Three-dimensional Diamond Lattice Research Articles

Studies on temperature-dependent bandgap and gap-to-midgap ratio in diamond lattice photonic crystal with biosensing applications

The present study examines the temperature dependence of the photonic bandgap, the corresponding wavelength and the gap-to-midgap ratio in a three-dimensional diamond lattice photonic crystal. The bandgap calculations establish that the structure shows a complete photonic bandgap centered around 1550 nm at 300 K. The thermo-optic effect, observed in silicon, is employed to compute the photonic bandgap, band-edge wavelengths and mid-bandgap wavelength at various temperatures in the range of 300 K–400 K. The gap-to-midgap ratio, for the proposed structure, is also evaluated at different temperatures. It is seen that the upper and lower band-edge wavelengths and the mid-bandgap wavelength show a linear temperature dependence. The sensitivity of the structure is observed to be 0.0518 nm/K, thus supporting temperature sensing applications. It is found that the gap-to-midgap ratio, for the proposed diamond lattice structure, shows linear variation with temperature. The effect of variation of the dielectric constant and the fill factor on the gap-to-midgap ratio for the diamond structure has also been analyzed. The proposed design has also been analyzed as a refractive index sensor with a sensitivity of 254.9 nm/RIU for sensing the different components of blood.

Diamond lattice Heisenberg antiferromagnet

We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.

First Brillouin Polytope and Band Structure of Diamond Lattice in Four Dimensions

We study the diamond lattice in four dimensions — a descendant of the three-dimensional diamond lattice. As a four-dimensional polytope, we determine the first Brillouin zone and draw the band structure of the corresponding tight-binding model on two-dimensional paper in the usual manner. In the polyhedral decomposition, we find the zone boundary of the first Brillouin zone in four dimensions to be the omnitruncated 5-cell, which comprises ten truncated octahedra glued to 20 hexagonal prisms. We find Dirac line nodes inside the hexagonal prisms.

Absence of nematic ordering transition in a diamond lattice: Application toFeSc2S4

Recent neutron scattering observations by Plumb et al. [1] reveal that the ground state of $FeSc_2S_4$ is magnetic with two distinct Fe environments, instead of a quantum spin liquid as had been previously thought. Starting with the relevant O(N)-symmetric vector model of $FeSc_2S_4$, we study how the discrete ($Z_2$) and continuous rotational symmetries are successively broken, yielding nematic and ordered phases. At high temperatures, we find that the nematic order parameter falls as $T^{-\gamma}$ ($\gamma>0$), and therefore, $FeSc_2S_4$ lacks any distinct nematic ordering temperature. This feature indicates that the three-dimensional diamond lattice of $FeSc_2S_4$ is highly susceptible to the breaking of Ising symmetries, and explains the two distinct Fe environments that is present even at high temperatures, as seen by M\"ossbauer and far infrared optical spectroscopy.

Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states

We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the square lattice is a universal resource for the measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 POVM on all spins. We also argue that the spin-2 AKLT state on the three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region that the ground state can still support a universal resource before making a transition in its quantum computational power.

Three-dimensional topological phase on the diamond lattice

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice, which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a nonzero winding number introduced by Schnyder et al. [Phys. Rev. B 78, 195125 (2008)] for the ensemble of Hamiltonians with both particle-hole and time-reversal symmetries. The topological character of the weak pairing phase is protected by a discrete symmetry.

Improvement of the Photonic Bandgap in Three-Dimensional Diamond Lattice Microstructures Obtained by Two-Photon Polymerization

Two-photon polymerization, Photonic bandgap, IR transmittanceA photonic crystal (PhC) represents a promising way tocontrol photons in optoelectronic devices. They are periodicstructures consisting of photonic band gaps blockingselected frequencies in all directions within the PhCdepending on its lattice parameters. This effect of PhC onlight is similar to the way in which electronic energy ismanipulated by semiconductor.

Ion Beam Assisted Square Spiral Photonic Crystal Fabrication

AbstractPhotonic crystals currently hold exciting potential in waveguiding applications with the ability to greatly reduce waveguide bend radii, allowing for the realization of photonic networks with increased complexity and device density. Square spiral photonic crystals are comprised of periodic arrays of slanted cylindrical columns with periodic abrupt 90° changes in the column growth direction. The abrupt changes produce elbows which correspond to points in the three-dimensional diamond lattice, which are commonly referred to as diamond:n photonic crystal structures based on the nth nearest neighbor lattice point between column arms. The diamond:n structures are characterized by four parameters: column separation, spiral pitch, column diameter, and column growth angle. These structures have been shown theoretically to have a three-dimensional relative bandgap of approximately 15% for a direct silicon diamond:1 structure and approximately 24% for an inverse silicon diamond:5 structure with circular column cross sections. Silicon square spiral photonic crystals can be grown by a single-step thin film deposition process known as glancing angle deposition (GLAD), which utilizes rotation of lithographically patterned substrates and advanced control algorithms. While using GLAD to grow square spiral photonic crystals in a single-step process is desirable, it does have inherent limitations. Physical vapor deposited films deposited at oblique incidence angles form columns with angle ≤ 60° relative to the substrate normal. This deviates from the optimal diamond:1 and diamond:5 structures which require film growth angles of approximately 64° and 74°, respectively. Here we present SEM images of periodic silicon square spiral films grown with a vapor source incidence angle of 85° that indicate an average column tilt angle of 57˚ for films grown with the basic GLAD process and an average column tilt angle between 61˚ and 65˚ using an ion-assisted GLAD process. Photonic simulations indicating that square spiral films with complete three-dimensional photonic bandgaps are only achievable via ion-assisted GLAD are also presented.

Study on ceramic photonic bandgap structure with three-dimensional diamond lattice

A novel process, which was based on powder injection molding, was investigated for the fabrication of ceramic photonic bandgap structure with three-dimensional diamond lattice. The SiO 2-TiO 2 ceramic powder was mixed with a water-soluble agent to produce slurry. The slurry was then injected into an epoxy mold with inverse diamond lattice, fabricated by the stereolitographic rapid prototyping process. To increase the density of the green compact, cold isostatic pressing was applied on the unit. Using thermal de-binding, the water-soluble agent and the epoxy were extracted at 360 and 650 K, respectively. Sintering was immediately done at 950 K for 5 h and the desired three-dimensional ceramic structure was obtained. The calculated band diagram for this structure indicated the existence of an absolute photonic bandgap for all wave vectors. At 14.7–18.5 GHz, a complete band gap was located with a maximum attenuation of 30 dB at 17 GHz, when transmission was measured in the <100> direction between 10 and 20 GHz.

Three-dimensional functional model proteins: Structure function and evolution

The mapping of phenotype onto genotype for a set of functional model proteins is accomplished by exhaustive enumeration on a three-dimensional diamond lattice. Chains of up to 25 monomers are investigated and their evolution characterized. The model is used to investigate the origins of designability. Highly designable functional model protein structures possess contact maps that have a relatively little commonality with other physically allowed contact maps. Although the diamond lattice has the same coordination number as the square lattice, differences between three-dimensional and two-dimensional functional model proteins are observed. One difference is the lower frequency of structures of low designability on the three-dimensional lattice. In other respects, the conclusions drawn from previous studies using the square lattice remain valid in three dimensions. For example, we observe the tendency for longer chains to form larger networks of sequences with greater stability to mutation. We identify various topographical characteristics of the landscapes: evolutionary bottlenecks bridge otherwise unconnected networks, and hub sequences allow rapid movement between the different neutral networks. The diversity of landscapes that arises from even a minimalist model suggests that real proteins have a rich variety of evolutionary landscapes.

Random walks with nearest neighbors prohibited on the diamond lattice

Random walks with nearest neighbors prohibited, of lengths N up to 1024 steps, are studied on the three-dimensional diamond lattice. This is a model to describe steric effects given by geometrical constraints on the conformation of macromolecules. Short walks (N⩽20) are exactly enumerated, whereas longer walks are examined by Monte Carlo simulation. A crossover is revealed between two distinct behaviors of the mean values (end-to-end distance and gyration radius), which is due to a short-range influence of the imposed geometrical constraints. The shapes of random walks with nearest neighbors prohibited are also studied. The results are compared to those for self-avoiding random walks on the diamond lattice.

Hubbard model on the infinite-dimensional diamond lattice.

We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, ${\mathit{U}}_{\mathit{c}}$/t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at ${\mathit{U}}_{\mathit{c}}$=0.

An example of a chiral set discontinuous at any point

We consider the set of nodes in a three-dimensional diamond lattice, in which each node is surrounded by four neighbors (Fig. i). We obtain the required model by labeling the nodes with the identity symbol U alternately (elements of the first kind), which certainly can be done because all cycles in the lattice contain even numbers of atoms. All the other nodes (elements of the second kind) are the centers of tetrahedra, each of which has four identical 0 ligands in the immediate environment, which in order to avoid uncertainty we restrict to being related to an infinite structure. All the nodes of the first type are chiral if all the nodes of the second type are enumerated in any sequence by natural numbers. The decomposition of the set into chiral and achiral subclasses persists also when we reduce the number of kinds of ligands (i.e., nodes of the second kind) to some small number if one assumes a definite order for their disposition, for example, as shown in Fig. i. We specify a certain order in the relative disposition of the nodes of the first and second kinds in the same basic lattice to obtain in general different x:a = m:n, while the chiral and/or achiral zones may be made not point ones (of zero dimensions) but instead of one or two dimensions, or else three, and either with an insular structure or extending indefinitely throughout the lattice. Figure 2 shows an example of such a structure containing infinite achiral ribbons, which also has x:a = i:i.

An interstitial model for fluid water

As in the usual interstitial model, disorder is introduced by the displacement of molecules from a bonded ice-like framework onto interstitial sites. However, in this model the interstitial sites are distributed in such a way that its properties can be derived from those of an Ising model on the framework sites. Frameworks considered are the three-dimensional diamond lattice and the two-dimensional honeycomb and square lattices. Accurate liquid/vapour phase diagrams are obtained, density maxima and compressibility minima being found on the liquid branch for appropriate ratios of the non-bonding interaction energy e to the bonding energy w. Results are compared with those of the zeroth-order and first-order approximations and isobars are calculated using the latter. For the range of e/w giving best qualitative agreement between the three-dimensional model and experiment, the first-order and accurate results are very close in the part of the state surface where anomalous water-like properties occur.

A new approach to the CPA and its generalizations. II. The disordered alloy in three dimensions

For pt.I see abstr. A60719 of 1974. Following the generalization of the CPA introduced by Bishop and Mookerjee, the CCPA averaged density of states for a 50-50 disordered binary alloy on a three-dimensional diamond lattice is presented. The cluster considered consists of a central vertex with its four nearest neighbours. This is embedded in a CP medium.

Density of Zeros on the Lee-Yang Circle for Two Ising Ferromagnets

Extrapolations of high-field and high-temperature series expansions have been used to construct numerical approximations to the density of zeros $g(\ensuremath{\theta})$ on the Lee-Yang circle for the Ising ferromagnets on a two-dimensional square and a three-dimensional diamond lattice. For temperatures above the critical temperature the density is zero for $|\ensuremath{\theta}|&lt;{\ensuremath{\theta}}_{G}$ and then varies as ${(\ensuremath{\theta}\ensuremath{-}{\ensuremath{\theta}}_{G})}^{\ensuremath{\mu}}$, with $\ensuremath{\mu}\ensuremath{\simeq}\ensuremath{-}0.1 \mathrm{and} +0.1$ for the square and diamond lattices, respectively.