Linear Tetrahedron Method Research Articles

Phonon-limited electron mobility in Si, GaAs, and GaP with exact treatment of dynamical quadrupoles

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense $\mathbf{q}$ meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology.

Calculating electron momentum densities and Compton profiles using the linear tetrahedron method

A method for computing electron momentum densities and Compton profiles from ab initio calculations is presented. Reciprocal space is divided into optimally-shaped tetrahedra for interpolation, and the linear tetrahedron method is used to obtain the momentum density and its projections such as Compton profiles. Results are presented and evaluated against experimental data for Be, Cu, Ni, Fe3Pt, and YBa2Cu4O8, demonstrating the accuracy of our method in a wide variety of crystal structures.

Improved tetrahedron method for the Brillouin-zone integration applicable to response functions

We improve the linear tetrahedron method to overcome systematic errors due to overestimations (underestimations) in integrals for convex (concave) functions, respectively. Our method is applicable to various types of calculations such as the total energy, the harge (spin) density, response functions, and the phonon frequency, in contrast with the Bl\"ochl correction, which is applicable to only the first two. We demonstrate the ability of our method by calculating phonons in MgB$_2$ and fcc lithium.

A finite temperature linear tetrahedron method for electronic structure calculations of periodic systems.

A finite-temperature linear tetrahedron method for electronic structure calculations of periodic systems is developed. When compared to widely used simple temperature broadening, the number of k points necessary for accurate integration at finite temperatures is reduced. The utility of the method is demonstrated with benchmark calculations on 1D, 2D, and 3D systems.

An Improvement of the Linear Tetrahedron Method for Compton Profile Calculations

An improvement of the linear tetrahedron method for the Compton profile calculation is proposed. Analytical formulae are given for the two dimensional integration of the Brillouin zone along an arbitrary scattering vector. Consequently, programming code becomes very simple and the calculation time is improvable about 70% faster. Although we examine to the cubic system in this work, this idea can be applied to the other structures similarly.

Magnetic Compton-Profiles of Fe3Pt

Directional magnetic Compton-profiles of simple cubic Fe 3 Pt alloy are calculated by the full potential linearized augmented-plane-wave (FLAPW) method coded in WIEN97 and a linear tetrahedron method for the two dimensional integration. They are compared with experimental ones. Similarly to the situation for the element metals, the theoretical Compton profiles which are based upon independent-particle model (IPM) are a little greater than the experimental ones around the origin of the momentum space.

A Linear Tetrahedron Method of Compton Profiles for Cubic Crystals

A linear tetrahedron method is introduced to calculate directional Compton profiles of valence electrons for cubic crystals. For the two dimensional integration a linear interpolation of both the energy and momentum density is used within each tetrahedron. They cover one 48th of the BZ (Brillouin zone) of each reciprocal vector. The program is linked to the output of FLAPW (full potential linearized augmented-plane-wave) method coded in WIEN97. As an example results for Al are described.

Calculation of optical properties and density of states for systems with huge unit cells

We present a method for the ab initio calculation of spectral properties of systems with huge unit cells. Translationally invariant systems with elementary cells containing several hundred atoms in the unit cell are characterized by a large number of bands in a very small Brillouin zone. This makes the allocation of energies at different $\mathbf{k}$ points to one band impossible. For that reason a quadratic extrapolation of the band energies is performed starting from a single $\mathbf{k}$ point ${\mathbf{k}}_{0}.$ The band energies and momentum operator matrix elements are calculated at ${\mathbf{k}}_{0}$ using the projector augmented wave method. The Brillouin-zone integration is carried out by means of the linear tetrahedron method following a resampling procedure. The viability of the method is demonstrated for nonprimitive large supercells by reproducing the absorption coefficient and the density of states of an ideal crystal. The method is applied to 216- and 512-atom simple-cubic supercells. A germanium cluster embedded in a host material is treated as an example of a perturbed system.

Ab initiocalculation of the reflectance anisotropy of surfaces: The triangle method

We modify the analytic linear tetrahedron method to calculate the optical properties of surfaces. As a test case, the reflectance anisotropy of InP(110) is calculated within the density-functional theory in the local-density approximation. The convergence with respect to the number of k points and the choice of the triangles is extensively discussed. The resulting spectra are interpreted and compared with experimental results.

Ab initiosecond-harmonic susceptibilities of semiconductors: Generalized tetrahedron method and quasiparticle effects

We report numerical calculations of the frequency-dependent second-order optical susceptibility. The results are based on an ab initio treatment of the geometry and the electronic structure within the density-functional theory in local-density approximation. The plane-wave-pseudopotential method is combined with a generalized tetrahedron method to perform the $\mathbf{k}$-space integration. The analytic linear tetrahedron method has to be improved because of the energy-dependent prefactors of the $\ensuremath{\delta}$ functions describing the energy conservation. We also present results for spectra of the second-harmonic generation where many-body quasiparticle effects are included beyond the scissors-operator approximation. Zinc-blende semiconductors are considered as model substances.

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N atoms 2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

Temperature dependence of the transition-metal magnetic susceptibilities.

We present a method for calculating accurate Brillouin zone integrals of the Lindhard function at temperatures other than absolute zero. Within the linear tetrahedron method our expression is exact for the imaginary part and accurate to any arbitrary precision for the real part. We apply our method to calculate the temperature-dependent contribution to the bulk susceptibility for a range of transition metals as a function of temperature using linear muffin-tin orbital (LMTO) bands. For paramagnets our results follow the expected ${\mathit{T}}^{2}$ dependence. However our results for ferromagnets deviate qualitatively from the quadratic law. The different behavior is attributed to interband and matrix element effects. Our results for Fe exhibit two distinct behaviors. We discuss the implications for calculation of anomalies arising from spin fluctuations. \textcopyright{} 1996 The American Physical Society.

An extended tetrahedron method for determining Fourier components of Green functions in solids

The linear tetrahedron method (LTM) is extended in order to deal with a rapidly oscillating term in the integrand. This extension, ELTM, is inspired by the need for accurate values of the Fourier components of Green functions in solids. It is shown that LTM and ELTM have a basic equation in common and that the several versions differ only in the expressions for the weighting factors. The presentation of five versions of (E)LTM is given. The symmetry aspects are dealt with extensively, merely implying the introduction of modified weighting factors. After some examples with test purposes ELTM is applied to Cu. The results demonstrate that ELTM is an efficient way of evaluating the Brillouin zone integrals required.