Orthogonal Tight-binding Model Research Articles

Tight-binding bond parameters for dimers across the periodic table from density-functional theory

We obtain parameters for nonorthogonal and orthogonal tight-binding (TB) models from two-atomic molecules for all combinations of elements of period 1 to 6 and group 3 to 18 of the periodic table. The TB bond parameters for 1711 homoatomic and heteroatomic dimers show clear chemical trends. In particular, using our parameters we compare to the rectangular $d$-band model, the reduced $sp$ TB model, as well as canonical TB models for $sp$- and $d$-valent systems, which have long been used to gain qualitative insight into the interatomic bond. The transferability of our dimer-based TB bond parameters to bulk systems is discussed exemplarily for the bulk ground-state structures of Mo and Si. Our dimer-based TB bond parameters provide a well-defined and promising starting point for developing refined TB parametrizations and for making the insight of TB available for guiding materials design across the periodic table.

Comparative study of the electron–electron interactions on optoelectronic properties of carbon nanotube within orthogonal and nonorthogonal tight-binding model

We investigate the electron–electron (e–e) interactions effect on the optoelectronic properties of single-walled carbon nanotubes (SWCNTs). We study theoretically the effect of e–e interactions on the optoelectronic properties of zigzag carbon nanotubes and obtain some useful expressions for the band structure and optical absorption of nanotubes for the first nearest-neighbor (1NN) and second nearest-neighbor (2NN) approximation in tight-binding (TB) model. Our computational approach is based on combination of the orthogonal (o-TB) and nonorthogonal (n-TB) tight-binding method with Hubbard model for zigzag SWCNTs. In nonorthogonal tight-binding model we consider the effect of orbital overlap on optoelectronic properties of nanotubes. We also obtain the optical absorption spectrum of zigzag SWCNTs under e–e interactions effect with considering orthogonal and nonorthogonal tight-binding method for 1NN and 2NN approximation. We investigate optical absorption for the incident light polarized parallel to the tube axis and obtain all allowed optical transitions. Our results show some variations in the band structure and optical absorption spectrum of nanotubes under e–e interactions effect when we use orthogonal tight-binding model compare with nonorthogonal tight-binding model.

Multilayer phosphorene quantum dots in an electric field: Energy levels and optical absorption

Triangular and hexagonal multilayer phosphorene quantum dots with armchair and zigzag terminations are investigated with the orthogonal tight-binding model. The effect of increasing the number of layers is revealed. The obtained results show that in a small size multilayer quantum dot, the edge states are as sensitive to the out-of-plane external electric fields as the edge states in a single layer dot to the in-plane external electric fields. The investigated optical absorption cross sections show that armchair phosphorene quantum dots have a regular behavior which should be useful for infrared detectors. In particular, it was found that in hexagonal armchair phosphorene dots, absorption peaks can be increased, decreased, or totally removed from the low-energy region depending on the orientation of the applied electric field. The effect of spurious doping can suppress the transitions <0.4 eV, while the effect of the finite temperature is almost negligible.

Optoelectronic properties of silicon nanotubes with electron–electron interactions in orthogonal tight-binding model

We investigate the electron–electron (e–e) interactions effect on the optoelectronic properties of zigzag silicon hexagonal nanotubes (Si h-NTs). Analytic expressions for the band structure and optical absorption of Si h-NTs have been derived based on orthogonal tight-binding (OTB) method. We combine OTB method and Hubbard model and show electron–electron interactions effect on the band structure of metallic and semiconducting zigzag nanotubes for the first and second-nearest neighbor. Moreover, the optical matrix elements and optical absorption are analytically derived for light polarization parallel to the tube axis in low energy for first nearest-neighbor (1NN) and second nearest-neighbor (2NN) approximation. It is found that the electron–electron interactions do not modify the optical absorption spectrum of zigzag Si h-NTs. These results can be beneficial for the explanation of resonant Raman Spectra of nanotube samples.

Hidden correlation between absorption peaks in achiral carbon nanotubes and nanoribbons

In this paper we study the effect of absorption peak correlation in finite length carbon nanotubes and graphene nanoribbons. It is shown, in the orthogonal π-orbital tight-binding model with the nearest neighbor approximation, that if the ribbon width is a half of the tube circumference the effect takes place for all achiral ribbons (zigzag, armchair and bearded), and corresponding tubes, starting from lengths of about 30 nm. This correlation should be useful in designing nanoribbon-based optoelectronics devices fully integrated into a single layer of graphene.

Grain boundaries in bcc-Fe: a density-functional theory and tight-binding study

Grain boundaries (GBs) have a significant influence on material properties. In the present paper, we calculate the energies of eleven low-Σ () symmetrical tilt GBs and two twist GBs in ferromagnetic bcc iron using first-principles density functional theory (DFT) calculations. The results demonstrate the importance of a sufficient sampling of initial rigid body translations in all three directions. We show that the relative GB energies can be explained by the miscoordination of atoms at the GB region. While the main features of the studied GB structures were captured by previous empirical interatomic potential calculations, it is shown that the absolute values of GB energies calculated were substantially underestimated. Based on DFT-calculated GB structures and energies, we construct a new d-band orthogonal tight-binding (TB) model for bcc iron. The TB model is validated by its predictive power on all the studied GBs. We apply the TB model to block boundaries in lath martensite and demonstrate that the experimentally observed GB character distribution can be explained from the viewpoint of interface energy.

Publisher's Note: Orthogonal tight-binding model for the thermal conductivity of Si [Phys. Rev. B93, 155203 (2016)

Publisher's Note: Orthogonal tight-binding model for the thermal conductivity of Si [Phys. Rev. B<b>93</b>, 155203 (2016)

Orthogonal tight-binding model for the thermal conductivity of Si

Predictive modeling of the thermal conductivity of nanostructures remains a large challenge. Ab initio studies rely on parametrized models of scattering rates of the nanostructure elements. Simplified interatomic potentials, on the other hand, often fail in the quantitative prediction of thermal conductivity. We have developed a simple and short-ranged orthogonal tight-binding model for the thermal properties of Si. We systematically introduce separate handles to tune the value and slope of the potential energy with respect to interatomic distance. Furthermore, we add an embedding potential in our model to capture the correct structural stability trend in Si. The model shows excellent transferability to the thermal properties of diamond Si along with good reproduction of the relative stabilities of different structures. We demonstrate the improvement over earlier tight-binding models and contrast the transferability of our model with simple interatomic potentials.

Structural features and thermal properties of W/Cu compounds using tight-binding potential calculations

We present an orthogonal tight-binding (TB) potential model for W/Cu binary systems. This model can reasonably predict the electronic structures, elastic properties, and thermodynamics properties of W/Cu systems. Furthermore, by performing the TB Monte Carlo simulations and the TB molecular dynamics simulations, we find that (1) the W(110) surface in the fusion reactor exhibits pre-melting behaviors, (2) W and Cu atoms in a W/Cu binary system prefer to form single element domains, and (3) the interface between a W domain and a Cu domain degrades the transport property of the heat in a W/Cu system significantly.

Competition between crystal-field, overlap, and three-center contributions inHNeigenspectra

The environment dependence of the on-site energy levels and intersite bond integrals within an orthogonal tight-binding (OTB) model for $s$-valent systems is determined by the competition between the attractive crystal-field and three-center terms and the repulsive overlap contribution. This is demonstrated explicitly for the case of symmetric ${\mathrm{H}}_{N}$ clusters, where the OTB parameters can be expressed analytically in terms of the nonorthogonal tight-binding (NOTB) on-site, intersite, and overlap matrix elements. The values of the OTB parameters are obtained directly from the density-functional theory eigenspectra of the ${\mathrm{H}}_{N}$ clusters with the on-site energy levels being found to be very sensitive to the local atomic environment but the intersite bond integrals much less so. This different behavior is shown to result from the large cancellations between the crystal-field, overlap, and three-center contributions. The common first-order expression for the OTB on-site energy level as the sum of the NOTB crystal field and a two-body overlap repulsion is found to be a poor approximation due to the sizable values of the overlap in these ${\mathrm{H}}_{N}$ clusters around equilibrium.

Convergence of an analytic bond-order potential for collinear magnetism in Fe

Analytic bond-order potentials (BOPs) for magnetic transition metals are applied for pure iron as described by an orthogonal d-valent tight-binding (TB) model. Explicit analytic equations for the gradients of the binding energy with respect to the Hamiltonian on-site levels are presented, and are then used to minimize the energy with respect to the magnetic moments, which is equivalent to a TB self-consistency scheme. These gradients are also used to calculate the exact forces, consistent with the energy, necessary for efficient relaxations and molecular dynamics. The Jackson kernel is used to remove unphysical negative densities of states, and approximations for the asymptotic recursion coefficients are examined. BOP, TB and density functional theory results are compared for a range of bulk and defect magnetic structures. The BOP energies and magnetic moments for bulk structures are shown to converge with increasing numbers of moments, with nine moments sufficient for a quantitative comparison of structural energy differences. The formation energies of simple defects such as the monovacancies and divacancies also converge rapidly. Other physical quantities, such as the position of the high-spin to low-spin transition in ferromagnetic fcc (face centred cubic) iron, surface peaks in the local density of states, the elastic constants and the formation energies of the self-interstitial atom defects, require higher moments for convergence.

Parameterized electronic description of carbon cohesion in iron grain boundaries

We employ a recently developed iron–carbon orthogonal tight-binding model in calculations of carbon in iron grain boundaries. We use the model to evaluate the properties of carbon near and on the Σ5 (3 1 0)[0 0 1] symmetric tilt grain boundary (GB) in iron, and calculations show that a carbon atom lowers the GB energy by 0.29 eV/atom in accordance with DFT. Carbon segregation to the GB is analyzed, and we find an energy barrier of 0.92 eV for carbon to segregate to the carbon-free interface while segregation to a fully filled interface is disfavored. Local volume (via Voronoi tessellation), magnetic, and electronic effects are correlated with atomic energy changes, and we isolate two different mechanisms governing carbon's behavior in iron: a volumetric strain which increases the energy of carbon in interstitial α iron and a non-strained local bonding which stabilizes carbon at the GB.

LESSONS OF NANOELECTRONICS: NON-EQUILLIBRIUM GREEN’S FUNCTIONS METHOD IN MATRIX REPRESENTATION. II. MODEL TRANSPORT PROBLEMS

Non-equilibrium Green’s functions method in matrix form is applied to model transport problems for 1D and 2D conductors using a nearest neighbor orthogonal tight-binding model in the frame of the «bottom – up» approach of modern nanoelectronics. General method to account the electric contacts in Schrödinger equation within solving of electron quantum transport problems is presented

Development of orthogonal tight-binding models for Ti-C and Ti-N systems

We develop $p$-$d$ orthogonal tight-binding (OTB) models for the description of TiC${}_{x}$ and TiN${}_{x}$ compounds in the $1.0&gt;x&gt;0.5$ composition range. For the parametrization of bond integrals we use a recently developed method allowing projection of the one-electron wave functions obtained within the density functional theory onto optimized atom-centered orbitals. The performance of the OTB models is investigated for a wide range of properties: binding energy of elements and compounds, density of states, formation energy of vacancy-ordered defects, elastic constants, and phonon dispersions. The models provide a good description of the ground state properties at 1:1 composition and show a fair transferability for various atomic environments in elemental and binary phases.

Transferability of Orthogonal and Nonorthogonal Tight-Binding Models for Aluminum Clusters and Nanoparticles.

Several semiempirical tight-binding models are parametrized and tested for aluminum clusters and nanoparticles using a data set of 808 accurate AlN (N = 2-177) energies and geometries. The effects of including overlap when solving the secular equation and of incorporating many-body (i.e., nonpairwise) terms in the repulsion and electronic matrix elements are studied. Pairwise orthogonal tight-binding (TB) models are found to be more accurate and their parametrizations more transferable (for particles of different sizes) than both pairwise and many-body nonorthogonal tight-binding models. Many-body terms do not significantly improve the accuracy or transferability of orthogonal TB, whereas some improvement in the nonorthogonal models is observed when many-body terms are included in the electronic Hamiltonian matrix elements.

Analytic approach to the linear susceptibility of zigzag carbon nanotubes

A general analytical expression for the linear optical susceptibility of single walled zigzag carbon nanotubes for light polarized parallel to the nanotube axis has been obtained. Using a simple orthogonal tight binding model with nearest neighbor interactions, the electric dipole matrix element and subsequently the susceptibility as a function of optical frequency, have been investigated. For light polarized perpendicular to the nanotube axis, no analytic solution for the susceptibility has been found. However, a closed-form expression for the electric dipole matrix element has been obtained. Hence, numerical evaluation of the perpendicular susceptibility is greatly simplified.

Extended Hückel theory for band structure, chemistry, and transport. II. Silicon

In this second paper, we develop transferable semiempirical extended Hückel theoretical (EHT) parameters for the electronic structure of another technologically important material, namely, silicon. The EHT parameters are optimized to experimental target values of the band dispersion of bulk silicon. We quantitatively benchmark our parameters to bulk electronic properties such as band edge energies and locations, effective masses, and spin-orbit coupling parameters, competitive with a nearest-neighbor sp3d5s* orthogonal tight-binding model for silicon of T. Boykin et al. [Phys. Rev. B 69, 115201 (2004)] that has been widely used to model silicon-based devices (see, e.g., A. Rahman et al. [Jpn. J. Appl. Phys. Part I 44, 2187 (2005)] and J. Wang et al. [Appl. Phys. Lett. 86, 093113 (2005)]). The transferability of the parameters is checked for multiple physical and chemical configurations, specifically, two different reconstructed surfaces, Si(100)-(2×1) and Si(111)-(2×1). The robustness of the parameters to different environments is demonstrated by comparing the surface band structures with density functional theory GW calculations and photoemission/inverse photoemission experiments. We further apply the approach to calculate the one-dimensional band dispersion of an unrelaxed rectangular silicon nanowire and explore the chemistry of surface passivation by hydrogen. Our EHT parameters thus provide a quantitative model of bulk silicon and silicon-based interfaces such as contacts and reconstructed surfaces, which are essential ingredients towards a quantitative quantum transport simulation through silicon-based heterostructures.

Tight-binding modeling of thermoelectric properties of bismuth telluride

A parameterized orthogonal tight-binding model with sp3d5s* orbitals, nearest-neighbor interactions, and spin-orbit coupling is developed for bismuth telluride (Bi2Te3) and used to study its thermoelectric properties. Thermoelectric transport coefficients and figures of merit for n-doped and p-doped Bi2Te3 are calculated by solving Boltzmann’s transport equation within the constant-relaxation-time approximation. The dependence of the computed thermoelectric figure of merit on the electrical conductivity is in good agreement with experiment. The parameterized tight-binding model serves as a basis for studies of confined Bi2Te3 systems in search of enhanced thermoelectric properties.

Universal tight-binding model for transition metals: from bulk to cluster

A universal orthogonal tight-binding (TB) model is developed for transition metals, withspecial emphasis on spin-polarized self-consistent calculations. The parameters of the TBmodel are directly obtained from the ab initio bulk calculations within the linear muffin-tinorbital atomic sphere approximation method, without any fitting. With the environmentaldependence of the Hamiltonian included in the localized structure constants, the TB modelcan be reliably applied to various situations, from periodic bulk structures to smallclusters, for both pure metals and alloys. We have tested the model in spin-polarizedcalculations against ab initio results for small computational cell systems, andapplied the model to study the spin and orbital magnetism of some large clusters.

Comparative study of the optical properties of single-walled carbon nanotubes within orthogonal and nonorthogonal tight-binding models

The dielectric response function of single-walled carbon nanotubes is calculated within tight-binding models with different levels of complexity. First, the effects of the orbital basis set of the model, the orbitals overlap, and the structural optimization on the electronic band structure and the dielectric function of three small-radius nanotubes are investigated in detail. Second, the optical transition energies for a large number of nanotubes are derived from the peak positions of the imaginary part of the dielectric function for parallel and perpendicular light polarization. These results can be useful for the assignment of absorption spectra of nanotube samples and for the determination of the conditions for resonant Raman scattering from nanotubes. The obtained results are compared to recent spectrofluorimetric data on isolated single-walled carbon nanotubes.