattice rotational symmetry. The errors in the values of the phase boundaries, which are implicit in the number of significant figures quoted, correspond purely to the error in the extrapolation of our finite-size results to the thermodynamic limit. [ABSTRACT FROM AUTHOR]

Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakes with such reczag defective edges, emphasis is placed on topological aspects and connections underlying the patterns dominating the spectra of these systems. The electronic spectra of trigonal graphene nanoflakes with reczag edge terminations exhibit certain unique features, in addition to those that are well known to appear for graphene dots with zigzag edge termination. These unique features include breaking of the particle-hole symmetry, and they are associated with nonlinear dispersion of the energy as a function of momentum, which may be interpreted as nonrelativistic behavior. The general topological features shared with the zigzag flakes include the appearance of energy gaps at zero and low magnetic fields due to finite size, the formation of relativistic Landau levels at high magnetic fields, and the presence between the Landau levels of edge states (the so-called Halperin states) associated with the integer quantum Hall effect. Topological regimes, unique to the reczag nanoflakes, appear within a stripe of negative energies eb < e < 0, and along a separate feature forming a constant-energy line outside this stripe. The Si, lower bound specifying the energy stripe is independent of size. Prominent among the patterns within the eb < e < 0 energy stripe is the formation of three-member braid bands, similar to those present in the spectra of narrow graphene nanorings', they are associated with Aharonov-Bohm-type oscillations, i.e., the reczag edges along the three sides of the triangle behave like a nanoring (with the comers acting as scatterers) enclosing the magnetic flux through the entire area of the graphene flake. Another prominent feature within the eb < e < 0 energy stripe is a subregion of Halperin-type edge states of enhanced density immediately below the zero-Landau level. Furthermore, there are features resulting from localization of the Dirac quasiparticles at the corners of the polygonal flake. A main finding concerns the limited applicability of the continuous Dirac-Weyl equation, since the latter does not reproduce the special reczag features. Due to this discrepancy between the tight-binding and continuum descriptions, one is led to the conclusion that the linearized Dirac-Weyl equation fails to capture essential nonlinear physics resulting from the introduction of a multiple topological defect in the honeycomb graphene lattice. [ABSTRACT FROM AUTHOR]

We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized Rokhsar-Kivelson points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacdng (1 + 1)-dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground-state correlations are shown to be short ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramatic even-odd effect depending on the circumference and propose that this can be used as a numerical diagnostic of gapped spin-liquid phases, more generally. [ABSTRACT FROM AUTHOR]

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition. [ABSTRACT FROM AUTHOR]

We study the ground-state phase diagram of the quantum J1 -- J2 model on the honeycomb lattice by means of an entangled-plaquette variational ansatz. Values of energy and relevant order parameters are computed in the rangeO&LES;J2/J1 &LES; 1- The system displays classical order for J2/J1i &PRAP; 0.2 (Néel) and for j2/J1&PRAP;0.4 (collinear). In the intermediate region, the ground state is disordered. Our results show that the reduction of the half-filled Hubbard model to the model studied here does not yield accurate predictions [ABSTRACT FROM AUTHOR]

Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization-group method to compute the magnetic susceptibility and to determine the ordered and disordered states of the model. Aside from antiferromagnetic-, collinear-, and spiral-order domains, we find a large paramagnetic region at intermediate J2 coupling. For larger J2 within this domain, we find a strong tendency for staggered dimer ordering, while the remaining paramagnetic regime for low J2 shows only weak plaquette and staggered dimer responses. We suggest this regime to be a promising region for looking for quantum spin-liquid states when charge fluctuations would be included. [ABSTRACT FROM AUTHOR]

We study the ground-state (gs) phase diagram of the frustrated spin-½ J1-J2-J3 antiferromagnet with J2 = J3 = κ J1 on the honeycomb lattice using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for κ < κc1 ≈ 0.47, a collinear striped AFM phase for κ > κc2 ≈ 0.60, and a paramagnetic PVBC phase for κc1 ≲ κ ≲ κc2. The transition at κc2 appears to be of first-order type, while that at κc1 is continuous. Since the Néel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at κc1. [ABSTRACT FROM AUTHOR]

In this paper, we study transport properties of electrons on the two-dimensional honeycomb lattice. We consider a half-filled system in the vicinity of a symmetry-breaking transition from a semimetallic phase toward an insulating phase with either charge-density- or spin-density-wave order. The effect of either order is to break the sublattice inversion symmetry, which induces a finite gap for the electronic single-particle excitations. Phenomenologically, such a scenario is described in the framework of a Gross-Neveu theory. We analyze two related formulations of the model by means of (i) a controlled renormalization-group calculation and (ii) the large-N method, both of which in combination with a Boltzmann transport equation. We determine the quantum critical conductivity and also discuss crossover behavior from quantum critical behavior into the insulating and/or the semimetallic phases. We find that at asymptotically low temperatures, the quantum critical conductivity is given by a temperature-independent universal number. Over a large temperature window, the temperature-independent quantum-critical conductivity is masked by a logarithmically temperature-dependent contribution due to the marginally irrelevant long-range Coulomb interaction. We discuss possible origins of this peculiarity in the two complementary formulations of the model. Furthermore, we consider possible relations of our findings to recent experiments, with a special emphasis on the quantum-critical-to-insulator crossover. We find that our results are in remarkably good qualitative and quantitative agreement with a recent analysis of the data sets under the hypothesis of an underlying gap in the single-particle spectrum. [ABSTRACT FROM AUTHOR]

The role of nonlocal Coulomb correlations in the honeycomb lattice is investigated within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. The paramagnetic semimetal-to-insulator transition is found to be in excellent agreement with finite-size determinantal quantum Monte Carlo simulations and with cluster dynamical mean field calculations based on the continuous-time quantum Monte Carlo approach. As expected, the critical Coulomb energy is much lower than within a local or single-site formulation. Short-range correlations are shown to give rise to a pseudogap and concomitant non-Fermi-liquid behavior within a narrow range below the Mott transition. [ABSTRACT FROM AUTHOR]