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We derive the critical line of the O(n) loop model on the martini lattice as a function of the loop weight n basing on the critical points on the honeycomb lattice conjectured by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. In the limit n -*· 0 we prove the connective constant p = 1.750564 5579 … of self-avoiding walks on the martini lattice. A finite-size scaling analysis based on transfer matrix calculations is also performed. The numerical results coincide with the theoretical predictions with a very high accuracy. Using similar numerical methods, we also study the 0(«) loop model on the 3-12 lattice. We obtain similarly precise agreement with the critical points given by Batchelor [J. Stat. Phys. 92, 1203 (1998)]. [ABSTRACT FROM AUTHOR]

An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the model reduces to the two-dimensional Ising model in the height representation. When the Ising model constraint of single height steps is relaxed, the critical temperature and critical exponents are continuously varying functions of the parameter controlling height steps larger than one. Numerical estimates of the critical exponents can be mapped via a single parameter, the Coulomb gas coupling, to the exponents of the 0(«) loop model on the honeycomb lattice with n < 1. [ABSTRACT FROM AUTHOR]

T graphene, a two-dimensional carbon allotrope with tetrarings, is investigated by first-principles calculations. We demonstrate that buckled T graphene has Dirac-like fermions and a high Fermi velocity similar to graphene even though it has nonequivalent bonds and possesses no hexagonal honeycomb structure. New features of the linear dispersions that are different from graphene are revealed, &pai; and &pai;* bands and the two comprising sublattices are the key factors for the emergence of Dirac-like fermions. T graphene and its two types of nanoribbon are expected to possess additional properties over graphene due to its different band structure. [ABSTRACT FROM AUTHOR]

We demonstrate the presence of Dirac cones in the dispersion relation of acoustic waves propagating on the surface of a plate of methyl methacrylate containing a honeycomb lattice of cylindrical boreholes. This structure represents the acoustic analogue of graphene, the cylindrical cavities playing the role of carbon atoms while acoustic surface waves are the equivalent of electronic waves in graphene. Analytical expressions for the Dirac frequency and Dirac velocity in acoustics are given as a function of the radius and depth of boreholes. These parameters have been experimentally determined for a constructed structure and the data are in fairly good agreement with the predicted values. [ABSTRACT FROM AUTHOR]

Because of its unique physical properties, graphene, a 2D honeycomb arrangement of carbon atoms, has attracted tremendous attention. Silicene, the graphene equivalent for silicon, could follow this trend, opening new perspectives for applications, especially due to its compatibility with Si-based electronics. Silicene has been theoretically predicted as a buckled honeycomb arrangement of Si atoms and having an electronic dispersion resembling that of relativistic Dirac fermions. Here we provide compelling evidence, from both structural and electronic properties, for the synthesis of epitaxial silicene sheets on a silver (111) substrate, through the combination of scanning tunneling microscopy and angular-resolved photoemission spectroscopy in conjunction with calculations based on density functional theory. [ABSTRACT FROM AUTHOR]

The competition between Kitaev and Heisenberg interactions away from half filling is studied for the hole-doped Kitaev-Heisenberg t-JK-JH model on a honeycomb lattice. While the isotropic Heisenberg coupling supports a time-reversal violating d-wave singlet state, we find that the Kitaev interaction favors a time-reversal invariant p-wave superconducting phase, which obeys the rotational symmetries of the microscopic model, and is robust for JH < JK/2. Within the p-wave superconducting phase, a critical chemical potential |μ| = μc &ap; t separates a topologically trivial phase for |μ| < μc from a topologically nontrivial Z2 time-reversal invariant spin-triplet phase for |μ| > μc. [ABSTRACT FROM AUTHOR]

The phase diagram of the fully frustrated XY model on a honeycomb lattice is shown to incorporate three different ordered phases. In the most unusual of them, a long-range order is related not to the dominance of a particular periodic vortex pattern but to the orientation of the zero-energy domain walls separating domains with different orientations of vortex stripes. The phase transition leading to the destruction of this phase can be associated with the appearance of free fractional vortices and is of the first order. The stabilization of the two other ordered phases (existing at lower temperatures) relies on a positive contribution to the domain-wall free energy induced by the presence of spin waves. This effect has a substantial numerical smallness, in accordance with which these two phases can be observed only in the systems of really macroscopic sizes. In physical systems (like magnetically frustrated Josephson junction arrays and superconducting wire networks), the presence of additional interactions must lead to a better stabilization of a phase with a long-range order in terms of vortex pattern and improve the possibilities of its observation. [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 report inelastic neutron scattering measurements on Na2Ir03, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below TN = 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange. [ABSTRACT FROM AUTHOR]

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2Ir03 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from &thetas; = --125 K for Na2Ir03 to &thetas; &thkap; --33 K for Li2Ir03, while the ordering temperature remains roughly the same TN &thkap; 15 K. Using functional renormalization group calculations we show that this evolution of &thetas; and TN as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2Ir03 is deep in a magnetically ordered regime, while Li2Ir03 appears to be close to a spin-liquid regime. [ABSTRACT FROM AUTHOR]

We determine the frictional figures of merit for a pair of layered honeycomb nanostructures, such as graphane, fluorographene, MoS2 and W02 moving over each other, by carrying out ab initio calculations of interlayer interaction under constant loading force. Using the Prandtl-Tomlinson model we derive the critical stiffness required to avoid stick-slip behavior. We show that these layered structures have low critical stiffness even under high loading forces due to their charged surfaces repelling each other. The intrinsic stiffness of these materials exceeds critical stiffness and thereby the materials avoid the stick-slip regime and attain nearly dissipationless continuous sliding. Remarkably, tungsten dioxide displays a much better performance relative to others and heralds a potential superlubricant. The absence of mechanical instabilities leading to conservative lateral forces is also confirmed directly by the simulations of sliding layers. [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]

Phase coherence and vortex order in the fully frustrated XY model on a two-dimensional honeycomb lattice are studied by extensive Monte Carlo simulations using the parallel tempering method and finite-size scaling. No evidence is found for an equilibrium order-disorder or a spin/vortex-glass transition, suggested in previous simulation works. Instead, the scaling analysis of correlations of phase and vortex variables in the full equilibrated system is consistent with a phase transition where the critical temperature vanishes and the correlation lengths diverge as a power law with decreasing temperatures and corresponding critical exponents vphand vv. This behavior and the near agreement of the critical exponents suggest a zero-temperature transition scenario where phase and vortex variables remain coupled on large length scales [ABSTRACT FROM AUTHOR]

Using a first-principle plane-wave method we investigate the effects of static charging on the structural, electronic, and magnetic properties of suspended, single-layer graphene, graphane, fluorographene, BN, and MoS2 in a honeycomb structure. The limitations of periodic boundary conditions in the treatment of negatively charged layers are clarified. Upon positive charging, the band gaps between the conduction and valence bands increase, but the single-layer nanostructures become metallic owing to the Fermi level dipping below the maximum of valence band. Moreover, their bond lengths increase, leading to phonon softening. As a result, the frequencies of Raman active modes are lowered. A high level of positive charging leads to structural instabilities in single-layer nanostructures, since their specific phonon modes attain imaginary frequencies. Similarly, excess positive charge is accumulated at the outermost layers of metallized BN and MoS2 sheets comprising a few layers. Once the charging exceeds a threshold value, the outermost layers are exfoliated. Charge relocation and repulsive force generation are in compliance with classical theories. [ABSTRACT FROM AUTHOR]

Motivated by the observation of a disordered spin ground state in the S = 3/2 material Bi3Mn4O12NO3, we study the ground-state properties and excitation spectra of the S = 3/2 (and for comparison S = 1/2) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the Néel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in 1/&lgr; = J1/J⊥, where J⊥ is an in-plane exchange constant and Jx is the exchange constant between the layers, are used to study properties of the spin singlet phase. For the unfrustrated case, our results for the phase transitions are in very good agreement with recent quantum Monte Carlo studies. We also obtain the excitation spectra in the disordered phase and study the change in the critical &lgr; when frustrating exchange interactions are added to the S = 3/2 system and find a rapid suppression of the ordered phase with frustration. Implications for the material Bi3Mn4O12NO3 are discussed. [ABSTRACT FROM AUTHOR]

The electrical transport properties of a MoGe thin film with a honeycomb array of nanoscale holes are investigated. The critical current of the system shows nonmatching anomalies as a function of applied magnetic-field, enabling us to distinguish between multiquanta vortices trapped in the holes and interstitial vortices located between the holes. The number of vortices trapped in each hole is found to be larger than the saturation Dumber predicted for an isolated hole and shows a nonlinear field dependence, leading to the caging effect as predicted from the Ginzburg-Landau (GL) theory. Our experimental results are supplemented by numerical simulations based on the GL theory. [ABSTRACT FROM AUTHOR]

A Kitaev-Heisenberg- J2-J3 model is proposed to describe the Mort-insulating layered iridates A2IrO3 (A = Na, Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest-neighbor couplings J1, J2, and J3. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings. [ABSTRACT FROM AUTHOR]

We investigate the exact solution of the honeycomb model proposed by Kitaev and derive an explicit formula for the projector onto the physical subspace. The physical states are simply characterized by the parity of the total occupation of the fermionic eigenmodes. We consider a general lattice on a torus and show that the physical fermion parity depends in a nontrivial way on the vortex configuration and the choice of boundary conditions. In the vortex-free case with a constant gauge field we are able to obtain an analytical expression of the parity. For a general configuration of the gauge field the parity can be easily evaluated numerically, which allows the exact diagonalization of large spin models. We consider physically relevant quantities, as in particular the vortex energies, and show that their true value and associated states can be substantially different from the one calculated in the unprojected space, even in the thermodynamic limit. [ABSTRACT FROM AUTHOR]

We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time, our results directly apply to Kitaev's honeycomb model in a vortex superlattice. [ABSTRACT FROM AUTHOR]

The conductivity properties between Luttinger liquids are analyzed by exact renormalization-group methods. We prove that in a two chain system or in a model of bilayer graphene, described by two coupled Fermionic honeycomb lattices interacting with a gauge field, the transverse optical conductivity at finite temperature is anomalous and decreasing together with the frequency as a power law with a Luttinger liquid exponent. [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]

We propose an experimentally feasible setup with ultracold alkaline-earth-metal atoms to simulate the dynamics of U(1) lattice gauge theories in 2 + 1 dimensions with a Chern-Simons term. To this end we consider the ground-state properties of spin-5/2 alkaline-earth-metal fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin-liquid state with 2π/3 flux per plaquette, which violates time-reversal invariance. We demonstrate that due to the breaking of time-reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge-field dynamics. We discuss also properties of the lowest energy competing orders. [ABSTRACT FROM AUTHOR]

We study the dimensional crossover from two dimensional to one dimensional (1D) in the structure of the graphene honeycomb lattice when one of the dimensions of the layer is reduced by analyzing the thermally excited rippling. Through a joint study, by Monte Carlo (MC) simulations using a quasiharmonic potential and by analytical calculations, we find that the normal-normal correlation function does not change its power law behavior in the long wavelength limit. However, the dependency of the square of the out-of-plane displacement (⟨h2⟩) against the system size changes its scaling behavior when going from a layer to a nanoribbon. We show that a new scaling law appears which corresponds to a truly 1D behavior and we estimate the ratio of the sample dimensions where the crossover takes place as R2D↔1D≈1.609. Having explored a wide number of realistic system sizes, we conclude that narrow ribbons present stronger corrugations than the square graphene layers and we discuss the implications for the electronic properties of free-standing graphene samples. [ABSTRACT FROM AUTHOR]

We report a combined experimental and theoretical investigation of the magnetic structure of the honeycomb- lattice magnet Na2IrO3, a candidate for a realization of a gapless spin liquid. Using resonant x-ray magnetic scattering at the Ir L3 edge, we find three-dimensional long-range antiferromagnetic order below TN = 13.3 K. From the azimuthal dependence of the magnetic Bragg peak, the ordered moment is determined to be predominantly along the a axis. Combining the experimental data with first-principles calculations, we propose that the most likely spin structure is a zig-zag structure. [ABSTRACT FROM AUTHOR]

Absence of magnetic ordering in Bi3Mn4O12(NO3) (BMNO) which has a magnetic subsystem that consists of honeycomb bilayers of Mn4+ ions with spin S=3/2 has raised the expectation that its ground state is strongly frustrated due to longer range antiferromagnetic interactions. We calculate the magnetic exchange coupling constants of the BMNO complex within a density functional approach and find that the dominating interactions between Mn spins are the antiferromagnetic nearest-neighbor J1 and the effective interlayer interaction Jc. The largest interaction is Jc, which substantially exceeds J1. Longer range interactions are antiferromagnetic but not strongly frustrating. [ABSTRACT FROM AUTHOR]

In this paper, we describe a mechanism by which the destruction of the Kondo coherence at the same time gives rise to antiferromagnetic ordering. This picture is in contrast to the Doniach picture of the competition of Kondo coherence and antiferromagentic ordering. Our study is done in the honeycomb lattice at half-filling, where Kondo coherence gives rise to a Kondo insulator. We go beyond mean-field (large N) formulation of Kondo coherence in Kondo lattices and consider excitations we call Kondo vortices. A Kondo vortex is a configuration where at its core the Kondo amplitude vanishes while far away from the core it retains the uniform Kondo amplitude. A Kondo vortex in our model brings four zero modes to the chemical potential. The zero modes play a crucial role as they allow us to construct spin-1 operators. We further study the transformation of these spin-1 Kondo vortex operators under various symmetry transformations of the Kondo Hamiltonian and find a class of operators that transform like an antiferromagnetic order parameter. This gives a novel picture of how one can create antiferromagnetic ordering by proliferating Kondo vortices inside a Kondo coherent phase. We finish by studying the universality class of this Kondo vortex mediated antiferromagnetic transition and conclude that it is in the O(3) universality class. [ABSTRACT FROM AUTHOR]

Recent synthesis of fluorinated graphene introduced interesting stable derivatives of graphene. In particular, fluorographene (CF), namely, fully fluorinated chair conformation, is found to display crucial features, such as high mechanical strength, charged surfaces, local magnetic moments due to vacancy defects, and a wide band gap rapidly reducing with uniform strain. These properties, as well as structural parameters and electronic densities of states, are found to scale with fluorine coverage. However, most of the experimental data reported to date neither for CF nor for other CnF structures complies with the results obtained from first-principles calculations. In this study, we attempt to clarify the sources of disagreements. [ABSTRACT FROM AUTHOR]

Recent theoretical and experimental works on carbon nanotubes and graphene samples have revealed that spin-orbit interactions, though customarily ignored in carbon-based materials, are more important and complex than it was thought. We study the intrinsic spin-orbit coupling effects on graphene nanoribbons, both flat and bent. Calculations are performed within the tight-binding model with the inclusion of a four-orbital basis set; thereby the full symmetry of the honeycomb lattice and the hybridization of ⢃ and π bands are considered. In addition to the zero-energy π-edge states, ⢃-derived edge states are found for the three investigated ribbon geometries. The ⢃ states are also spin filtered and localized at the boundaries of the ribbons. The calculated spin-orbit splittings are larger for the ⢃- than for the π-derived edge states. Due to this enhancement, spin-orbit splittings of the ⢃ states reach values of the order of a few Kelvin. These spin-filtered edge states are robust under ⢃-π hybridization and curvature effects. [ABSTRACT FROM AUTHOR]

Motivated by the current interest in the quantum dimer model on the triangular lattice, we investigate the phase diagram of the closely related fully frustrated transverse-field Ising model on the honeycomb lattice using classical and semiclassical approximations. We show that, in addition to the fully polarized phase at a large field, the classical model possesses a multitude of phases that break the translational symmetry which, in the dimer language, correspond to a plaquette phase and a columnar phase separated by an infinite cascade of mixed phases. The modification of the phase diagram by quantum fluctuations has been investigated in the context of linear spin-wave theory. The extrapolation of the semiclassical energies suggests that the plaquette phase extends down to zero field for spin 1/2, in agreement with the √12×√12 phase of the quantum dimer model on the triangular lattice with only kinetic energy. [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]

The study of the magnonic thermal Hall effect in magnets with Dzyaloshinskii-Moriya interaction (DMI) has recently drawn attention because of the underlying topology. Topological phase transitions may arise when there exist two or more distinct topological phases, and they are often revealed by a gap-closing phenomenon. In this work, we consider the magnons in honeycomb ferromagnets described by a Heisenberg Hamiltonian containing both an out-of-plane DMI and a Zeeman interaction. We demonstrate that the magnonic system exhibits temperature (or magnetic field) driven topological phase transitions due to magnon-magnon interactions. Specifically, when the temperature increases, the magnonic energy gap at Dirac points closes and reopens at a critical temperature, Tc. By showing that the Chern numbers of the magnonic bands are distinct above and below Tc, we confirm that the gap-closing phenomenon is indeed a signature for the topological phase transitions. Furthermore, our analysis indicates that the thermal Hall conductivity in the magnonic system exhibits a sign reversal at Tc, which can serve as an experimental probe of its topological nature. Our theory predicts that in CrI3 such a phenomenon exists and is experimentally accessible. [ABSTRACT FROM AUTHOR]

Using a realistic band structure for twisted WSe2 materials, we develop a theory for the interaction-driven correlated insulators to conducting metals transitions through the tuning of the filling factor around commensurate fractional fillings of the moiré unit cell in the 2D honeycomb lattice, focusing on the dominant half-filled Mott insulating state, which exists for both long- and short-range interactions. We find metallic states slightly away from half-filling, as have recently been observed experimentally. We discuss the stabilities and the magnetic properties of the resulting insulating and metallic phases, and comment on their experimental signatures. We also discuss the nature of the correlated insulator states at the rational fractional fillings. [ABSTRACT FROM AUTHOR]

We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam. [ABSTRACT FROM AUTHOR]

Motivated by recent experiments on the Kitaev honeycomb magnet α-RuCl3, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid's chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings. [ABSTRACT FROM AUTHOR]

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN4. A triclinic phase of beryllium tetranitride tr-BeN4 was synthesized from elements at ∼85  GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN4 layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated π systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN4 layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN4 layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions. [ABSTRACT FROM AUTHOR]

Despite being relevant to better understand the properties of honeycomblike systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on interacting Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings provide quantitative and qualitative descriptions of the model at intermediate coupling strengths, and may shed light on the emergence of many-body properties in honeycomblike systems. [ABSTRACT FROM AUTHOR]

Bond-dependent magnetic interactions can generate exotic phases such as Kitaev spin-liquid states. Experimentally determining the values of bond-dependent interactions is a challenging but crucial problem. Here, I show that each symmetry-allowed nearest-neighbor interaction on triangular and honeycomb lattices has a distinct signature in paramagnetic neutron-diffraction data, and that such data contain sufficient information to determine the spin Hamiltonian unambiguously via unconstrained fits. Moreover, I show that bond-dependent interactions can often be extracted from powder-averaged data. These results facilitate experimental determination of spin Hamiltonians for materials that do not show conventional magnetic ordering. [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene develops quasiflat bands at specific "magic" interlayer rotation angles through an unconventional mechanism connected to carrier chirality. Quasiflat bands are responsible for a wealth of exotic, correlated-electron phases in the system. In this Letter, we propose a mechanical analog of twisted bilayer graphene made of two vibrating plates patterned with a honeycomb mesh of masses and coupled across a continuum elastic medium. We show that flexural waves in the device exhibit vanishing group velocity and quasiflat bands at magic angles in close correspondence with electrons in graphene models. The strong similarities of spectral structure and spatial eigenmodes in the two systems demonstrate the chiral nature of the mechanical flat bands. We derive analytical expressions that quantitatively connect the mechanical and electronic models, which allow us to predict the parameters required for an experimental realization of our proposal. [ABSTRACT FROM AUTHOR]

Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancylike defect in the lattice, we observe an anisotropically localized polariton distribution in a single sublattice, a consequence of the semi-Dirac dispersion. Our work opens up new horizons for the study of transport and localization in lattices with chiral symmetry and exotic Dirac dispersions. [ABSTRACT FROM AUTHOR]