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We consider a system of spinless fermions on the honeycomb lattice with substrate-induced modulated electrostatic potentials tripling the unit cell. The resulting non-Abelian SU(2) gauge fields act cooperatively to realize a quadratic band crossing point (QBCP). Using a combination of mean-field theory and renormalization group techniques, we show that in the QBCP regime, arbitrarily weak repulsive electronic interactions drive the system into the quantum anomalous Hall state. This proves that substrate-induced local voltages are an effective knob to induce the spontaneous formation of a topological quantum phase. [ABSTRACT FROM AUTHOR]

A recent study predicted that a 2D single layer of antimony in buckled honeycomb as well as asymmetric washboard structures, named antimonene, is stable at high temperature and displays semiconducting properties. Based on first-principles, spin-polarized density functional calculations,we investigated chemisorption of selected adatoms and physisorption of molecules on two antimonene phases. Since adspecies-adspecies interaction is minimized by using large supercells, our results mimic the effects of isolated, single adatoms or molecules. We found that molecules such as H2, O2, and H2O neither form strong chemical bonds nor dissociate; they are physisorbed with a weak binding energy without affecting the properties of antimonene. The adatoms, such as H, Li, B, C, N, O, Al, In, Si, P, Cl, Ti, As, and Sb, are chemisorbed with significant binding energy, whereby the atomic and electronic structures are modified locally. Boron and carbon adatoms are implemented into buckled antimonene crystal leading to a local reconstruction of the crystal.Nitrogen gives rise to Stone-Wales type defects. The localized states originating from adatoms give rise to diversity of electronic structure. The lowest conduction and highest valence bands of antimonene in asymmetric washboard structures have very high curvature. Once combined with adatom states, these bands offer a variety of features. Specific adatoms lead to spin polarization, attain magnetic moments, and can attribute a half-metallic character to antimonene. [ABSTRACT FROM AUTHOR]

We derive the low-energy Hamiltonian for a honeycomb lattice with anisotropy in the hopping parameters. Taking the reported Dirac Hamiltonian for the anisotropic honeycomb lattice, we obtain its optical conductivity tensor and its transmittance for normal incidence of linearly polarized light. Also, we characterize its dichroic character due to the anisotropic optical absorption. As an application of our general findings, which reproduce the previous case of uniformly strained graphene, we study the optical properties of graphene under a nonmechanical distortion. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) topological insulators (TIs), which can be integrated into the modern silicon industry, are highly desirable for spintronics applications. Here, using first-principles electronic structure calculations, we show that the Au/Si(111)-√3 substrate can provide a platform for hosting 2D TIs obtained through the formation of surface alloys with a honeycomb pattern of adsorbed atoms. We systematically examined elements from groups III to VI of the periodic table at 2/3 monolayer coverage on Au/Si(111)-√ 3, and found that In, Tl, Ge, and Sn adsorbates result in topologically nontrivial phases with band gaps varying from 0 to 50 meV. Our scanning tunneling microscopy and low-energy electron diffraction experiments confirm the presence of the honeycomb pattern when Bi atoms are deposited on Au/Si(111)- √ 3, in accord with our theoretical predictions. Our findings pave the way for using surface alloys as a potential route for obtaining viable 2D TI platforms. [ABSTRACT FROM AUTHOR]

Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensionalDirac systems based on the space groups and discuss our findings within the context of a minimal two-band model. In particular, we show that the emergence of massless Dirac fermions can be attributed to the mirror symmetries of the materials. Moreover, we uncover several novel Dirac systems that have up to 12 inequivalent Dirac cones and showthat these can be realized in (twisted) bilayers. Hereby, we obtain systems with an emergent SU(2N) valley symmetry with N = 1,2,4,6,8,12. Our results pave the way to engineer different Dirac systems, in addition to providing a simple and unified description of materials ranging from square and β-graphynes to Pmmn boron, TiB2, phosphorene, and anisotropic graphene. [ABSTRACT FROM AUTHOR]

The peculiar features of quantum magnetism sometimes forbid the existence of gapped "featureless" paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1 dimensions. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb, and Tasaki to a class we call "slave-spin" states, we propose featureless wave functions for these models. The featurelessness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear. [ABSTRACT FROM AUTHOR]

We present a comprehensive 1/S study of the field-induced dynamical properties of the nearest-neighbor XXZ antiferromagnet on a honeycomb lattice using the formalism of nonlinear spin-wave theory developed for this model. The external magnetic field controls spin frustration in the system and induces noncollinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone wherein decays of spin excitations are prominent, a detailed classification of the decay channels involving magnons from both excitation branches, and a thorough analysis of the singularities in the magnon spectra due to coupling to the two-magnon continuum, all of which are illustrated for several field and anisotropy values. We highlight a number of features related to either the non-Bravais nature of the lattice or the existence of the Dirac-like points in the spectrum. In addition, the asymptotic behavior of the decay rates near high-symmetry points is analyzed in detail. The inelastic neutron-scattering spin-spin structure factor is obtained in the leading 1/S order and is shown to exhibit qualitatively distinct fingerprints of the decay-induced magnon dynamics such as quasiparticle peaks broadened by decays and strong spectral weight redistribution. [ABSTRACT FROM AUTHOR]

Transfer-matrix methods are used for a tight-binding description of electron transport in graphenelike geometries in the presence of spin-orbit couplings. Application of finite-size scaling and phenomenological renormalization techniques shows that, for strong enough spin-orbit interactions and increasing on-site disorder, this system undergoes a metal-insulator transition characterized by the exponents v - 2.71 (8), n = 0.174(2). We show how one can extract information regarding spin polarization decay with distance from an injection edge, from the evolution of wave-function amplitudes in the transfer-matrix approach. For (relatively weak) spin-orbit coupling intensity μ, we obtain that the characteristic length As for spin-polarization decay behaves as Δs α μ-2. [ABSTRACT FROM AUTHOR]

We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal density-density interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem-free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground-state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strong-coupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism. [ABSTRACT FROM AUTHOR]

Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first-(J1) and second-neighbor (J2) interactions (0.0≤J2/J1≤0.5) by means of density-matrix renormalization group. In the parameter regime J2/J1≲0.27, the system sustains a Néel antiferromagnetic phase. At the large J2 side J2/J1≳0.32, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases 0.27≲J2/J1≲0.32, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/2 system. [ABSTRACT FROM AUTHOR]

Motivated by recent synthesis of the hyperhoneycomb material β-Li2IrO3, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalized degrees of freedom are Majorana fermions and emergent flux loops. The properties of this 3D model are known to differ in important ways from those of its 2D counterpart--it has a finite-temperature phase transition, as well as distinct features in the Raman response. We show, however, that the qualitative behavior of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs. [ABSTRACT FROM AUTHOR]

BaFe2(PO4)2 is an unusual Ising insulating ferromagnet based on the Fe2+ spin S = 2 ion, the susceptibility of which suggests a large orbital component to the Fe local moment. We apply density functional theory based methods to obtain a microscopic picture of the competing interactions and the critical role of spin-orbit coupling (SOC) in this honeycomb lattice system. The low-temperature ferromagnetic phase displays a half-semimetallic Dirac point pinning the Fermi level and preventing gap opening before consideration of SOC, presenting a case in which correlation effects modeled by a repulsive Hubbard U fail to open a gap. Simultaneous inclusion of both correlation and SOC drives a large orbital moment in excess of 0.7 μB (essentially L = 1) for spin aligned along the ĉ axis, with a gap comparable with the inferred experimental value. The large orbital moment accounts for the large Ising anisotropy, in spite of the small magnitude of the SOC strength on the 3d (Fe) ion. Ultimately, the Mott-Hubbard gap is enabled by degeneracy lifting by SOC and the large Fe moments, rather than by standard Hubbard interactions alone. We suggest that competing orbital occupations are responsible for the structural transitions involved in the observed reentrant rhombohedral-triclinic-rhombohedral sequence. [ABSTRACT FROM AUTHOR]

A systematic study of 32 honeycomb monolayer II-VI semiconductors is carried out by first-principles methods. While none of the two-dimensional (2D) structures can be energetically stable, it appears that BeO, MgO, CaO, ZnO, CdO, CaS, SrS, SrSe, BaTe, and HgTe honeycomb monolayers have a good dynamic stability. The stability of the five oxides is consistent with the work published by Zhuang et al. [Appl. Phys. Lett. 103, 212102 (2013)]. The rest of the compounds in the form of honeycomb are dynamically unstable, revealed by phonon calculations. In addition, according to the molecular dynamic (MD) simulation evolution from these unstable candidates, we also find two extra monolayers dynamically stable, which are tetragonal BaS [P4/nmm(129)] and orthorhombic HgS [P21/m(11)]. The honeycomb monolayers exist in the form of either a planar perfect honeycomb or a low-buckled 2D layer, all of which possess a band gap and most of them are in the ultraviolet region. Interestingly, the dynamically stable SrSe has a gap near visible light, and displays exotic electronic properties with a flat top of the valence band, and hence has a strong spin polarization upon hole doping. The honeycomb HgTe has recently been reported to achieve a topological nontrivial phase under appropriate in-plane tensile strain and spin-orbital coupling (SOC) [J. Li et al., arXiv: 1412.2528]. Some II-VI partners with less than 5% lattice mismatch may be used to design novel 2D heterojunction devices. If synthesized, potential applications of these 2D II-VI families could include optoelectronics, spintronics, and strong correlated electronics. [ABSTRACT FROM AUTHOR]

We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has a honeycomb geometry with a staggered energy offset that explicitly breaks the inversion symmetry. Distinct density-ordered phases are identified using noise correlation measurements of the atomic momentum distribution. For weak interactions the geometry induces a charge density wave. For strong repulsive interactions we detect a strong suppression of doubly occupied sites, as expected for a Mott insulating state, and the externally broken inversion symmetry is not visible anymore in the density distribution. The local density distributions in different configurations are characterized by measuring the number of doubly occupied lattice sites as a function of interaction and energy offset. We further probe the excitations of the system using direction dependent modulation spectroscopy and discover a complex spectrum, which we compare with a theoretical model. [ABSTRACT FROM AUTHOR]

Magnetic vortices in nanodots own a switchable circulation sense. These nontrivial magnetization configurations can be arranged into extended and interacting patterns. We have experimentally created large arrays of magnetically reconfigurable vortex patterns in nonplanar honeycomb lattices using particle lithography. Optimizing height asymmetry of the vertices and applying an in-plane magnetic field provide means to switch between homocircular and staggered vortex patterns with a potentially high impact on magnonics and spintronics relying on chiral noncollinear spin textures. To this end, exchange coupling of extended vortex lattices with an out-of-plane magnetized layer allows one to realize artificial skyrmionic core textures with controllable circulation and topological properties in extended exchange coupled honeycomb lattices that may pave the way towards magnetic memory and logic devices based on artificial skyrmions. [ABSTRACT FROM AUTHOR]

We study the high-temperature magnetic order in a quasi-two-dimensional honeycomb compound SrRu2O6 by measuring magnetization and neutron powder diffraction with both polarized and unpolarized neutrons. SrRu2O6 crystallizes into the hexagonal lead antimonate (PbSb2O6, space group P31¯m) structure with layers of edge-sharing RuO6 octahedra separated by Sr2+ ions. SrRu2CO6 is found to order at TN = 565 K with Ru moments coupled antiferromagnetically both in plane and out of plane. The magnetic moment is 1.30(2) μB/Ru at room temperature and is along the crystallographic c axis in the G-type magnetic structure. We perform density functional calculations with constrained random-phase approximation (RPA) to obtain the electronic structure and effective intra- and interorbital interaction parameters. The projected density of states shows strong hybridization between Ru 4d and O 2p. By downfolding to the target t2g bands we extract the effective magnetic Hamiltonian and perform Monte Carlo simulations to determine the transition temperature as a function of interand intraplane couplings. We find a weak interplane coupling, 3% of the strong intraplane coupling, permits three-dimensional magnetic order at the observed TN. [ABSTRACT FROM AUTHOR]

We highlight the effect of structural hierarchy and deformation on band structure and wave-propagation behavior of two-dimensional phononic crystals. Our results show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the band gaps and directionality of phononic crystals. The work provides insights into the role of structural organization and hierarchy in regulating the dynamic behavior of phononic crystals, and opportunities for developing tunable phononic devices. [ABSTRACT FROM AUTHOR]

The notion of a dynamical quantum phase transition (DQPT) was recently introduced [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the nonanalytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model is studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the nondegenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model. [ABSTRACT FROM AUTHOR]

We propose a family of structures that have "Dirac loops," closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon. [ABSTRACT FROM AUTHOR]

Based on first-principles calculations, we have found that a family of two-dimensional transition-metal dichalcogenide haeckelites with square-octagonal lattice MX2-4-8(M = Mo, W and X = S, Se and Te) can host quantum spin Hall effect. The phonon spectra indicate that they are dynamically stable, and the largest band gap is predicted to be around 54 meV. These will pave the way for potential applications of topological insulators. We have also established a simple tight-binding model on a squarelike lattice to achieve a topologically nontrivial quantum state, which extends the study from honeycomb lattice to squarelike lattice and broadens the promising topological material systems greatly. [ABSTRACT FROM AUTHOR]

The pseudolayered character of 3D bulk crystals of antimony has led us to predict its 2D single-layer crystalline phase named antimonene in a buckled honeycomb structure like silicene. Sb atoms also form an asymmetric washboard structure like black phospherene. Based on an extensive analysis comprising ab initio phonon and finite-temperature molecular dynamics calculations, we show that these two single-layer phases are robust and can remain stable at high temperatures. They are nonmagnetic semiconductors with band gaps ranging from 0.3 eV to 1.5 eV, and are suitable for 2D electronic applications. The washboard antimonene displays strongly directional mechanical properties, which may give rise to a strong influence of strain on the electronic properties. Single-layer antimonene phases form bilayer and trilayer structures with wide interlayer spacings. In multilayers, this spacing is reduced and eventually the structure changes to 3D pseudolayered bulk crystals. The zigzag and armchair nanoribbons of the antimonene phases have fundamental band gaps derived from reconstructed edge states and display a diversity of magnetic and electronic properties depending on their width and edge geometry. Their band gaps are tunable with the widths of the nanoribbons. When grown on substrates, such as germanene or Ge(111), the buckled antimonene attains a significant influence of substrates. [ABSTRACT FROM AUTHOR]

The two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling (Si - Sj)n, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multiorbital Mott insulators. We focus on t2g electrons on the honeycomb lattice and propose a physical realization of the spin-3/2 AKLT state. We find a phase transition from the AKLT to the Neel state on increasing Hund's rule coupling, which is confirmed by density matrix renormalization group simulations. An experimental signature of the AKLT state consists of protected, free 5 = 1/2 spins on lattice vacancies, which may be detected in the spin susceptibility. [ABSTRACT FROM AUTHOR]

We derive in the present work topological photonic states purely based on conventional dielectric material by deforming a honeycomb lattice of cylinders into a triangular lattice of cylinder hexagons. The photonic topology is associated with a pseudo-time-reversal (TR) symmetry constituted by the TR symmetry supported in general by Maxwell equations and the C6 crystal symmetry upon design, which renders the Kramers doubling in the present photonic system. It is shown explicitly for the transverse magnetic mode that the role of pseudospin is played by the angular momentum of the wave function of the out-of-plane electric field. We solve Maxwell equations and demonstrate the new photonic topology by revealing pseudospin-resolved Berry curvatures of photonic bands and helical edge states characterized by Poynting vectors. [ABSTRACT FROM AUTHOR]

We study the Hubbard model on the frustrated honeycomb lattice with nearest-neighbor hopping t1 and second nearest-neighbor hopping t2, which is isomorphic to the bilayer triangle lattice, using the SU(2)- invariant slave boson theory. We show that the Coulomb interaction U induces antiferromagnetic (AF) chiral spin density wave (χSDW) order in a wide range of k = t2/t1 where both the two-sublattice AF order at small κ and the decoupled three-sublattice 120° order at large k are strongly frustrated, leading to three distinct phases with different anomalous Hall responses. We find a continuous transition from a χSDW semimetal with the anomalous Hall effect to a topological chiral Chem insulator exhibiting the quantum anomalous Hall effect, followed by a discontinuous transition to χSDW insulator with a zero total Chem number but an anomalous ac Hall effect. The χSDW is likely a generic phase of strongly correlated and highly frustrated hexagonal lattice electrons. [ABSTRACT FROM AUTHOR]

The doping of the honeycomb lattice compound Na2IrO3 with cations having smaller ionic radius such as lithium was supposed to drive the system into a Kitaev spin liquid phase. Even at the smallest doping level the long range magnetic order, present in the parent compound, got suppressed as evidenced by susceptibility and heat capacity measurements. At low doping levels, the long range ordered magnetic phase is accompanied by the formation of a glassy state with a transition temperature of TF~5 K as determined by dc and ac magnetic susceptibility. The magnetic excitation spectrum, measured by inelastic neutron scattering, shows a significant change with doping. Our inelastic neutron scattering data can be well described by linear spin wave theory, revealing the formation of a spiral magnetic phase. [ABSTRACT FROM AUTHOR]

Hexagonal α-Ru trichloride single crystals exhibit a strong magnetic anisotropy and we show that upon applying fields up to 14 T in the honeycomb plane the successive magnetic order at T1 = 14 K and T2 = 8 K could be completely suppressed whereas in the perpendicular direction the magnetic order is robust. Furthermore the field dependence of Χ(T) implies coexisting ferro- and antiferromagnetic exchange between in-plane components of Ru3+spins, whereas for out-of-plane components a strong antiferromagnetic exchange becomes evident. 101Ru zero-field nuclear magnetic resonance in the ordered state evidence a complex (probably non coplanar chiral) long-range magnetic structure. The large orbital moment on Ru3+ is found in density-functional calculations. [ABSTRACT FROM AUTHOR]

A ternary compound, MgPtSi, was synthesized by solid-state reaction. An examination of the compound by powder x-ray diffraction revealed that it crystallizes in the orthorhombic TiNiSi-type structure with the Pnma space group. The structure comprises alternately stacked layers of Mg and PtSi honeycomb network, which is reminiscent of MgB2, and the buckling of the honeycomb network causes orthorhombic distortion. Electrical and magnetic studies revealed that MgPtSi exhibited superconductivity with a transition temperature of 2.5 K. However, its isostructural compounds, namely, MgRhSi and MgIrSi, were not found to exhibit superconductivity. [ABSTRACT FROM AUTHOR]

We use numerical linked cluster expansions to study the thermodynamic properties of the two-dimensional classical Ising, quantum XY, and quantum Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattice. In all cases, the nearest-neighbor coupling between the spins takes values ± J with equal probability. We obtain the disorder-averaged (over ah disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case. These results are compared with the corresponding ones in the clean models. Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature. [ABSTRACT FROM AUTHOR]

Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is raised in a region where the ground state is a trivial metal. [ABSTRACT FROM AUTHOR]

Despite intense interest and considerable works, definitive experimental evidence for time-reversal-invariant topological superconductivity is still lacking. Hence searching for such superconductivity in real materials remains one of the main challenges in the field of topological material. Previously it has been shown that in the buckled honeycomb lattice structure, hydrogenated single bilayer Bi, namely BiH, is a topological insulator. Here we predict that upon n-type doping, BiH is a time-reversal-invariant topological superconductor. Interestingly the edge states of such a superconductor consist of both helical complex fermion modes and helical Majorana fermion modes. [ABSTRACT FROM AUTHOR]

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semiempirical model for anharmonic couplings of third and fourth orders, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Grtineisen parameters, the thermal tension and the thermal expansion coefficients as a function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions, we obtain the renormalization and decay rate of in-plane and flexural phonons as a function of temperature, wave vector, and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There, we find that the transition temperature Tα from negative to positive thermal expansion is lowered with smaller system size. Renormalization of the flexural mode has the opposite effect and leads to values of Tα ≈ 300 K for systems of macroscopic size. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of normal and umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals. [ABSTRACT FROM AUTHOR]

We study the combined effects of lattice deformation, e-e interaction, and spin-orbit coupling in a twodimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation--generalized dimerization and a Kekulé distortion--and calculate topological invariants for the noninteracting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator. [ABSTRACT FROM AUTHOR]

We use quantum Monte Carlo methods to study the ground-state phase diagram of a S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange J (favoring Néel order) competes with two different multispin interaction terms: a six-spin interaction Q3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction Q2 that favors staggered VBS order. For Q3~Q2⪢J, we establish that the competition between the two different VBS orders stabilizes Néel order in a large swath of the phase diagram even when J is the smallest energy scale in the Hamiltonian. When Q3⪢(Q2,J) [Q2⪢(Q3,J)], this model exhibits at zero temperature phase transition from the Néel state to a columnar (staggered) VBS state. We establish that the Néel-columnar VBS transition is continuous for all values of Q2, and that critical properties along the entire phase boundary are well characterized by critical exponents and amplitudes of the noncompact CP1 (NCCP1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising threefold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the Q2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional XY model with a fourfold anisotropy field which is known to be weakly irrelevant at the three-dimensional XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations. [ABSTRACT FROM AUTHOR]

Recently, phosphorene, a monolayer honeycomb structure of black phosphorus, was experimentally manufactured and has attracted rapidly growing interest. Motivated by phosphorene, here we investigate the stability and electronic properties of the honeycomb structure of the arsenic system based on first-principles calculations. Two types of honeycomb structures, buckled and puckered, are found to be stable. We call them arsenenes, as in the case of phosphorene. We find that both buckled and puckered arsenenes possess indirect gaps. We show that the band gap of puckered and buckled arsenenes can be tuned by applying strain. The gap closing occurs at 6% strain for puckered arsenene, where the bond angles between the nearest neighbors become nearly equal. An indirect-to-direct gap transition occurs by applying strain. Specifically, 1% strain is enough to transform puckered arsenene into a direct-gap semiconductor. We note that a bulk form of arsenic called gray arsenic exists which can be used as a precursor for buckled arsenene. Our results will pave the way for applications to light-emitting diodes and solar cells. [ABSTRACT FROM AUTHOR]

We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time evolution of wave packets on the edge of the system. We consider the optimal driving regime for experimentally observing the Floquet topological Anderson insulator, and discuss its possible realization in photonic lattices. [ABSTRACT FROM AUTHOR]

We investigate the realization of a topological superconductor in a generic bucked honeycomb system equipped with four types of mass-generating terms, where the superconductor gap is introduced by attaching the honeycomb system to an s-wave superconductor. Constructing the topological phase diagram, we show that Majorana modes are formed in the phase boundary. In particular, we analyze the honeycomb system with antiferromagnetic order in the presence of perpendicular electric field Ez. It becomes topological for ∣Ez∣ > EzCT and trivial for ∣Ez∣ < EzCT, with EzCT a certain critical field. It is possible to create a topological spot in a trivial superconductor by controlling applied electric field. One Majorana zero-energy bound state appears at the phase boundary. We can arbitrarily control the position of the Majorana fermion by moving the spot of applied electric field, which will be made possible by a scanning tunneling microscope probe. [ABSTRACT FROM AUTHOR]

We present a theoretical investigation on the electron-phonon superconductivity of honeycomb MX2 layered structures where X is one element of group IV (C, Si, or Ge) and M is an alkali or an alkaline-earth metal. Among the studied compositions we predicta Tc of 7 K in RbGe2, 9 K in RbSi2, and 11 K in SrC2. All these compounds feature a strongly anisotropic superconducting gap. Our results show that despite the different doping levels and structural properties, the three families of materials fall into a similar description of their superconducting behavior. This allows us to estimate an upper critical temperature of about 20 K for the class of intercalated group-IV structures, including intercalated graphite and doped graphene. [ABSTRACT FROM AUTHOR]

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric S=1/2 antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form D(r⃗ )∼cos(Q⋅r⃗ )/∣r⃗∣ηw(2), where Q=(2π/3,−2π/3) is the wave vector corresponding to “columnar” valence-bond solid order on the honeycomb lattice, and ηw(2)≈1.49(3). We use a recently introduced large-g expansion approach to relate bond-energy correlators of the SU(g) wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength V(g)=−ln(1+1/g2). Putting g=2, we find numerically that the dimer correlation function Dd(r⃗ ) of this dimer model has power-law behavior Dd(r⃗ )∼cos(Q⋅r⃗ )/∣r⃗∣ηd(2) with ηd(2)≈1.520(15), in rather good agreement with the wave function results. We also study the same quantities for g=3,4,10 and find that the bond-energy correlations in the SU(g) wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model. [ABSTRACT FROM AUTHOR]

Recently, the long-sough quantum anomalous Hall effect was realized in a magnetic topological insulator. However, the requirement of an extremely low temperature (approximately 30 mK) hinders realistic applications. Based on ah initio band structure calculations, we propose a quantum anomalous Hall platform with a large energy gap of 0.34 and 0.06 eV on honeycomb lattices comprised of Sn and Ge, respectively. The ferromagnetic (FM) order forms in one sublattice of the honeycomb structure by controlling the surface functionalization rather than dilute magnetic doping, which is expected to be visualized by spin polarized STM in experiment. Strong coupling between the inherent quantum spin Hall state and ferromagnetism results in considerable exchange splitting and, consequently, an FM insulator with a large energy gap. The estimated mean-field Curie temperature is 243 and 509 K for Sn and Ge lattices, respectively. The large energy gap and high Curie temperature indicate the feasibility of the quantum anomalous Hall effect in the near-room-temperature and even room-temperature regions. [ABSTRACT FROM AUTHOR]

A chiral time-reversal symmetry breaking d + id-wave superconducting state is likely to emerge in graphene doped close to the Van Hove singularity. As heavy doping procedures are expected to introduce defects, we investigate here the effects of microscopic defects on the d + id-wave superconducting state at the Van Hove singularity. We find that, while the superconducting order is reduced near a defect, the d + id-wave state remains intact and recovers in an exponential manner away from the defect. The recovery length is found to be on the order of one lattice constant for weak couplings, and, as we show, this is comparable to the recovery length of a conventional 5-wave state on the graphene honeycomb lattice, thereby demonstrating that the unconventional d + id-wave state is quite resilient to defects. Moreover, we find no significant changes between a single site defect and more extended defects, such as a bivacancy. While the d + id-wave state is fully gapped, we also show that defects introduce localized midgap states with nonzero energies, which should be accessible via scanning probe experiments. [ABSTRACT FROM AUTHOR]

Motivated by the recent synthesis of two insulating Li2IrO3 polymorphs, where Ir4+ Seff = 1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting β-Li2IrO3 hyperhoneycomb lattice and γ-Li2IrO3 stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90° Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z2 flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with Tc ≈ ∣ K ∣ /100. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop l is relatively large in these structures, we construct an l → oo approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint. [ABSTRACT FROM AUTHOR]

We theoretically and experimentally demonstrate the existence of complete surface acoustic wave band gaps in surface phonon-polariton phononic crystals, in a completely monolithic structure formed from a two-dimensional honeycomb array of hexagonal shape domain-inverted inclusions in single crystal piezoelectric Z-cut lithium niobate. The band gaps appear at a frequency of about twice the Bragg band gap at the center of the Brillouin zone, formed through phonon-polariton coupling. The structure is mechanically, electromagnetically, and topographically homogeneous, without any physical alteration of the surface, offering an ideal platform for many acoustic wave applications for photonics, phononics, and microfluidics. [ABSTRACT FROM AUTHOR]

We investigate the edge states of real group IV honeycomb crystals by means of ab initio methods. We fully take spin-orbit coupling into account. Thereby germanene, the germanium-based counterpart to graphene, is used as the model system. We focus on the topological properties depending on the non-, antiferro-, and ferromagnetic edges of the ribbon. We show that, in contrast to model studies, the dispersion of the edge states is strongly nonlinear, destroying gapless Dirac bands. Applying an electric field we further study the topological phase transition to a trivial insulator above a critical field strength. The results are critically discussed and compared with tight-binding predictions. [ABSTRACT FROM AUTHOR]

We synthesize and study single crystals of the layered honeycomb lattice Mott insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(474) ions. The newly found Na2RuO3 features a nearly ideal honeycomb lattice and orders antiferromagnetically at 30 K. Single crystals of Li2RuO3 adopt a honeycomb lattice with either C2/m or more distorted P21/m below 300 K, depending on detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a well-defined magnetic state, in contrast to the singlet ground state found in polycrystalline Li2RuO3. A phase diagram generated based on our results uncovers a new, direct correlation between the magnetic ground state and basal-plane distortions in the honeycomb ruthenates. [ABSTRACT FROM AUTHOR]

In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A2IrO3 includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We alsofind that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro- and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. We find that the zigzag-type antiferromagnetic order occupies a large part of the phase diagram of this model and, for the ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na2IrO3, it can be stabilized at small and even at zero third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na2IrO3 is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors. [ABSTRACT FROM AUTHOR]

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]