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In this paper, we use the determinant quantum Monte Carlo method to study the effect of the electric field on the magnetic order in a bilayer Hubbard model on a honeycomb lattice, in which only the direct interlayer hopping energy is included. Our results qualitatively support the layered antiferromagnetic, spin-density wave ground state found in the mean-field theory at the charge neutrality point. The obtained magnetic moments, however, are much smaller than what are estimated in the mean-field theory. As the electric field increases, the magnetic order parameter rapidly decreases. [ABSTRACT FROM AUTHOR]

An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows us to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3. [ABSTRACT FROM AUTHOR]

Motivated by the absence of both spin freezing and a cooperative Jahn-Teller effect at the lowest measured temperatures, we study the ground state of Ba3CuSb2O9. We solve a general spin-orbital model on both the honeycomb and the decorated honeycomb lattice, revealing rich phase diagrams. The spin-orbital model on the honeycomb lattice contains an SU(4) point, where previous studies have shown the existence of a spin-orbital liquid with algebraically decaying correlations. For realistic parameters on the decorated honeycomb lattice, we find a phase that consists of clusters of nearest-neighbor spin singlets, which can be understood in terms of dimer coverings of an emergent square lattice. While the experimental situation is complicated by structural disorder, we show qualitative agreement between our theory and a range of experiments. [ABSTRACT FROM AUTHOR]

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]

Effects of spontaneous parity breaking by charge, spin, and orbital orders are investigated in a two-band Hubbard model on a honeycomb lattice. This is a minimal model in which the interorbital hopping, atomic spin-orbit coupling, and strong electron correlation give rise to fascinating properties, such as the magnetoelectric effects, quantum spin Hall effect, and spin or valley splitting in the band structure. We perform the symmetry analysis of possible broken-parity states and the mean-field analysis of their competition. We find that the model at 1/4 filling exhibits a spin-orbital composite ordered state and a charge ordered state, in addition to a paramagnetic quantum spin Hall insulator. We show that the composite ordered phase exhibits two types of magnetoelectric responses. The charge ordered state shows spin splitting in the band structure, while the topological nature varies depending on electron correlations. [ABSTRACT FROM AUTHOR]

We generalize the Kitaev's spin-1/2 model on the honeycomb by introducing a two-dimensional Z3 clock model on the triangular lattice with three-body interaction. We discuss various properties of this model and show that the low energy theory of the Z3 generalized Kitaev model (GKM) is described by a single Z3 parafermion per lattice site coupled to a Z3 gauge field. We also introduce a slave-fermion approach for this GKM, treat the resulting fermionic Hamiltonian at the mean-field level, solve the mean-field parameters self-consistently, and obtain the low energy effective Chem-Simons (CS) gauge theory. The resulting CS gauge theory is identical to that of a (221) fractional quantum Hall state. We then go beyond the mean-field approximation and demonstrate that fluctuations generate a uniform interlayer pairing for the dual (221) bilayer state. We argue that this perturbed system can undergo a phase transition to the Fibonacci phase by tuning the interlayer pairing strength. [ABSTRACT FROM AUTHOR]

We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral d + id'-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the t-J model and quantum Monte Carlo calculations of the Hubbard-U model we show that the d + id'-wave state is the favored superconducting state for a wide range of on-site repulsion U, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality d-wave state, where the overall chirality cancels. We find that a state with d + id'-wave symmetry in one valley but d - id'-wave symmetry in the other valley is not possible in the t-J model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekule distortion, we find no energetically favorable d-wave solution with an overall zero chirality within the restriction of the t-J model. [ABSTRACT FROM AUTHOR]

Graphene, with its quantum Hall topological (Chem) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization associated with a second topological number in the Diophantine equation for the Hofstadter problem, and the adiabatic continuity, earlier shown to exist between the square and honeycomb lattices by Hatsugai et al. Specifically, the adiabatic continuity enables us to regard graphene as a simulator of square lattice with half flux quantum per unit cell, which implies, with a semiclassical treatment around rational fluxes implemented here, that the polarization topological numbers in graphene in weak magnetic fields is 1 /2 per Dirac cone for the energy region between the van Hove singularities. Possible experimental setups for observing this topological numbers in cold atoms are proposed as well. [ABSTRACT FROM AUTHOR]

The growth of the √3 × √3 reconstructed silicene on Ag substrate has been frequently observed in experiments while its atomic structure and formation mechanism is poorly understood. Here, by first-principles calculations, we show that √3 × √3 reconstructed silicene is constituted by dumbbell units of Si atoms arranged in a honeycomb pattern. Our model shows excellent agreement with the experimentally reported lattice constant and STM image. We propose a new mechanism for explaining the spontaneous and consequential formation of√3 × √3 structures from 3 x 3 structures on Ag substrate. We show that the √3 × √3 reconstruction is mainly determined by the interaction between Si atoms and have weak influence from Ag substrate. The proposed mechanism opens the path to understanding of multilayer silicon. [ABSTRACT FROM AUTHOR]

A graphenelike two-dimensional boron honeycomb is inherently prohibited due to its empty π valence band. Based on chemical intuition and first-principles calculations, we design a two-dimensional crystal MoB4 with two graphenelike boron honeycombs sandwiching a triangular molybdenum layer. It has the attractive electronic structure of double Dirac cones near Fermi level with high Fermi velocity, which are contributed by the coupling of Mo d orbitals and B pz orbitals. Such a metal stabilized boron honeycomb system could even have both superconductivity and ferromagnetism through appropriate selection of the metal layer, such as manganese. The unique electronic properties of these two-dimensional systems inspire broad interest in nanoelectronics. [ABSTRACT FROM AUTHOR]

The independent predictions of edge ferromagnetism and the quantum spin Hall phase in graphene have inspired the quest of other two-dimensional honeycomb systems, such as silicene, germanene, stanene, iridates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but a larger spin-orbit coupling. Here, we study the interplay of ferromagnetic order and spin-orbit interactions at the zigzag edges of these graphenelike systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conducting edge channels that should result in large changes of electronic properties upon rotation of the magnetization. [ABSTRACT FROM AUTHOR]

The recent proposal of Romero-Isart et al. [Phys. Rev. Lett. 111, 145304 (2013)] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultracold-atom-based quantum emulators raises the need to create and control vortex lattices of different symmetries. Here we propose a mechanism by which honeycomb, hexagonal, square, and kagome vortex lattices could be created in superconducting systems with multiscale intervortex interactions. Multiple scales of the intervortex interaction can be created and controlled in layered systems made of different superconducting materials or with differing interlayer spacings. [ABSTRACT FROM AUTHOR]

Silica or SiO2, the main constituent of Earth's rocks has several 3D complex crystalline and amorphous phases, but it does not have a graphitelike layered structure in 3D. Our theoretical analysis and numerical calculations from the first principles predict a single-layer honeycomblike allotrope, hα silica, which can be viewed to be derived from the oxidation of silicene and it has intriguing atomic structure with reentrant bond angles in hexagons. It is a wide band gap semiconductor, which attains remarkable electromechanical properties showing geometrical changes under an external electric field. In particular, it is an auxetic metamaterial with a negative Poisson's ratio and has a high piezoelectric coefficient. While it can form stable bilayer and multilayer structures, its nanoribbons can show metallic or semiconducting behavior depending on their chirality. Coverage of dangling Si orbitals by foreign adatoms can attribute new functionalities to hα silica. In particular, Si2O5 , where Si atoms are saturated by oxygen atoms from top and bottom sides altematingly can undergo a structural transformation to make silicatene, another stable, single layer structure of silica. [ABSTRACT FROM AUTHOR]

We study the nonequilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground-state degeneracies and associated topological sectors. We present the notion of "topological blocking," experienced by the dynamics due to a mismatch in degeneracies between two phases, and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through nonlocal maps of each of these systems, we effectively study spinless fermionic p-wave paired topological superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered. [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]

Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of onsite Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg universality class"). Our calculation yields an estimate of the critical exponents υ ≃ 1.31, ηϕ ≃ 1.01, and ηψ ≃ 0.08, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method, we use the conventional Gross-Neveu-Yukawa theory with Z2 order parameter ("chiral king universality class") as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in 2 + 1 dimensions, our chiral Ising results agree with the best available predictions from other methods within the single-digit percent range for υ and ηψ and the double-digit percent range for ηϕ. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented. [ABSTRACT FROM AUTHOR]

We investigate the ac electric field induced quantum anomalous Hall effect in honeycomb lattices and derive the full phase diagram for arbitrary field amplitude and phase polarization. We show how to induce antichiral edge modes as well as topological phases characterized by a Chem number larger than 1 by means of suitable drivings. In particular, we find that the Chem number develops plateaus as a function of the frequency, providing a time-dependent analog to the ones in the quantum Hall effect. [ABSTRACT FROM AUTHOR]

The Hubbard and extended Hubbard models on the honeycomb lattice can be seen as prototype models of a single-layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the absence of a sign problem at half-filling, we study this problem with clusters up to 96 sites with the determinant quantum Monte Carlo method as an impurity solver for the dynamical cluster approximation at finite temperatures. After determining the stability of the semimetallic phase to interaction-induced spin-density wave (SDW), charge-density wave (CDW), and Mott insulating phases, we study the single-particle dynamics of the Dirac fermions. We show that when spontaneous symmetry breaking is avoided, the semimetallic phase is a stable Fermi liquid in the presence of repulsive interactions and that Kondo screening dominates the low temperature regime, even though there is a p(ω) = ∣ω∣ type local density of states. We also investigate the impact of the correlation effects on the renormalization of the Fermi velocity vF. We find that vF is not renormalized when only on-site repulsion U is present, but that near-neighbor repulsion V does renormalize vF. This may explain the variations between different measurements of vF in graphene. [ABSTRACT FROM AUTHOR]

The discovery of (4×4) silicene formation on Ag(111) raised the question whether silicene maintains its Dirac fermion character, similar to graphene, on a supporting substrate. Previous photoemission studies indicated that the π band forms Dirac cones near the Fermi energy, while theoretical investigations found it shifted at deeper binding energy. By means of angle-resolved photoemission spectroscopy and density-functional theory calculations we show instead that the π-symmetry states lose their local character and the Dirac cone fades out. The formation of an interface state of free-electron-like Ag origin is found to account for spectral features that were theoretically and experimentally attributed to silicene bands of π character. [ABSTRACT FROM AUTHOR]

The recently synthesized silicene as well as theoretically discussed germanene are examples of buckled honeycomb structures. The buckled structures allow one to manipulate asymmetry between two underlying sublattices of honeycomb structures. Here by taking germanene as a prototype of buckled honeycomb lattices, we explore magnetism induced by breaking sublattice symmetry through saturating chemical bonds on one side of the buckled honeycomb lattice. It is shown that when fractions of chemical bonds on one side are saturated, two narrow bands always exist at half filling. Furthermore, the narrow bands generally support flat band ferromagnetism in the presence of the Hubbard U interaction. The induced magnetization is directly related to the saturation fraction and is thus controllable in magnitude through the saturation fraction. Most importantly, we find that depending on the saturation fraction, the ground state of a one-side-saturated germanene may become a quantum anomalous Hall (QAH) insulator characterized by a Chem number that vanishes for larger magnetization. The nonvanishing Chem number for smaller magnetization implies that the associated quantum Hall effect tends to survive at high temperatures. Our findings provide a potential method to engineer buckled honeycomb structures into high-temperature QAH insulators. [ABSTRACT FROM AUTHOR]

We explore the dielectric properties of graphene-like two-dimensional Kane-Mele topological insulators manifest in buckled honeycomb lattices (such as silicene and germanene). The effect of an on-site potential difference (Δz) between sublattices is given particular attention. We present the results for the real and imaginary parts of the dynamical polarization function. We show that these results display features of three regimes (topological insulator, valley-spin polarized metal, and trivial band insulator) and may be used to extract information on the strength of the intrinsic spin-orbit coupling. We study the inverse dielectric function and provide numerical results for the plasmon branch. We discuss the behavior of the plasmon as a function of sublattice potential difference and show that the behavior of the plasmon branch as Δz is varied is dependent on the location of the chemical potential with respect to the gaps. The static polarization is discussed and numerical results for the screening of a charged impurity are provided. We observe a beating phenomenon in the effective potential which is dependent on Δz. [ABSTRACT FROM AUTHOR]

We exploit a natural projected entangled-pair state (PEPS) representation for the resonating Affleck-Kennedy- Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On the kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a Z2 spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range resonating valence bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulation, we analyze phase transitions of two antiferromagnetic (AFM) triangular Blume-Capel (BC) models with AFM interactions between third-nearest neighbors. One model has hard-core exclusions between the nearest-neighbor (1NN) particles (3NN1 model) and the other has them between the nearest-neighbor and next-nearest-neighbor particles (3NN12 model). Finite-size scaling analysis reveals that in these models, the transition from the paramagnetic to long-range order (LRO) AFM phase is either of the first order or goes through an intermediate phase which might be attributed to the Berezinskii-Kosterlitz-Thouless (BKT) type. The properties of the low-temperature phase transition to the AFM phase of the 1NN, 3NN1, and 3NN12 models are found to be very similar for almost all values of a normalized single-ion anisotropy parameter, 0 < γ < 1.5. Higher temperature behavior of the 3NN12 and 3NN1 models is rather different from that of the 1NN model. Three phase transitions are observed for the 3NN12 model: from the paramagnetic phase to the phase with domains of the LRO AFM phase at Tc, from this structure to the diluted frustrated BKT-type phase at T2, and from the frustrated phase to the AFM LRO phase at T 1. For the 3NN12 model, Tc > T2 > T1 at 0 < γ < 1.15 (range I), Tc ≈ T2 > T1 at 1.15 < γ < 1.3 (range II), and Tc = T2 = T1 at 1.3 < γ < 1.5 (range III). For the 3NN1 model, Tc ≈ T2 > T1 at 0 < γ < 1.2 (range II) and Tc = T2 = T1 at 1.2 < γ < 1.5 (range III). There is only one first-order phase transition in range III. The transition at T c is of the first order in range II and either of a weak first order or a second order in range I. [ABSTRACT FROM AUTHOR]

Density functional calculations predict that the InySi( 111 )-(2 x 2) surface, a key intermediate phase leading to the complex In phase development on Si(l 11), consists of an intriguing one-atom-thick In overlayer. In atoms of 1 monolayer (ML) (referred to as one In atom per surface Si) there forms a quasihoneycomb network of two In units, a monomer and a triangular trimer, which well accounts for the measured microscopy images and In 4d core-level shifts. This In single layer is, however, semiconducting with a band gap of 0.47 eV and thus could not represent the long-sought two-dimensional (2D) limit of metallic In ovedayers. But its In coverage of 1 ML sets a definite lower bound on the coverage for such a 2D-metalIic one-atom-thick In overlayer. [ABSTRACT FROM AUTHOR]

We report on total-energy electronic-structure calculations in the density-functional theory performed for both monolayer and bilayer silicene on Ag(111) surfaces. The √3×√3 structure observed experimentally and argued to be the monolayer silicene in the past [Chen et al., Phys. Rev. Lett. 110, 085504 (2013)] is identified as the bilayer silicene on the Ag(111) surface. The identification is based on our accurate density-functional calculations in which three approximations, the local density approximation, the generalized-gradient approximation, and the van der Waals density-functional approximation, to the exchange-correlation energy have been carefully examined. We find that the structural tristability exists for the √3×√3 bilayer silicene. The calculated energy barriers among the three stable structures are in the range of 7-9 meV per Si atom, indicating possible flip-flop motions among the three. We have found that the flip-flop motion between two of the three structures produces the honeycomb structure in the STM images, whereas the motion among the three does the 1×1 structure. We have found that the electron states which effectively follow the Dirac equation in the freestanding silicene couple with the substrate Ag orbitals due to the bond formation, and shift downwards deep in the valence bands. This feature is common to all the stable or metastable silicene layer on the Ag(111) substrate. [ABSTRACT FROM AUTHOR]

We examine the stability of classical states with a generic incommensurate spiral order against quantum fluctuations. Specifically, we focus on the frustrated spin-1/2 XY and Heisenberg models on the honeycomb lattice with nearest-neighbor J1 and next-nearest-neighbor J2 antiferromagnetic couplings. Our variational approach is based on the Jastrow wave functions, which include quantum correlations on top of classical spin waves. We perform a systematic optimization of wave vectors and Jastrow pseudopotentials within this class of variational states and find that quantum fluctuations favor collinear states over generic coplanar spirals. The Néel state with Q = (0,0) extends its stability well beyond the classical value J2/J1 = 1/6. Most importantly, the collinear states with Q = (0,2π/√3) (and the two symmetry-related states) are found to be stable in a large regime with intermediate frustration, while at the classical level they are limited to the point J2/J1 = 0.5. For large frustration, the 120° state is stabilized for finite values of J2/J1 in both models. [ABSTRACT FROM AUTHOR]

The linear thermal expansion coefficients of two-dimensional honeycomb structures graphene, h-BN, h-MoS2, and h-MoSe2 are systematically studied by using first-principles based quasiharmonic approximation. This approach is first tested on diamond crystal and excellent agreement with the available experimental data is achieved. Our simulations show that the linear thermal expansion coefficients of graphene and h-BN are more negative than that of their multilayered counterparts graphite and white graphite. In addition, there is a remarkable distinction between the coefficients of these two materials in particular at low temperatures. Contrary to graphene and h-BN, lattice thermal expansion coefficient of MOS2 and MoSea are always positive, and the values are comparable with those predicted for diamond. [ABSTRACT FROM AUTHOR]

We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion V2 induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large V2 by mean-field theory. Consequently, the system undergoes a direct transition from the semimetal to the charge-modulated phase. For the latter, charge fluctuations also play a key role. While the phase, which is related to pinball liquids, is stabilized by the repulsion V2, the energy of its low-lying charge excitations scales with the electronic hopping t, as in a band insulator. [ABSTRACT FROM AUTHOR]

We study the finite-temperature phase diagram of the Heisenberg-Kitaev model on a three-dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte Carlo simulations, we investigate quantum and thermal order-by-disorder, as well as the magnetic-ordering temperature. We find the parameter regime where quantum and thermal fluctuations favor different magnetic orders, which leads to an additional finite-temperature phase transition within the ordered phase. This transition, however, occurs at a relatively low temperature and the entropic effects may dominate most of the finite-temperature region below the ordering temperature. In addition, we explore the magnetization process in the presence of a magnetic field and discover spin-flop transitions which are sensitive to the applied-field direction. We discuss implications of our results for future experiments on a hyperhoneycomb lattice system such as the recently discovered β-Li2IrO3. [ABSTRACT FROM AUTHOR]

We report on the modulation of two-dimensional (2D) bands of Cu(111) surface-state electrons by three isostructural supramolecular honeycomb architectures with different periodicity or constituent molecules. Using Fourier-transformed scanning tunneling spectroscopy and model calculations, we resolved the 2D band structures and found that the intrinsic surface-state band is split into discrete bands. The band characteristics including band gap, band bottom, and bandwidth are controlled by the network unit cell size and the nature of the molecule-surface interaction. In particular, Dirac cones emerge where the second and third bands meet at the K points of the Brillouin zone of the supramolecular lattice. [ABSTRACT FROM AUTHOR]

We systematically explore the ground-state phase diagram of the Kane-Mele-Kondo lattice model on the honeycomb lattice; particularly, we focus on its magnetic properties, which are ubiquitous and important in many realistic heavy-fermion materials but have not been clearly studied in the previous publication [X. Y. Feng, J. Dai, C. H. Chung, and Q. Si, Phys. Rev. Lett. Ill, 016402 (2013)]. Besides the Kondo insulator found in that paper, two kinds of antiferromagnetic spin-density-wave phases are discovered. One is the normal antiferromagnetic spin-density-wave state and the other is a nontrivial topological antiferromagnetic spin-density-wave state, which shows the unexpected Z2 topological order with a quantized spin Hall conductance and a helical edge state similar to the hotly studied topological insulators. The quantum spin Hall insulator in the work of Feng et al. is found to be absent since it is always unstable to antiferromagnetic spin-density-wave states at least at the mean-field level in our model. Interestingly, the transition between the two spin-density-wave phases is an exotic topological quantum phase transition, whose critical behavior is described by an emergent three-dimensional quantum electrodynamics, in which conduction electrons contribute to the low-energy Dirac fermions while the spin-wave fluctuation of local spins gives rise to an effective dynamic U( 1) gauge field. Such nontrivial transition shows radical critical thermodynamic, transport, and single-particle behaviors, which provide a fingerprint for this transition. Additionally, the transition of antiferromagnetic spin-density-wave states to the Kondo insulator is found to be first order. The introduction of two novel magnetic phases and their topological quantum phase transition show rich and intrinsic physics involved in the Kane-Mele-Kondo lattice model. [ABSTRACT FROM AUTHOR]

We show that the SixGe1-x random alloys in the honeycomb monolayer structure are nontrivial topological insulators with the same topological classification Z2 = 1 as pristine silicene and germanene. The application of an external electric field decreases the band gap up to its closure at a critical value of the field, ∣ Ec∣. For absolute values of the field larger than ∣ Ec∣ the band gap increases again, and the systems are now trivial insulators. Thus, similarly to what happens for zinc-blend SixGe1-x alloys, these materials will bring new possibilities in the design of devices, such as band gap and mobility engineering, with the added feature that they will exhibit a quantum spin Hall effect due to the gap generated by the spin-orbit coupling. [ABSTRACT FROM AUTHOR]

We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of 9/16, 5/8, and 3/4 that were identified in a previous study of a related quantum model. In particular, both the 9/16 and the 5/8 phase exhibit an extensive ground-state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the 9/16 phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the 5/8 phase. We find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the 5/8 phase, which we obtain via an exact mapping of the ground-state manifold to a hard-core dimer model on an embedded honeycomb superlattice. [ABSTRACT FROM AUTHOR]

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-½ Heisenberg model on a honeycomb lattice with first (J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size N = 2 × 6 × 6. With increasing J2, we find a Néel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ms² on finite-size cylinders to the thermodynamic limit, we find the Néel order vanishing at J2/J1 ≃ 0.22. For 0.25 < J2/J1 ⩽ 0.35, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22 < J2 < 0.25, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region. [ABSTRACT FROM AUTHOR]

Honeycomb structures formed by the growth of perovskite 5d transition metal oxide heterostructures along the (ill) direction in a t2g5 configuration can give rise to topological ground states characterized by a topological index v = 1, as reported by Xiao et al. [Nat. Commun. 2, 596 (2011)]. Using a combination of a tight binding model and ab initio calculations we study the multilayers (SrTiO3)7/(SrIrO3)2 and (KTaO3)7/(KPtO3)2 as a function of parity asymmetry, on-site interaction U, and uniaxial strain and detemiine the nature and evolution of the gap. According to our density functional theory calculations, (SrTiO3)7/(SrIrO3)2 is found to be a topological semimetal whereas (KTaO3)7/(KPtO3)2 is found to present a topological insulating phase that can be understood as the high U limit of the previous one, that can be driven to a trivial insulating phase by a perpendicular external electric field. [ABSTRACT FROM AUTHOR]

Combining an. analytical and numerical approach we investigate the dispersion of the topologically protected spin-filtered edge states of the quantum spin Hall state on honeycomb and ruby nets with zigzag (ZZ) and armchair (AC) edges. We show that the Fermi velocity of the helical edge states on ZZ edges increases linearly with the strength of the spin-orbit coupling (SOC) whereas for AC edges the Fermi velocity is independent of the SOC. Also the decay length of edge states into the bulk is dramatically different for AC and ZZ edges, displaying an inverse functional dependence on the SOC. [ABSTRACT FROM AUTHOR]

The moiré superstructure of a single layer of carbon on ruthenium, where 25×25 graphene honeycombs sit on 23×23 substrate unit cells, is determined from first principles. The density functional theory (DFT) calculations predict two kinds of structural units, Ω and Y, in the supercell, which are identified as moiré beatings or moirons. The related topographic bucklings, or “hills,” have distinct carbon conformations and a height of 1.16 Å. The different moirons are observed with scanning tunneling microscopy (STM), and surface x-ray diffraction (SXRD) also discriminates the two. This connects ab initio DFT calculations with STM and SXRD experiments in unit cells containing more than 4000 atoms. [ABSTRACT FROM AUTHOR]

We study the properties of localized vibrational modes associated with structural defects in a sheet of graphene. For the examples of the Stone-Wales defects, one- and two-atom vacancies, many-atom linear vacancies, and adatoms in a honeycomb lattice, we demonstrate that the local defect modes are characterized by stable oscillations with the frequencies lying outside the linear frequency bands of an ideal graphene. In the frequency spectral density of thermal oscillations, such localized defect modes lead to the additional peaks from the right side of the frequency band of the ideal sheet of graphene, which indicate the presence of defects in the graphene flakes. [ABSTRACT FROM AUTHOR]

We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic cooling in the presence of a trap, which, starting with even relatively high entropies, can drive the system to have a Mott insulating phase with substantial antiferromagnetic correlations. [ABSTRACT FROM AUTHOR]

We experimentally study the propagation of microwaves in an artificial honeycomb lattice made of dielectric resonators. This evanescent propagation is well described by a tight-binding model, very much like the propagation of electrons in graphene. We measure the density of states, as well as the wave function associated with each eigenfrequency. By changing the distance between the resonators, it is possible to modulate the amplitude of next-(next-)nearest-neighbor hopping parameters and to study their effect on the density of states. The main effect is the density of states becoming dissymmetric and a shift of the energy of the Dirac points. We study the basic elements: an isolated resonator, a two-level system, and a square lattice. Our observations are in good agreement with analytical solutions for corresponding infinite lattice. [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]

Silicene is a honeycomb structure of silicon atoms which shares many intriguing properties with graphene. We investigate the electronic properties of a silicene nanodisk, which is silicene with a closed edge. In the case of a graphene nanodisk, the number of the zero-energy modes is given by the lower bound of the inequality in a bipartite system, ξ0 ⩾ 2 ¦NA - NB¦, where ξ0 is the number of zero-energy modes and NA/B is the number of sites in a A/B sublattice. They are standing wave states. In the case of a silicene nanodisk, they propagate around a nanodisk as a helical current, because silicene is a topological insulator due to the spin-orbit interaction. We have found the counting rule of the zero-energy states and constructed the low-energy theory of zigzag triangular silicene. We also show the validity of the bulk-edge correspondence in a nanodisk with a rough edge by calculating the local probability amplitude and current. Finally, the signatures of the topological phase transition induced by an external electric field are discussed. Our results will be observable by means of scanning tunneling microscopy experiments. [ABSTRACT FROM AUTHOR]

Dynamical Jahn-Teller (DJT) effect in a spin-orbital coupled system on a honeycomb lattice is examined, motivated from recently observed spin-liquid behavior in Ba3CuSb209. An effective vibronic Hamiltonian, where the superexchange interaction and the DJT effect are taken into account, is derived. We find that the DJT effect induces a spin-orbital resonant state where local spin-singlet states and parallel orbital configurations are entangled with each other. This spin-orbital resonant state is realized in between an orbital-ordered state, where spin-singlet pairs are localized, and an antiferromagnetic ordered state. Based on the theoretical results, a possible scenario for Ba3CuSb209 is proposed. [ABSTRACT FROM AUTHOR]