Spin frustration and magnetic ordering in triangular lattice antiferromagnet Ca_3CoNb_2O_9

We synthesized a quasi-two-dimensional distorted triangular lattice antiferromagnet Ca3CoNb2O9, in which the effective spin of Co2＋is 1/2 at low temperatures, whose magnetic properties were studied by dc susceptibility and magnetization techniques. The x-ray diffraction confirms the quality of our powder samples. The large Weiss constant θCW --55 K and the low Neel temperature TN- 1.45 K give a frustration factor f =｜ θCW/TN｜≈ 38, suggesting that Ca3 Co Nb2O9resides in strong frustration regime. Slightly below TN, deviation between the susceptibility data under zero-field cooling（ZFC）and field cooling（FC） is observed. A new magnetic state with 1/3 of the saturate magnetization Ms is suggested in the magnetization curve at 0.46 K. Our study indicates that Ca3 Co Nb2O9is an interesting material to investigate magnetism in triangular lattice antiferromagnets with weak anisotropy.

Rare-Earth Chalcogenides:A Large Family of Triangular Lattice Spin Liquid Candidates

Frustrated quantum magnets are expected to host many exotic quantum spin states like quantum spin liquid（QSL）, and have attracted numerous interest in modern condensed matter physics. The discovery of the triangular lattice spin liquid candidate YbMgGaO_4 stimulated an increasing attention on the rare-earth-based frustrated magnets with strong spin-orbit coupling. Here we report the synthesis and characterization of a large family of rare-earth chalcogenides AReCh_2（A = alkali or monovalent ions, Re = rare earth, Ch = O,S,Se）. The family compounds share the same structure（R3 m） as YbMgGaO_4,and antiferromagnetically coupled rare-earth ions form perfect triangular layers that are well separated along the c-axis. Specific heat and magnetic susceptibility measurements on NaYbO_2,NaYbS_2 and NaYbSe_2 single crystals and polycrystals, reveal no structural or magnetic transition down to 50 mK. The family, having the simplest structure and chemical formula among the known QSL candidates, removes the issue on possible exchange disorders in YbMgGaO_4. More excitingly, the rich diversity of the family members allows tunable charge gaps, variable exchange coupling, and many other advantages.This makes the family an ideal platform for fundamental research of QSLs and its promising applications.

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403（2）. A convincing finite-size scaling analysis of the model yields ν=0.9995（21）, β/ν=0.12400（17）, γ/v=1.75223（22）, γ^1/ν=1.7555（22）, α/ν=0.00077（420） （scaling） and α/ν=0.0010（42） （hyperscaling）. The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.

Flux phases in the extended Hubbard model on the triangular lattice

Using the unrestricted Hartree-Fock variational method,we study the extended Hubbard model in the triangular lattice at 3/4 filling.Due to the nesting instability of the Fermi surface,various density wave states compatible with the 2×2 supercell are found as the ground state by tuning the onsite and nearest neighbor repulsions U and V.Surprisingly,the flux phases with complex bond order parameters are realized in a wide range of the U-V phase diagram.They also acquire nontrivial topological properties due to the spontaneous breaking of the time-reversal symmetry.Our study suggests that the flux phases can be stabilized by the interplay between short-range repulsive interactions in correlated electron systems.

PHONONIC BAND GAPS IN TWO-DIMENSIONAL HYBRID TRIANGULAR LATTICE

Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.

Fast Tree Search for A Triangular Lattice Model of Protein Folding

Using a triangular lattice model to study the designability of proteinfolding, we overcame the parity problem of previous cubic lattice model and enumerated all thesequences and compact structures on a simple two-dimensional triangular lattice model of size4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, andachieved 2^(23)+2^(12) different sequences excluding the reverse symmetry sequences. The totalstring number of distinct compact structures was 219,093, excluding reflection symmetry in theself-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fastsearch algorithm by constructing a cluster tree. The algorithm decreased the computation bycomputing the objective energy of non-leaf nodes. The parallel experiments proved that the fast treesearch algorithm yielded an exponential speed-up in the model of size 4+5+6+5+4. Designabilityanalysis was performed to understand the search result.

Double Exchange Model in Triangular Lattice Studied by Truncated Polynomial Expansion Method

The low temperature properties of double exchange model in triangular lattice are investigated via truncated polynomial expansion method(TPEM),which reduces the computational complexity and enables parallel computation.We found that for the half-filling case a stable 120◦spin configuration phase occurs owing to the frustration of triangular lattice and is further stabilized by antiferromagnetic(AF)superexchange interaction,while a transition between a stable ferromagnetic(FM)phase and a unique flux phase with small finite-size effect is induced by AF superexchange interaction for the quarter-filling case.

Quantum phase transitions of fermionic atoms in an anisotropic triangular optical lattice

The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte-Carlo algorithm. The quantum phase diagrams which reflect the temperature-interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system. Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value. The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect. A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed, in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.

Tunable triangular and honeycomb plasma structures in dielectric barrier discharge with mesh-liquid electrodes

We demonstrate a method to generate tunable triangular and honeycomb plasma structures via dielectric barrier discharge with uniquely designed mesh-liquid electrodes.A rapid reconfiguration between the triangular lattice and honeycomb lattice has been realized.Novel structures comprised of triangular plasma elements have been observed and a robust angular reorientation of the triangular plasma elements withθ=π/3 is suggested.An active control on the geometrical shape,size and angular orientation of the plasma elements has been achieved.Moreover,the formation mechanism of different plasma structures is studied by spatial-temporal resolved measurements using a high-speed camera.The photonic band diagrams of the plasma structures are calculated by use of finite element method and two large omnidirectional band gaps have been obtained for honeycomb lattices,demonstrating that such plasma structures can be potentially used as plasma photonic crystals to manipulate the propagation of microwaves.The results may offer new strategies for engineering the band gaps and provide enlightenments on designing new types of 2D and possibly 3D metamaterials in other fields.

Indications of c-axis Charge Transport in Hole Doped Triangular Antiferromagnets

The c-axis charge transport of the hole doped triangular antiferromagnet is investigated within the t-J model by considering the incoherent interlayer hopping. It is shown that the c-axis charge transport of the hole doped triangular antiferromagnet is essentially determined by the scattering from the in-plane fluctuation. The c-axis conductivity spectrum shows a low-energy peak and the unusual high-energy broad band, while the c-axis resistivity is characterized by a crossover from the high temperature metallic-like behavior to the low temperature insulating-like behavior, which is qualitatively consistent with those of the hole doped square lattice antiferromagnet.

L(1, 2)-edge-labelings for lattices

For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.

Edge span of L(d,1)-labeling on some graphs

Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.

Absolute band gaps of a two-dimensional triangular-lattice dielectric photonic crystal with different shapes

Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper.Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes,it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air,corresponding to 19.8% of the middle frequency.The influence of the different factors on the width of the absolute band gaps is also discussed.

Synthesis,disorder and Ising anisotropy in a new spin liquid candidate PrMgAl_(11)O_(19)

Here we report the successful synthesis of large single crystals of triangular frustrated PrMgAl_(11)O_(19)using the optical floating zone technique.Single crystal x-ray diffraction(XRD)measurements unveiled the presence of quenched disorder within the mirror plane,specifically~7%of Pr ions deviating from the ideal 2d site towards the 6h site.Magnetic susceptibility measurements revealed an Ising anisotropy with the c-axis being the easy axis.Despite a large spin–spin interaction that develops below~10 K and considerable site disorder,the spins do not order or freeze down to at least 50 mK.The availability of large single crystals offers a distinct opportunity to investigate the exotic magnetic state on a triangular lattice with an easy axis out of the plane.