We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or triangular lattices. Numerical results are complemented by analytical equations for weak and strong confinements. In the second part we discuss the phase diagram and the evolution of Dirac points in honeycomb lattices applying a tight-binding description with arbitrary nearest-neighbor hoppings. With increasing asymmetry between the hoppings the Dirac points approach each other. At a critical asymmetry the Dirac points merge to open an energy gap, thus changing the topology of the eigenspectrum. We analyze the trajectory of the Dirac points and study the density of states in the different phases. Manifestations of the phase transition in the temperature dependence of the specific heat and in the structure factor are discussed.
The zigzag edge graphene nanoribbon, which is an antiferromagnetic insulator, is found from the density-function theory calculation to display a robust Dirac point after N and B doping at the zigzag edge. More interestingly, we found that the robust Dirac point is a common feature of the honeycomb structure nanoribbon with appropriate edge sites. The zigzag edge honeycomb nanoribbon is therefore expected to provide a very useful platform for material design and development.
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 case of uniformly strained graphene, we study the optical properties of graphene under a nonmechanical distortion.
We study the band structure of electrons hopping on a honeycomb lattice with 1/q (q integer) flux quanta through each elementary hexagon. In the nearest neighbor hopping model the two bands that eventually form the n = 0 Landau level have 2q zero energy Dirac touchings. In this work, we study the conditions needed for these Dirac points and their stability to various perturbations. We prove that these touchings and their locations are guaranteed by a combination of an anti-unitary particle-hole symmetry and the lattice symmetries of the honeycomb structure. We also study the stability of the D…
Theory anticipates that the in-plane px, py orbitals in a honeycomb lattice lead to new and potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s-p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orb…
We derive the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitary direction. Zigzag boundary conditions result generically once the boundary is not parallel to the bonds. Since a honeycomb strip with zigzag edges is gapless, this implies that confinement by lattice termination does not in general produce an insulating nanoribbon. We consider the opening of a gap in a graphene nanoribbon by a staggered potential at the edge and derive the corresponding boundary condition for the Dirac equation. We a…
Silicene, a sheet of silicon atoms in a honeycomb lattice, was proposed to be a new Dirac-type electron system similar as graphene. We performed scanning tunneling microscopy and spectroscopy studies on the atomic and electronic properties of silicene on Ag(111). An unexpected $\sqrt{3}\times \sqrt{3}$ reconstruction was found, which is explained by an extra-buckling model. Pronounced quasi-particle interferences (QPI) patterns, originating from both the intervalley and intravalley scattering, were observed. From the QPI patterns we derived a linear energy-momentum dispersion and a large Fermi…
Carbon allotropes such as diamond, nano-tube, Fullerene, and Graphene, have unique lattice symmetries of crystal lattice, but these are topologically trivial. We have proposed a topologically-nontrivial allotrope, named Hopfene, which has three-dimensional (3D) arrays of Hopf-links to bind 2D Graphene sheets both vertically and horizontally. Here, we describe the electronic structures of Hopfene by simple tight-binding calculations. We confirmed the original Dirac points of 2D Graphene were topologically protected upon the introduction of the Hopf links, and low-energy excitations are describe…
We consider different generalizations of the honeycomb lattice to three dimensional structures. We address the family of the hyper-honeycomb lattice, which is made up of alternating layers of 2D honeycomb nano-ribbons, with each layer rotated by $π/2$ with the layer below. When the orbitals of the lattice sites are symmetric with respect to the planes of the trigonal links, these structures can produce a Dirac loop, a closed line of Dirac nodes in momentum space. For orbitals that break that symmetry, such as the carbon $p$-wave orbitals, hyper-honeycomb lattices do not possess the loop struct…
We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb n…
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 topol…
We show by means of ab initio calculations and tight-binding modeling that an oxide system based on a honeycomb lattice can sustain topologically non-trivial states if a single orbital dominates the spectrum close to the Fermi level. In such situation, the low energy spectra is described by two Dirac equations that become non-trivially gapped when spin-orbit coupling (SOC) is switched on. We provide one specific example for this but the recipe is general. We discuss a realization of this starting from a conventional spin-a-half honeycomb antiferromagnet whose states close to the Fermi energy a…
In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report a…
Powered by effective parquet nesting a commensurate chiral honeycomb superstructure in a trigonally packed transition metal dichalcogenide TaSe$_2$ results in a Dirac cone anomaly in one-particle excitation spectrum. However, the formation of the well defined Dirac point seems to be hindered by effective scattering on 2D plasmons.
A honeycomb lattice system has four types of Dirac electrons corresponding to the spin and valley degrees of freedom. We consider a state that contains only one type of massless electrons and three types of massive ones, which we call the single Dirac-cone state. We analyze quantum Hall (QH) effects in this state. We make a detailed investigation of the Chern and spin-Chern numbers. We make clear the origin of unconventional QH effects discovered in graphene. We also show that the single Dirac-cone state may have arbitrary large spin-Chern numbers in magnetic field. Such a state will be genera…
Motivated by the recent proposal of Bosonic Dirac materials (BDM), we revisited the Ising model on a honeycomb lattice in the presence of the longitudinal and transverse fields. We apply linear spin-wave theory to obtain the magnon dispersion and its degenerated points. These special degenerated points emerge on the excitation spectrum as a function of the external fields and can be identified as Bosonic Dirac Points (BDP). Since that, in the vicinity of these points the Magnons becomes massless with a linear energy spectrum as well as insensible in relation to weak impurity, exactly as it occ…
We investigate the spectrum and the dispersion relation of the Schrödinger operator with point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level dispersion bands have conic singularities near Dirac points, which are the vertices of the first Brillouin Zone. The existence of such conic dispersion bands plays an important role in various electronic properties of honeycomb-structured materials such as graphene. We then prove that for a honeycomb lattice, the spectra generated by higher-level dispersion relations are all connected so the complete spectrum cons…
Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancy-like defect in the lattice,…
Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines wh…
Moving, merging and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states…
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
We propose a family of free fermion lattice models 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…
Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of t…
Pseudorelativistic Dirac quasiparticles have emerged in a plethora of artificial graphene systems that mimic the underlying honeycomb symmetry of graphene. However, it is notoriously difficult to manipulate their properties without modifying the lattice structure. Here we theoretically investigate polaritons supported by honeycomb metasurfaces and, despite the trivial nature of the resonant elements, we unveil rich Dirac physics stemming from a non-trivial winding in the light-matter interaction. The metasurfaces simultaneously exhibit two distinct species of massless Dirac polaritons, namely …
In a recent article [10], the authors proved that the non-relativistic Schrödinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.
We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. …
The discovery of monolayer graphene has initiated two fertile fields in modern condensed matter physics, Dirac semimetals and atomically-thin layered materials. When these trends meet again in transition metal compounds, which possess spin and orbital degrees of freedom and strong electron correlations, more exotic phenomena are expected to emerge in the cross section of topological states of matter and Mott physics. Here, we show by using ab initio calculations that a monolayer form of transition metal trichalcogenides (TMTs), which has a honeycomb network of transition metal cations, may exh…
We consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting a localized surface plasmon, and study the quantum properties of the collective plasmons resulting from the near field dipolar interaction between the nanoparticles. We analytically investigate the dispersion, the effective Hamiltonian and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarization points close to the normal to the plane the spectrum presents Dirac cones, similar to those present in the electronic band structure of graph…
It have been demonstrated that the zigzag honeycomb nanoribbons exhibit an intriguing edge magnetism. Here the effect of the anisotropy on the edge magnetism in zigzag honeycomb nanoribbons is investigated by using two kinds of large-scale quantum Monte Carlo simulations. The anisotropy in zigzag honeycomb nanoribbons is characterized by the ratios of nearest-neighboring hopping integrals $t_{1}$ in one direction and $t_{2}$ in another direction. Considering the electron-electron correlation, it is shown that the edge ferromagnetism could be enhanced greatly as $t_{2}/|t_{1}|$ increase from $1…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in $(2+1)$--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the …
Recently, a concept of orthogonal metal has been introduced to reinterpret the disordered state of slave-spin representation in the Hubbard model as an exotic gapped metallic state. We have extended this concept to study the slave-spin representation of Hubbard model on the honeycomb lattice.[Phys. Rev. B \textbf{86}, 165134 (2012)] It is found that a novel gapped metallic state coined orthogonal Dirac semimetal is identified. Such state corresponds to the disordered phase of slave-spin and has the same thermal-dynamical and transport properties as Dirac semimetal but its singe-particle excita…
Spin-1 Dirac dispersion and Chern insulating phases in 2D honeycomb Sierpiński fractal
Indian Institute of Science Education and Research (IISER) Tirupati（印度科学教育与研究研究所蒂鲁帕提分校）；Kwansei Gakuin University（关西学院大学）；National Institute for Materials Science (NIMS)（国立材料研究所）
We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio frequency regime so that the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.
We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Appearance of the pairn of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is rather generic for a class of two-dimensional lattices that interpolate between square and $π$-flux lattices. Persistence of the peculiar QHE is interpreted as a topological stability. (ii) While we have the massless Dirac …
We study, theoretically and experimentally, optical properties of different types of honeycomb photonic structures, known also as `photonic graphene'. First, we employ the two-photon polymerization method to fabricate the honeycomb structures. In experiment, we observe a strong diffraction from a finite number of elements, thus providing a unique tool to define the exact number of scattering elements in the structure by a naked eye. Then, we study theoretically the transmission spectra of both honeycomb single layer and 2D structures of parallel dielectric circular rods. When the dielectric co…
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of Brillouin zone (BZ) in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is o…
The electronic band topology of monolayer $β$-Sb (antimonene) is studied from the flat honeycomb to the equilibrium buckled structure using first-principles calculations and analyzed using a tight-binding model and low energy Hamiltonians. In flat monolayer Sb, the Fermi level occurs near the intersection of two warped Dirac cones, one associated with the $p_z$-orbitals, and one with the $\{p_x,p_y\}$-orbitals. The differently oriented threefold warping of these two cones leads to an unusually shaped nodal line, which leads to anisotropic in-plane transport properties and goniopolarity. A slig…
Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They have been created in the lab in the form of semiconductor 2DEGs, optical lattices, and photonic crystals. We show that, over a wide energy range, gases (of electrons, atoms, or photons) that propagate through these lattices are Lorentz gases and the corresponding classical dynamics is chaotic. Thus, honeycomb lattices are also of interest for understanding e…
A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the same thermaldynamical and transport properties as usual Dirac semimetal but its singe-particle excitation is gapped and has nontrivial topological order due to the $Z_{2}$ gauge structure. The quantum phase transition from this orthogonal Dirac semimetal to usual Dirac semimetal is described by a mean-field decoupling with complementary fluctuation analysis an…
The study of the magnonic thermal Hall effect in magnets with Dzyaloshinskii-Moriya interaction (DMI) has recently drawn attention because of the underlying topology. Topological phase transitions may arise when there exist two or more distinct topological phases, and they are often revealed by a gap-closing phenomenon. In this work, we consider the magnons in honeycomb ferromagnets described by a Heisenberg Hamiltonian containing both an out-of-plane DMI and a Zeeman interaction. We demonstrate that the magnonic system exhibits temperature (or magnetic field) driven topological phase transiti…
Photovoltaic Hall effect -- the Hall effect induced by intense, circularly-polarized light in the absence of static magnetic fields -- has been proposed in Phys. Rev. B 79, 081406R (2009) for graphene where a massless Dirac dispersion is realized. The photovoltaic Berry curvature (a nonequilibrium extension of the standard Berry curvature) is the key quantity to understand this effect, which appears in the Kubo formula extended to Hall transport in the presence of strong AC field backgrounds. Here we elaborate the properties of the photovoltaic curvature such as the frequency and field strengt…
We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field $E_z$. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field ($B$), a distinct signature of the t…
We present analytical expressions for the polarizability $P_μ(q_x,ω)$ of graphene modeled by the hexagonal tight-binding model for small wave number $q_x$, but arbitrary chemical potential $μ$. Generally, we find $P_μ(q_x,ω)=P_μ^<(ω/ω_q)+q_x^2P_μ^>(ω)$ with $ω_q=v_Fq_x$ the Dirac energy, where the first term is due to intra-band and the second due to inter-band transitions. Explicitly, we derive the analytical expression for the imaginary part of the polarizability including intra-band contributions and recover the result obtained from the Dirac cone approximation for $μ\rightarrow0$. For $μ<\…
We present systematic study of zero modes and gaps by introducing effects of anisotropy of hopping integrals for a tight-binding model on the honeycomb lattice in a magnetic field. The condition for the existence of zero modes is analytically derived. From the condition, it is found that a tiny anisotropy for graphene is sufficient to open a gap around zero energy in a magnetic field. This gap behaves as a non-perturbative and exponential form as a function of the magnetic field. The non-analytic behavior with respect to the magnetic field can be understood as tunneling effects between energy …
Graphene's honeycomb lattice structure is quite remarkable in the sense that it leads, in the long wavelength limit, to a massless Dirac equation description of nonrelativistic quasiparticles associated with electrons and holes present in the two dimensional crystallite. In the case of cold bosonic atoms trapped in a honeycomb optical lattice, Haddad and Carr (2009) have recently shown, by taking into account binary contact interactions, that the dynamics of these Bose-Einstein condensates is governed by a nonlinear Dirac equation (NLDE). In this paper, we study exact stationary solutions of s…
We review recent work of the authors on the non-relativistic Schrödinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-Δ+V$ and (ii) the two-dimensional Dirac equations, as a large, but finite time, effective description of $e^{-iH_Vt}ψ_0$, for data $ψ_0$, which is spectrally localized at a Dirac point. We conclude with a formal derivation and discussion of the effective large time evolution for the nonlinear Schrödinger - Gross Pitaevskii equation for small ampli…
Lattice deformation resulting from elastic strain is known to spatially modulate the wave function overlap of the atoms on the lattice and can drastically alter the properties of the quasiparticles. Here we elaborate that a twist lattice deformation in two-dimensional honeycomb quantum magnet nanoribbons is equivalent to an elastic gauge field giving rise to magnon Landau quantization. When the ground state is ferromagnetic, dispersive Dirac-Landau levels are induced in the center of magnon bands, while for antiferromagnetic nanoribbons, the twist results in dispersive equidistant Landau level…
Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the 2D electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps, and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coup…
Dirac points and Weyl phase in a honeycomb altermagnet
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University（中山大学物理学院）
Inspired by recent advances in atomic homo and heterostructures, we consider the vertical stacking of plasmonic lattices as a new degree of freedom to create a coupled system showing a modified optical response concerning the monolayer. The precise design of the stacking and the geometrical parameters of two honeycomb plasmonic lattices tailors the interaction among their metallic nanoparticles. Based on the similarity of the lattice symmetry, analogies can be drawn with stacked atomic crystals, such as graphene. We use the multipolar spectral representation to study the plasmonic vertical sta…
Artificial lattices have served as a platform to study the physics of unconventional superconductivity. We study semiconductor artificial graphene -- a honeycomb superlattice imposed on a semiconductor heterostructure -- which hosts the Dirac physics of graphene but with a tunable periodic potential strength and lattice spacing, allowing control of the strength of the electron-electron interactions. We demonstrate a new mechanism for superconductivity due to repulsive interactions which requires a strong lattice potential and a minimum doping away from the Dirac points. The mechanism relies on…
We derive ground state wave functions of superconducting instabilities on the honeycomb lattice induced by nearest-neighbor attractive interactions. They reflect the Dirac nature of electrons in the low-energy limit. For the order parameter that is the same irrespective of the direction to any of the nearest neighbors we find weak pairing (slowly decaying) behavior in the orbital part of the Cooper pair with no angular dependence. At the neutrality point, in the spin-singlet case, we recover a strong pairing behavior. We also derive ground state wave functions for the superconductivity on the …
We study theoretically "graphene-like" plasmonic metamaterials constituted by two-dimensional arrays of metallic nanoparticles, including perfect honeycomb structures with and without inversion symmetry, as well as generic bipartite lattices. The dipolar interactions between localised surface plasmons in different nanoparticles gives rise to collective plasmons that extend over the whole lattice. We study the band structure of collective plasmons and unveil its tunability with the orientation of the dipole moments associated with the localised surface plasmons. Depending on the dipole orientat…
