Method Of Band Structure Calculation Research Articles

An efficient and unified method for band structure calculations of 2D anisotropic photonic-crystal fibers

An efficient and unified method for band structure calculations of 2D anisotropic photonic-crystal fibers

Depicted simulation model for removal of second-generation antipsychotic drugs adsorbed on Zn-MOF: adsorption locator assessment.

Electronic durable behavior on the material surface was accompanied by a class of antipsychotic drugs (APD) to describe the surface modification in the designed adsorption model. Hierarchically Zn-MOF system was utilized for estimating its capacity for drug molecule removal. Geometrically optimized strategy on the studied systems was performed using DFT/GGA/PBE. FMOs analysis was depicted based on the same level of calculations, and molecular electrostatic potential surface (MEP) was generated for unadsorbed and adsorbed systems to illustrate the variation in the surface-active sites. By interpreting the electronic density of states (DOS), the atomic orbital can be identified as a major or minor electronic distribution by PDOS graph. Adsorption locating behavior was considered to detect the significant surface interaction mode between APD and Zn-MOF surface based on lower adsorption energy. The stability of the adsorbed model was best described through dynamic simulation analysis with time through elevated temperatures. The non-covalent interactions were described using RDG/NCI analysis to show the major favorable surface interaction predicting the highly stable adsorption system. The most accurate geometrical computations were performed using the materials studio software followed by surface cleavage and vacuum slab generation. The first principle of DFT was used to apply CASTEP module with GGA/PBE method for band structure and DOS calculations. Three systems of antipsychotic drugs were computationally studied using CASTEP simulation package and adsorbed on an optimized Zn-MOF surface. Adsorption locator module predicted the preferred adsorption mechanistic models, in which the first model was arranged to be more stable, to confirm the occurrence of some interactions in the adsorption mechanism.

Singular boundary method for band structure calculations of in-plane waves in 2D phononic crystals

In this study, the singular boundary method, which is a boundary collocation method, is first employed to calculate the band structures of in-plane waves in two-dimensional phononic crystals. When a unit cell of a phononic crystal is considered, the whole boundaries, including the continuity and periodic boundaries are discretized by the singular boundary method. Then, a linear eigenvalue equation is derived. For a given frequency, an eigenvalue that involves the Block wave can be calculated. Therefore, by sweeping the frequencies, the band structure can be obtained. The accuracy, efficiency and convergence of the proposed method are tested by several numerical examples, and the results demonstrate that the singular boundary method can provide stable and efficient results for band structure calculations of in-plane waves in two-dimensional phononic crystals.

Thorium dicarbide under high pressure and high temperature: Ab initio investigation

A systematic study on the structural stability of thorium dicarbide (ThC2) under hydrostatic compression has been carried out by exploiting the evolutionary structure search algorithm as implemented in the universal structure predictor: evolutionary Xtallography (USPEX) code in conjunction with the ab initio electronic band structure calculation method. At ambient conditions, ThC2 exists in a monoclinic crystallographic phase with space group (SG) C2/c. Our calculations under generalized gradient approximation (GGA) predict the high-pressure structural sequence of monoclinic-I (SG C2/c) → monoclinic-II (SG C2/m) → orthorhombic-I (SG Pmma) → orthorhombic-II (SG Immm) → hexagonal (SG P6/mmm) for this material with transition pressures of ∼3.3, 58.3, 191.6, and 255 GPa, respectively. Out of this theoretically predicted high-pressure structural phase transition sequence, only the first transition, i.e., monoclinic-I → monoclinic-II, could be compared with the available high-pressure experimental study by Guo et al. [Sci. Rep. 7, 45872 (2017)]. The theoretically determined phase transition qualitatively agrees with the experimental results [Y. Guo et al. Sci. Rep. 7, 45872 (2017)]. Interestingly, our predicted intermediate orthorhombic-I (SG Pmma) phase has an enthalpy lower than that of the previously predicted orthorhombic Cmmm phase by Guo et al. [Sci. Rep. 7, 45872 (2017)]. The high-pressure structural sequence so predicted through static lattice calculations has been further substantiated by confirming the elastic and lattice dynamic stability of each structure in the pressure regime of its structural stability. Additionally, the superconducting transition temperature for all these structures has been determined and it is found that the monoclinic-II (C2/m) phase has the highest transition temperature of 17 K at 5 GPa. Furthermore, the thermo-physical properties along with the temperature-induced phase transitions in ThC2 have also been investigated through both the lattice dynamic simulations (within quasi-harmonic approximation) and ab initio molecular dynamics simulations.

Band structure calculation of photonic crystals with frequency-dependent permittivities.

We propose a new method for band structure calculation of photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an operator function. Finite elements are then used for discretization. Finally, the spectral indicator method is employed to compute the eigenvalues. Numerical examples in both TE and TM cases are presented to show the effectiveness. There exist very few examples in literature for the TM case, and the examples in this paper can serve as benchmarks.

Spectral extended finite element method for band structure calculations in phononic crystals

This talk introduces the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes for computing the band structure of one- and two-dimensional phononic composites. The X-FEM enables the modeling of holes and inclusions in geometry through the framework of partition-of-unity enrichment. This reduces the burden on mesh generation, since meshes do not need to conform to geometric features in the periodic domain. Further, with iterative design processes such as phononic shape optimization, the need for remeshing is eliminated. To obtain theoretical rates of convergence with higher-order extended finite elements, careful consideration of curved geometry representation and numerical integration is required. In two dimensions, we adopt rational Bezier representation of conic sections or optimized cubic Hermite functions to model implicit boundaries described by level sets. Efficient computation of weak form integrals is realized through the homogeneous numerical integration scheme—a method that uses Euler’s homogeneous function theorem and Stokes’s theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used to improve matrix conditioning on finite elements that are cut by a hole. Band structure calculations on perforated materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes.

A Chebyshev collocation method for band structure calculations of the longitudinal elastic waves in phononic crystals

AbstractIn this study, a Chebyshev collocation method (CCM) is developed and applied to calculate the band structures of longitudinal elastic waves in periodically multi‐layered phononic crystals. The general form of the CCM for a unit‐cell is derived, in which the periodic boundary conditions and continuity conditions on the interface between different component materials are imposed directly to the CCM scheme. The band structures or dispersion relations can be obtained by solving the corresponding linear eigenvalue problem, where the unknown frequencies are the eigenvalues and the components of the Bloch wave vector are given. The proposed CCM is verified by using the corresponding results obtained by the transfer matrix method. Due to the advantages of the CCM, the CCM presented in this paper can be easily generalized and applied to the high‐dimensional such as two‐dimensional (2D) problems.

Spectral extended finite element method for band structure calculations in phononic crystals

In this paper, we compute the band structure of one- and two-dimensional phononic composites using the extended finite element method (X-FEM) on structured higher-order (spectral) finite element meshes. On using partition-of-unity enrichment in finite element analysis, the X-FEM permits use of structured finite element meshes that do not conform to the geometry of holes and inclusions. This eliminates the need for remeshing in phononic shape optimization and topology optimization studies. In two dimensions, we adopt a rational Bézier representation of curved (circular) geometries, and construct suitable material enrichment functions to model two-phase composites. A Bloch-formulation of the elastodynamic phononic eigenproblem is adopted. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes's theorem to reduce integration to the boundary of the domain. Ghost penalty stabilization is used on finite elements that are cut by a hole. Band structure calculations on perforated (circular holes, elliptical holes, and holes defined as a level set) materials as well as on two-phase phononic crystals are presented that affirm the sound accuracy and optimal convergence of the method on structured, higher-order spectral finite element meshes. Several numerical examples are presented to demonstrate the advantages of p-refinement made possible by the spectral extended finite element method. In these examples, fourth-order spectral extended finite elements deliver O(10−8) accuracy in frequency calculations with more than thirty-fold fewer degrees-of-freedom when compared to quadratic finite elements.

Investigations on the magnetic properties of the Fe5-xCoxSiB2 alloys by experimental and band structure calculation methods

We present theoretical and experimental investigations on the electronic and magnetic properties of the Fe5-xCoxSiB2 alloys (x = 0, 0.5, 1.0, 1.5, 2.5 and 5). Theoretical calculations show the dependence of the magnetic properties (magnetic moments, magneto-crystalline anisotropy, exchange-coupling parameters, Curie temperature) on the Fe/Co ratio and preferential occupation of Co atoms for 16l crystallographic site. The spontaneous magnetization as a function of temperature was measured and fitted using the Kuz'min function and modified Arrott-Belov plots. The first procedure shows the decrease of the spontaneous magnetization at 0 K with Co content, with obtained values between 8.79 µB/f.u. (x = 0) and 5.97 µB/f.u. (x = 1.5), in agreement with the theoretical calculations. Also, by thermo-magnetic measurements fitted using Kuz’min function Curie temperatures (Tc) have been obtained, which decrease with the Co content, from 845 K (x = 0) to 667 K (x = 1.5). According to the theoretical exchange-coupling parameters calculated for both Fe spins, the decrease of the Tc is mainly related to the decrease of the Fe 16l–Fe 16l exchange interaction. Moreover, the evolution of the magneto-crystalline anisotropy energy (MAE) with Co content shows good agreement between theoretical and experimental investigations. The 3d magnetism character is found to evolve from well localized behavior in the Fe5SiB2 compound, featured by critical exponents typical of Ising systems, to more delocalized upon Co for Fe substitution with larger range interactions and modified critical exponents.This study provides an insight regarding the influence of the Co doping on the stoichiometry and on the magnetic properties of the Fe5-xCoxSiB2 alloys, which have been previously suggested as good candidates for obtaining rare-earth free permanent magnets with enhanced MAE and higher coercivity.

The finite-element time-domain method for elastic band-structure calculations

The finite-element time-domain method for elastic band-structure calculations is presented in this paper. The method is based on discretizing the appropriate equations of motion by finite elements, applying Bloch boundary conditions to reduce the analysis to a single unit cell, and conducting a simulation using a standard time-integration scheme. The unit cell is excited by a wide-band frequency signal designed to enable a large number of modes to be identified from the time-history response. By spanning the desired wave-vector space within the Brillouin zone, the band structure is then robustly generated. Bloch mode shapes are computed using the well-known concept of modal analysis, especially as implemented in an experimental setting. The performance of the method is analyzed in terms of accuracy, convergence, and computation time, and is compared to the finite-difference time-domain method as well as to a direct finite-element (FE) solution of the corresponding eigenvalue problem. The proposed method is advantageous over FD-based methods for unit cells with complex geometries, and over direct FE in situations where the formulation of an eigenvalue problem is not straightforward. For example, the new method makes it possible to accurately solve a time-dependent Bloch problem, such as the case of a complex unit cell model of a topological insulator where an internal fluid flow or other externally controlled physical fields are present.

Improved LDA-1/2 method for band structure calculations in covalent semiconductors

The LDA-1/2 method for self-energy correction is a powerful tool for calculating accurate band structures of semiconductors, while keeping the computational load as low as standard LDA. Nevertheless, controversies remain regarding the choice between (1/2)e and (1/4)e charge stripping from the atoms in group IV semiconductors, the incorrect direct band gap predicted for Ge, and inaccurate band structures for III–V semiconductors. Here we propose an improved method named shell-LDA-1/2 (shLDA-1/2 for short), which is based on a shell-like trimming function for the self-energy potential. With the new approach, we obtained improved band structures for group IV, and for III–V and II–VI compound semiconductors. In particular, with shLDA-1/2 we reproduced the complete band structures of Ge in good agreement with experimental data. Moreover, we have defined clear rules for choosing the amount of charge that ought to be stripped in covalent semiconductors, i.e., (1/2)e or (1/4)e.

Effect of spin-orbit interactions on the structural stability, thermodynamic properties, and transport properties of lead under pressure

The paper investigates the role of spin-orbit interaction in the prediction of structural stability, lattice dynamics, elasticity, thermodynamic and transport properties (electrical resistivity and thermal conductivity) of lead under pressure with the FP-LMTO (full-potential linear-muffin-tin orbital) method for the first-principles band structure calculations. Our calculations were carried out for three polymorphous lead modifications (fcc, hcp, and bcc) in generalized gradient approximation with the exchange-correlation functional PBEsol. They suggest that compared to the scalar-relativistic calculation, the account for the SO effects insignificantly influences the compressibility of Pb. At the same time, in the calculation of phonon spectra and transport properties, the role of SO interaction is important, at least, for $P\ensuremath{\lesssim}150$ GPa. At higher pressures, the contribution from SO interaction reduces but not vanishes. As for the relative structural stability, our studies show that SO effects influence weakly the pressure of the $\mathrm{fcc}\ensuremath{\rightarrow}\mathrm{hcp}$ transition and much higher the pressure of the $\mathrm{hcp}\ensuremath{\rightarrow}\mathrm{bcc}$ transition.

Hybrid-DFT + Vw method for band structure calculation of semiconducting transition metal compounds: the case of cerium dioxide

Hybrid functionals’ non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a known drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT + Vw method (Ivády et al 2014 Phys. Rev. B 90 035146). Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT + Vw functional can be determined from approximate theoretical quasi-particle spectra without any fitting to experiment. The proposed method is illustrated on the charge self-consistent electronic structure calculation for cerium dioxide where itinerant valence states interact with well-localized 4f atomic like states, making this system challenging for conventional methods, either hybrid-DFT or LDA + U, and therefore allowing for a demonstration of the advantages of the proposed scheme.

Spectral element method for band-structure calculations of 3D phononic crystals

The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals.

High pressure behaviour of uranium dicarbide (UC2): Ab-initio study

The structural stability of uranium dicarbide has been examined under hydrostatic compression employing evolutionary structure search algorithm implemented in the universal structure predictor: evolutionary Xtallography (USPEX) code in conjunction with ab-initio electronic band structure calculation method. The ab-initio total energy calculations involved for this purpose have been carried out within both generalized gradient approximations (GGA) and GGA + U approximations. Our calculations under GGA approximation predict the high pressure structural sequence of tetragonal → monoclinic → orthorhombic for this material with transition pressures of ∼8 GPa and 42 GPa, respectively. The same transition sequence is predicted by calculations within GGA + U also with transition pressures placed at ∼24 GPa and ∼50 GPa, respectively. Further, on the basis of comparison of zero pressure equilibrium volume and equation of state with available experimental data, we find that GGA + U approximation with U = 2.5 eV describes this material better than the simple GGA approximation. The theoretically predicted high pressure structural phase transitions are in disagreement with the only high experimental study by Dancausse et al. [J. Alloys. Compd. 191, 309 (1993)] on this compound which reports a tetragonal to hexagonal phase transition at a pressure of ∼17.6 GPa. Interestingly, during lowest enthalpy structure search using USPEX, we do not see any hexagonal phase to be closer to the predicted monoclinic phase even within 0.2 eV/f. unit. More experiments with varying carbon contents in UC2 sample are required to resolve this discrepancy. The existence of these high pressure phases predicted by static lattice calculations has been further substantiated by analyzing the elastic and lattice dynamic stability of these structures in the pressure regimes of their structural stability. Additionally, various thermo-physical quantities such as equilibrium volume, bulk modulus, Debye temperature, thermal expansion coefficient, Gruneisen parameter, and heat capacity at ambient conditions have been determined from these calculations and compared with the available experimental data.

Periodic band structure calculation by the Sakurai–Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation

In this paper, we present a numerical method for periodic band structure calculation, which is associated with eigenvalue problems for periodic problems, using the boundary element method (BEM). In the BEM, the eigenvalue problems are converted into non-linear eigenvalue problems, which are not tractable with conventional eigensolvers. In the present study, to solve non-linear eigenvalue problems, the block Sakurai–Sugiura (SS) method, which can convert non-linear eigenvalue problems into generalised eigenvalue problems, is utilised. A fast direct solver for the BEM with a fast multipole representation is employed in the algorithm of the block SS method since algebraic equations need to be solved for multiple right-hand sides in the block SS method. We conduct several numerical experiments related to phononic structures to confirm the validity and efficiency of the proposed method. We confirm that the proposed method can calculate the band structure of the phononic structures, and the computational time with the proposed method is less than that with a conventional FEM-based eigensolvers with triangular linear elements even for relatively small problems.

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

SummaryA time‐domain method for calculating the band structure of one‐dimensional periodic structures is proposed. During the time‐stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix‐exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix–vector multiplication involved in each time‐step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finite‐difference time‐domain (FDTD) method. The time‐step with which the method runs stably can be much larger than the Courant–Friedrichs–Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large‐scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix‐pruning operation can be very effectively performed. In the numerical experiments for large‐scale quasi‐periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high. Copyright © 2016 John Wiley & Sons, Ltd.

Comprehensive comparison and experimental validation of band-structure calculation methods in III–V semiconductor quantum wells

We present and thoroughly compare band-structures computed with density functional theory, tight-binding, k·p and non-parabolic effective mass models. Parameter sets for the non-parabolic Γ, the L and X valleys and intervalley bandgaps are extracted for bulk InAs, GaAs and InGaAs. We then consider quantum-wells with thickness ranging from 3nm to 10nm and the bandgap dependence on film thickness is compared with experiments for In0.53Ga0.47As quantum-wells. The impact of the band-structure on the drain current of nanoscale MOSFETs is simulated with ballistic transport models, the results provide a rigorous assessment of III–V semiconductor band structure calculation methods and calibrated band parameters for device simulations.

Electronic and Magnetic Properties of CaS0.875M0.125 (M = C, Si, Ge and Sn) by First Principles Theory

The total energy, energy bands, density of sates and half-metallic ferromagnetism of CaS0.875M0.125 (M = C, Si, Ge and Sn) have been studied using band structure calculation methods namely full potential linearized augmented plane wave (FP-LAPW) as well as tight binding linear muffin orbital (TB-LMTO) method. We find that within the generalized gradient approximation (GGA) all dopants induce half-metallic ferromagnetism in CaS, whereas in the case of local spin density approximation (LSDA) C- doping only induce half-metallicity in CaS. The calculated magnetic moment is found to be 2.00 μB per formula unit. The magnetism arises mainly from the p states of dopant atoms. The ground state properties such as lattice constant, total energy difference between non-magnetic and ferromagnetic state, total and partial magnetic moments have been calculated. Within the GGA calculation all dopants enhance the stability of ferromagnetic state.

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit-cell designs for (1) out-of-plane, (2) in-plane, and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (~10(40) possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band-structure calculations. Focusing on high-symmetry plain-strain square lattices, we report unit-cell designs exhibiting record values of normalized band-gap size for all three categories. For the case of combined polarizations, we reveal a design with a normalized band-gap size exceeding 60%.