Honeycomb Symmetry Research Articles

Photonic Floquet topological insulators in atomic ensembles

We demonstrate the photonic Floquet topological insulator (PFTI) in an atomic vapor with nonlinear susceptibilities. The interference of three coupling fields splits the energy levels periodically to form a periodic refractive index structure with honeycomb symmetry that can be adjusted by the choice of frequency detunings and intensities of the coupling fields, which all affect the appearance of Dirac cones in the momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, we obtain a PFTI in the atomic vapor in which an obliquely incident beam moves along the zigzag edge without scattering energy into the PFTI, due to the confinement of the edge states. The appearance of Dirac cones and the formation of PFTI is strongly affected by the nonlinear susceptibilities; i.e. the PFTI can be shut off by the third-order nonlinear susceptibility and re-opened up by the fifth-order one.

Effective Hamiltonian for electron waves in artificial graphene: A first-principles derivation

We propose a first principles effective medium formalism to study the propagation of electron waves in semiconductor heterostructures with a zero-band gap. Our theory confirms that near the K-point the dynamics of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer. Furthermore, we highlight that even though other superlattices based on semiconductors with a zincblende-type structure can have a zero band-gap and a linear energy-momentum dispersion, the corresponding effective medium Hamiltonian is rather different from that of graphene, and can be based on a single-component wavefunction.

Tunable picosecond spin dynamics in two dimensional ferromagnetic nanodot arrays with varying lattice symmetry

Tunable configurational anisotropy in spin-waves with up to 8-fold symmetry in closely packed nanodot lattices with rectangular, honeycomb and octagonal symmetry. The extrinsic nature of the anisotropy is due to angular variation of the magnetostatic field distribution.

Discrete breathers in honeycomb Fermi–Pasta–Ulam lattices

We consider the two-dimensional Fermi–Pasta–Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analysis we reduce the governing lattice equations to a nonlinear Schrödinger equation coupled to a second equation for an accompanying slow mode. Two cases in which the latter equation can be solved and so the system decoupled are considered in more detail: firstly, in the case of a symmetric potential, we derive the form of moving breathers. We find an ellipticity criterion for the wavenumbers of the carrier wave, together with asymptotic estimates for the breather energy. The minimum energy threshold depends on the wavenumber of the breather. We find that this threshold is locally maximized by stationary breathers. Secondly, for an asymmetric potential we find stationary breathers, which, even with a quadratic nonlinearity generate no second harmonic component in the breather. Plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure. Finally, we compare the properties of stationary breathers in the square, triangular and honeycomb lattices.

Magnetic assembly and annealing of colloidal lattices and superlattices.

The ability to assemble mesoscopic colloidal lattices above a surface is important for fundamental studies related with nucleation and crystallization but also for a variety of technological applications in photonics and microengineering. Current techniques based on particle sedimentation above a lithographic template are limited by a slow deposition process and by the use of static templates, which make difficult to implement fast annealing procedures. Here it is demonstrated a method to realize and anneal a series of colloidal lattices displaying triangular, honeycomb, or kagome-like symmetry above a structure magnetic substrate. By using a binary mixture of particles, superlattices can be realized increasing further the variety and complexity of the colloidal patterns which can be produced.

Excitons in two-dimensional sheets with honeycomb symmetry

In this paper, we present results concerning ab initio calculations of the optical properties of group IV two-dimensional sheets and compare them with the prediction of an analytical model for excitons in two dimensions, which we explicitly derive. This comparison helps to understand the physics at the basis of the strong many-body effects present in the optical spectra of this class of materials. Although it demonstrates the need of full ab initio calculations for an accurate description of the two-dimensional excitons, it validates, at the same time, this simple approach to estimate, through a density functional theory calculation of the two-dimensional electronic and optical properties, the binding energy and the radius of the excitons in this class of materials.

New statistical lattice model with double honeycomb symmetry

Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.

Silicene-derived phases on Ag(111) substrate versus coverage:Ab initiostudies

Silicene is systematically investigated as an epitaxial overlayer on an Ag(111) substrate based on the ab initio density functional theory. The geometry and stability of five silicene-silver adsorbate systems with four coincidence lattices, $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ on $\sqrt{13}\ifmmode\times\else\texttimes\fi{}\sqrt{13}$, $3\ifmmode\times\else\texttimes\fi{}3$ on $4\ifmmode\times\else\texttimes\fi{}4$, $2\ifmmode\times\else\texttimes\fi{}2$ on $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$, and $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ on $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$, are related to the Si coverage, biaxial strain, and preparation conditions. Their phase diagram is calculated for varying chemical potential of the Si reservoir. The scanning tunneling microscopy images calculated for the optimized atomic geometries agree with those observed experimentally. The destruction of the original honeycomb symmetry and the strong adsorbate-substrate interaction significantly influence the electronic structure. Four peeled-off silicene sheets show conical linear bands, with small gaps. However, the band edges of the $3\ifmmode\times\else\texttimes\fi{}3$ on $4\ifmmode\times\else\texttimes\fi{}4$ geometry cannot be explained in terms of gap opening between Dirac cones for symmetry reasons. We confirm the conclusion that the linear bands observed by ARPES are due to folded Ag bands.

Featureless and nonfractionalized Mott insulators on the honeycomb lattice at 1/2 site filling

Significance Symmetries are increasingly shown to play various key roles determining the possible phases in condensed matter systems. We study bosonic particles (including electron Cooper pairs) living on the vertices of a honeycomb lattice at a density of 1/2 per site. Here the honeycomb symmetries forbid the usual fermionic band insulating state, and the conventional Mott (“strongly interacting”) insulator involves a whole number of particles frozen on each site, suggesting that featureless (fully symmetric) insulators might not exist in this system. Nevertheless, we explicitly construct quantum states and demonstrate that they are examples of featureless insulators on the honeycomb lattice at 1/2 site filling, with a procedure generalizing to lattices with symmorphic symmetry groups.

Tunable Magnonic Spectra in Two‐Dimensional Magnonic Crystals with Variable Lattice Symmetry

AbstractTunable magnonic properties are demonstrated in two‐dimensional magnonic crystals in the form of artificial ferromagnetic nanodot lattices with variable lattice symmetry. An all‐optical time‐domain excitation and detection of the collective precessional dynamics is performed in the strongly magnetostatically coupled Ni80Fe20 (Py) circular dot lattices arranged in different lattice symmetry such as square, rectangular, hexagonal, honeycomb, and octagonal symmetry. As the symmetry changes from square to octagonal through rectangular, hexagonal and honeycomb, a significant variation in the spin wave spectra is observed. The single uniform collective mode in the square lattice splits in two distinct modes in the rectangular lattice and in three distinct modes in the hexagonal and octagonal lattices. However, in the honeycomb lattice a broad band of modes are observed. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal collective modes with different spatial distributions with the variation in the lattice symmetry determined by the magnetostatic field profiles. For the hexagonal lattice, the most intense peak shows a six‐fold anisotropy with the variation in the azimuthal angle of the external bias magnetic field. Analysis shows that this is due to the angular variation of the dynamical component of magnetization for this mode, which is directly influenced by the variation of the magnetostatic field on the elements in the hexagonal lattice. The observations are important for tunable and anisotropic propagation of spin waves in magnonic crystal based devices.

Magnetic dipole configurations in honeycomb lattices: order and disorder

Dipolar spin ice has attracted much attention because of its intriguing ground state ordering and elementary excitation properties. We present experimental realizations of magnetic dipolar spin ice on periodic lattices with honeycomb symmetry. We have analyzed in particular the evolution and distribution of excitations with magnetic charges ±3 per vertex as a function of magnetic field and the distance b between the dipoles ranging from b = 0.4 to 1.7 μm. In all the dipole patterns investigated, we observe a surprisingly high abundance of ±3 magnetic charges at coercivity in the descending and ascending branches of the magnetic hysteresis. At the same time, these ±3 vertices form a charge ordered state with large domains, resembling an ionic crystal. Monte Carlo simulations of the magnetization reversal confirm in the framework of a macrospin model an enhanced abundance of ±3 magnetic charges at the coercive field. But much better agreement is achieved by taking into account the micromagnetic reversal mechanism, which proceeds via nucleation and domain wall propagation for dipoles aligned with the field and via coherent rotation for all others.

Anisotropy Effects in Atomic-Scale Friction

The static and kinetic friction experienced by a point mass elastically driven at different angles on surface lattices with square, hexagonal, and honeycomb symmetries are estimated by analytical and numeric calculations based on the Prandtl–Tomlinson (PT) model. Assuming a strong surface coupling, the anisotropy of static friction increases from 3.7 up to 46.3% when the density of packing of the surface atoms is reduced, but this is not the case for kinetic friction, the anisotropy of which is maximal on a square lattice. Although these results have not been supported by accurate experimental verifications so far, the PT model was successfully applied to interpret anisotropy effects in the friction force profiles measured, among other surfaces, on rectangular lattices with complex unit cells and on stepped crystal surfaces.

Fine control of critical dimension for the fabrication of large bandgap high frequency photonic and phononic crystals

In this work artificial crystal structures designed to exhibit large and simultaneous photonic and phononic bandgaps, known as phoXonic crystals, are fabricated in silicon. Simulations have shown that honeycomb and square symmetry phoXonic crystals with high filling-fractions can produce large bandgaps in the photonic and phononic dispersion relations. To achieve this at hypersonic phononic frequencies and infrared (telecommunications) photonic frequencies, critical dimensions smaller than 100nm are typically required. In this paper, dose variation for Electron Beam Lithography (EBL) combined with Reactive Ion Etching (RIE) and Thermal Oxidation (TO) are shown to be effective methods to carefully control these parameters.

Epitaxial Graphene on SiC(0001): More than Just Honeycombs

Using scanning tunneling microscopy with Fe-coated W tips and first-principles calculations, we show that the interface of epitaxial graphene/SiC(0001) is a warped graphene layer with hexagon-pentagon-heptagon (H(5,6,7)) defects that break the honeycomb symmetry, thereby inducing a gap and states below E(F near the K point. Although the next graphene layer assumes the perfect honeycomb lattice, its interaction with the warped layer modifies )the dispersion about the Dirac point. These results explain recent angle-resolved photoemission and carbon core-level shift data and solve the long-standing problem of the interfacial structure of epitaxial graphene on SiC(0001).

Ultracold fermions in a graphene-type optical lattice

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter ${t}_{0}$ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.

Simulation of formation process of the ordered nanocluster array on Si(111)7×7

We study the formation process of metal cluster arrays on the Si(111)7×7 reconstructed surface at high temperature using a kinetic Monte Carlo model, in which the formation of clusters is controlled by the two competing processes: the aggregation of adatoms to form clusters in the half cells of the 7×7 surface, and the dissociation of less stable clusters. Both processes are considered to be asymmetric with respect to the two different types of half cells. It leads to ordered self-organized growth of clusters, which occupy only the faulted half cells, forming a cluster array with triangular symmetry. Further, the model introduces a cluster interaction mechanism, which enhances the nucleation and growth in the neighborhood of existing clusters. The simulations show that the cluster interaction suppresses the growth asymmetry so that a low coverage deposition yields a compact aggregation of clusters, which occupy both faulted and unfaulted half cells, forming a local cluster array with a honeycomb symmetry. The simulation results are compared with relevant experimental results, and good qualitative agreements are found.

Engineering artificial graphene in a two-dimensional electron gas

At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity, which does not depend on carrier density. Here we show that modulating a two-dimensional electron gas with a long-wavelength periodic potential with honeycomb symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphenelike system and discuss an experimental realization in a modulation-doped GaAs quantum well. Ultrahigh-mobility electrons with linearly dispersing bands might open new venues for the studies of Dirac-fermion physics in semiconductors.

Lattice-Induced Double-Valley Degeneracy Lifting in Graphene by a Magnetic Field

We show that the recently discovered double-valley splitting of the Landau levels in the quantum Hall effect in graphene can be explained as the perturbative orbital interaction of intravalley and intervalley microscopic orbital currents with a magnetic field. This effect is facilitated by the translationally noninvariant terms that correspond to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac fermions in quantum electrodynamics. We discuss recent data in view of these findings.

A Columnar Phase of Dendritic Lipid−Based Cationic Liposome−DNA Complexes for Gene Delivery: Hexagonally Ordered Cylindrical Micelles Embedded in a DNA Honeycomb Lattice

Gene therapy holds great promise as a future approach to fighting disease and is explored in worldwide clinical trials. Cationic liposome (CL)-DNA complexes are a prevalent nonviral delivery vector, but their efficiency requires improvement and the understanding of their mechanism of action is incomplete. As part of our effort to investigate the structure-transfection efficiency relationships of self-assembled CL-DNA vectors, we have synthesized a new, highly charged (16+) multivalent cationic lipid, MVLBG2, with a dendritic headgroup. Our synthetic scheme allows facile variation of the headgroup charge and the spacer connecting hydrophobic and headgroup moieties as well as gram-scale synthesis. Complexes of DNA with mixtures of MVLBG2 and neutral 1,2-dioleoyl-sn-glycerophosphatidylcholine (DOPC) exhibit the well-known lamellar phase at 90 mol % DOPC. Starting at 20 mol % dendritic lipid, however, two novel nonlamellar phases are observed by synchrotron X-ray diffraction. The structure of one of these phases, present in a narrow range of composition around 25 mol % MVLBG2, has been solved. In this novel dual lattice structure, termed H(I)C, hexagonally arranged tubular lipid micelles are surrounded by DNA rods forming a three-dimensionally continuous substructure with honeycomb symmetry. Complexes in the H(I)C phase efficiently transfect mouse and human cells in culture. Their transfection efficiency, as well as that of the lamellar complexes containing only 10 mol% dendritic lipid, reaches and surpasses that of commercially available, optimized DOTAP-based complexes. In particular, complexes containing MVLBG2 are significantly more transfectant over the entire composition range in mouse embryonic fibroblasts, a cell line empirically known to be hard to transfect.

Emission characteristics of two-dimensional organic photonic crystal lasers fabricated by replica molding

We report on the far-field emission characteristics of two-dimensional photonic crystal-based organic waveguide lasers. The photonic crystals possess square vein, triangular, and honeycomb symmetries. The two-dimensional gratings are fabricated by employing soft lithographic methods. The far-field pattern that we observe is a result of out-of-plane diffractive coupling of the laser emission generated in the plane of the waveguide. This emission pattern offers a convenient and powerful way to evaluate the nature of laser action in such resonators. In devices which possess defects/breaks in the periodicity of the two-dimensional grating, laser emission generated in-plane is scattered in the plane of the waveguide. This phenomenon is the photonic crystal analogue of Kikuchi scattering in electronic crystals.