In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic separation with various decay ranges l examined. We calculate the density of states (DOS) and the Inverse Participation Ratio (IPR) for amorphous atomic configurations in one, two, and three dimensions. With a finite size scaling analysis of the IPR statistical distributions, it is shown that states are either extended or localized for a particular energy, and phase portraits for wave functions are obtained showing extended and localized behavior in the thermodynamic limit. While we conclude that all states are localized in 1D, in the 2D case there is a threshold for l above which some eigenstates appear to be extended and below which wave functions are entirely localized. For 3D geometries, there are two mobility boundaries flanking an intermediate range of energies where states are extended with eigenstates localized for energies above or below this range. While a zone of extended states persists even for very short l, the width of the region tends to zero exponentially (i.e. scaling as exp{-A/l}) for very small decay length scales.
We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the short-range nature of the density matrix to calculate the vibrational density of states which is then compared with the same obtained from a standard O($N^4$) algorithm. For the purpose of illustration, an 1000-atom model is studied to calculate the localization properties of the vibrational eigenstates using the participation numbers calculation.
We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencie…
The structural features of the interface between the cystalline and amorphous phases of Si solid are studied in simulations based on a combination of empirical interatomic potentials and a nonorthogonal tight-binding model. The tight-binding Hamiltonian was created and tested for the types of structures and distortions anticipated to occur at this interface. The simulations indicate the presence of a number of interesting features near the interface. The features that may lead to crystallization upon heating include <110> chains with some defects, most prominently dimers similar to those on th…
Ultra-precision machining of metals, the breaking of nanowires under tensile stress and fracture of nanoscale materials are examples of technologically important processes which are both extremely difficult and costly to investigate experimentally. We describe a multiscale method for the simulation of such systems in which the energetically active region is modelled using a robust tight-binding scheme developed at the Naval Research Laboratory (NRL-TB) and the rest of the system is treated with molecular dynamics. We present a computer code implementing the method, geared towards non-equilibri…
Analytical results for the asymptotic spatial decay of the density matrix $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime})$ in the tight-binding model of the two-dimensional metal are presented. In various dimensions D, it is found analytically and numerically that the density matrix decays with distance according to the power law, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime}) +AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$.
We investigate the band structure of chromium nitride using the $N$th-order muffin-tin orbitals (NMTO) based downfolding technique. We obtain downfolded Cr $d$ bands including both $e_{g}$ and $t_{2g}$ states and the hopping integrals of the tight-binding Cr $d$ bands for both cubic and orthorhombic lattice. We further analyze the chemical bonding and tight-binding parameters from the NMTO produced tight-binding Hamiltonian. The effect of lattice distortion is also discussed according to the downfolded tight-binding parameters.
In this work, transferable empirical tight binding parameters of strained group IV and III-V semiconductors are generated from ab-initio calculations. The empirical tight binding parameters show good transferability when applied to strained bulk materials as well as ultra-thin superlattices.
It is critical to capture the effect due to strain and material interface for device level transistor modeling. We introduced a transferable sp3d5s* tight binding model with nearest neighbor interactions for arbitrarily strained group IV and III-V materials. The tight binding model is parameterized with respect to Hybrid functional(HSE06) calculations for varieties of strained systems. The tight binding calculations of ultra small superlattices formed by group IV and group III-V materials show good agreement with the corresponding HSE06 calculations. The application of tight binding model to s…
We extend a tight-binding method to include the effects of spin-orbit coupling, and apply it to the study of the electronic properties of the actinide elements Th, U, and Pu. These tight-binding parameters are determined for the fcc crystal structure using the equivalent equilibrium volumes. In terms of the single particle energies and the electronic density of states, the overall quality of the tight-binding representation is excellent and of the same quality as without spin-orbit coupling. The values of the optimized tight-binding spin-orbit coupling parameters are comparable to those determ…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of aperiodic tight-binding models and the corresponding level statistics, which are well reproduced by random matrix theory. The eigenstates are characterised by multifractal analysis, and a construction of peculiar multifractal states on the Penrose tiling is discussed. We also consider quantum diffusion, and present some results on interacting electron system…
We present the Tight-Binding Studio (TBStudio) software package for calculating tight-binding Hamiltonian from a set of Bloch energy bands obtained from first principle theories such as density functional theory, Hartree-Fock calculations or Semi-empirical band structure theory. This will be helpful for scientists who are interested in studying the electronic properties of structures using Green's function theory in tight-binding approximation. TBStudio is a cross-platform application written in C++ with a graphical user interface design that is user-friendly and easy to work with. This softwa…
A procedure to obtain single-electron wavefunctions within the tight-binding formalism is proposed. It is based on linear combinations of Slater-type orbitals whose screening coefficients are extracted from the optical matrix elements of the tight-binding Hamiltonian. Bloch functions obtained for zinc-blende semiconductors in the extended-basis spds* tight-binding model demonstrate very good agreement with first-principles wavefunctions. We apply this method to the calculation of electron-hole exchange interaction, and obtain the dispersion of excitonic fine structure of bulk GaAs. Beyond semi…
We have analyzed the atomic rearrangements underlying self-diffusion in amorphous Si during annealing using tight-binding molecular dynamics simulations. Two types of amorphous samples with different structural features were used to analyze the influence of coordination defects. We have identified several types of atomic rearrangement mechanisms, and we have obtained an effective migration energy of around 1 eV. We found similar migration energies for both types of samples, but higher diffusivities in the one with a higher initial percentage of coordination defects.
We present a comparative ab initio computational study of sodium and lithium storage in amorphous (glassy) carbon (a-C) vs. graphite. Amorphous structures are obtained by fitting stochastically generated structures to a reference radial distribution function. Li insertion is thermodynamically favored in both graphite and a-C. While sodium insertion is thermodynamically unfavored in graphite, a-C possesses multiple insertion sites with binding energies stronger than Na cohesive energy, making it usable as anode material for Na-ion batteries.
We describe how we have used tight binding calculations as a quick, efficient tool to search for possible structures of Bi nanolines on Si(001). After identifying promising candidate structures, we have concentrated on these with \textit{ab initio} electronic structure techniques. The energetics of the tight binding are shown to be in good agreement with the density functional calculations and with experimental observations, and have proved invaluable in the search for a structure, validating the use of tightbinding as a search tool.
Tight-binding molecular dynamics simulations shed light into the fracture mechanisms and the ideal strength of tetrahedral amorphous carbon and of nanocomposite carbon containing diamond crystallites, two of the hardest materials. It is found that fracture in the nanocomposites, under tensile or shear load, occurs inter-grain and so their ideal strength is similar to the pure amorphous phase. The onset of fracture takes place at weakly bonded sp^3 sites in the amorphous matrix. On the other hand, the nanodiamond inclusions significantly enhance the elastic moduli, which approach those of diamo…
We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and transferable for f-electron systems as they are for d-electron systems. In both cases we have found it essential to take great care in constraining the fitting procedure by using a block-diagonalization procedure, which we describe in detail.
Projection of Bloch states obtained from quantum-mechanical calculations onto atomic orbitals is the fastest scheme to construct ab-initio tight-binding Hamiltonian matrices. However, the presence of spurious states and unphysical hybridizations of the tight-binding eigenstates has hindered the applicability of this construction. Here we demonstrate that those spurious effects are due to the inclusion of Bloch states with low projectability. The mechanism for the formation of those effects is derived analytically. We present an improved scheme for the removal of the spurious states which resul…
The formal link between the linear combination of atomic orbitals approach to density functional theory and two-center Slater-Koster tight-binding models is used to derive an orthogonal $d$-band tight-binding model for iron with only two fitting parameters. The resulting tight-binding model correctly predicts the energetic ordering of the low energy iron-phases, including the ferromagnetic BCC, antiferromagnetic FCC, HCP and topologically close-packed structures. The energetics of test structures that were not included in the fit are equally well reproduced as those included, thus demonstratin…
For a previously published study of the titanium hcp (alpha) to omega (omega) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wavefuctions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional c…
We have performed Linearized Augmented Plane Wave (LAPW) calculations for five crystal structures (alpha, dhcp, sc, fcc, bcc) of Boron which we then fitted to a non-orthogonal tight-binding model following the Naval Research Laboratory Tight-Binding (NRL-TB) method. The predictions of the NRL-TB approach for complicated Boron structures such as R105 (or \b{eta}-rhombohedral) and T190 are in agreement with recent first-principles calculations. Fully utilizing the computational speed of the NRL-TB method we calculated the energetic differences of various structures including those containing vac…
We refit the NRL tight binding parameterization for Aluminium by Mehl \emph{et al} [Phys. Rev. B, 61, 4894 (2000)], to a database generated via full potential Linearized Augmented Plane Wave (LAPW) Density Functional Theory (DFT) calculations. This is performed using a global optimization algorithm paying particular attention to reproducing the correct order of the angular symmetries of the tight binding fcc and bcc bandstructure. The resulting parameterization is found to better predict the hcp phase and both the stable and unstable planar stacking fault defect energies.
We present a first-principles and tight-binding model study of silicane and germanane, the hydrogenated derivatives of two-dimensional silicene and germanene. We find that the materials are stable in freestanding form, analyse the orbital composition, and derive a tight-binding model using first-principles calculations to fit the parameters.
The AB s-valent dimer is used to analyse bond formation and charge transfer within the tight-binding (TB) approximation. In this way a physical interpretation of the electronic structure and binding energy within density functional theory (DFT) is obtained which lends itself to the derivation of covalent and ionic interatomic potentials.
Maximally localized Wannier functions are localized orthogonal functions that can accurately represent given Bloch eigenstates of a periodic system at a low computational cost, thanks to the small size of each orbital. Tight-binding models based on the maximally localized Wannier functions obtained from different systems are often combined to construct tight-binding models for large systems such as a semi-infinite surface. However, the corresponding maximally localized Wannier functions in the overlapping region of different systems are not identical, and this discrepancy can introduce serious…
A generalization of the density-functional based tight-binding method (DFTB) for the use with range-separated exchange-correlation functionals is presented. It is based on the Generalized Kohn-Sham (GKS) formalism and employs the density matrix as basic variable in the expansion of the energy functional, in contrast to the traditional DFTB scheme. The GKS-TB equations are derived and appropriate integral approximations are discussed in detail. Implementation issues and numerical aspects of the new scheme are also covered.
We have examined a method of direct extraction of accurate tight-binding parameters from an ab-initio band-structure calculation. The linear muffin-tin potential method, in its full-potential implementation, has been used to provide the hamiltonian and overlap matrix elements in the momentum space. These matrix elements are Fourier transformed to real space to produce the tight-binding parameters. The feasibility of this method has been tested on the intermetallic alloy NiAl, using spd orbitals for each atom. The parameters generated for this alloy have been used as input to a real-space calcu…
Semiconducting transition metal dichalcogenides present a complex electronic band structure with a rich orbital contribution to their valence and conduction bands. The possibility to consider the electronic states from a tight-binding model is highly useful for the calculation of many physical properties, for which first principle calculations are more demanding in computational terms when having a large number of atoms. Here, we present a set of Slater-Koster parameters for a tight-binding model that accurately reproduce the structure and the orbital character of the valence and conduction ba…
In this paper we present a paradigmatic tight-binding model for single-layer as well as for multi-layered semiconducting MoS$_2$ and similar transition metal dichalcogenides. We show that the electronic properties of multilayer systems can be reproduced in terms of a tight-binding modelling of the single-layer hopping terms by simply adding the proper interlayer hoppings ruled by the chalcogenide atoms. We show that such tight-binding model permits to understand and control in a natural way the transition between a direct-gap band structure, in single-layer systems, to an indirect gap in multi…
A tight-binding model is fit to first-principles calculations for copper that include structures distorted according to elastic constants and high-symmetry phonon modes. With the resulting model the first-principles-based phonon dispersion and the free energy are calculated in the quasi-harmonic approximation. The resulting thermal expansion, the temperature- and volume-dependence of the elastic constants, the Debye temperature, and the Gruneisen parameter are compared with available experimental data.
CdSe nanoplatelets show perfectly quantized thicknesses of few monolayers. They present a situation of extreme, yet well defined quantum confinement. Due to large dielectric contrast between the semiconductor and its ligand environment, interaction between carriers and their dielectric images strongly renormalize bare single particle states. We discuss the electronic properties of this original system in an advanced tight-binding model, and show that Coulomb interactions, including self-energy corrections and enhanced electron-hole interaction, lead to exciton binding energies up to several hu…
We computed by a modified tight binding approximation, the total electronic energy of three different hybrid polymers: $H-SiO_2$, $CH_3-SiO_2$ and $C_6H_5-SiO_2$. We made the hypothesis that the structures of these polymers are amorphous. Computational results regarding the total electronic energy and experimental data \cite{ferchichi} on the toughness of these three hybrid polymers were compared. A good qualitative agreement was found between computations and experiments.
The role of local fields in the optical response of silicon nanocrystals is analyzed using a tight binding approach. Our calculations show that, at variance with bulk silicon, local field effects dramatically modify the silicon nanocrystal optical response. An explanation is given in terms of surface electronic polarization and confirmed by the fair agreement between the tight binding results and that of a classical dielectric model. From such a comparison, it emerges that the classical model works not only for large but also for very small nanocrystals. Moreover, the dependence on size of the…
A new tight-binding total energy method, which has been shown to accurately predict ground state properties of transition and noble metals, is applied to Manganese, the element with the most complex ground state structure among the $d$ metals. We show that the tight-binding method correctly predicts the ground state structure of Mn, and offers some insight into the magnetic properties of this state.
We investigate the effect of orbital overlap on optical matrix elements in empirical tight-binding models. Empirical tight-binding models assume an orthogonal basis of (atomiclike) states and a diagonal coordinate operator which neglects the intra-atomic part. It is shown that, starting with an atomic basis which is not orthogonal, the orthogonalization process induces intra-atomic matrix elements of the coordinate operator and extends the range of the effective Hamiltonian. We analyze simple tight-binding models and show that non-orthogonality plays an important role in optical matrix element…
The Landauer-Buettiker formalism combined with the tight-binding transfer matrix method is used to describe the results of recent experiments: the high tunneling magnetoresistance (TMR) in (Ga,Mn)As-based trilayers and highly polarized spin injection in p-(Ga,Mn)As/n-GaAs Zener diode. For both TMR and Zener spin current polarization, the calculated values agree well with those observed experimentally. The role played in the spin dependent tunneling by carrier concentration and magnetic ion content is also studied.
We calculate the transverse effective charges of zincblende compound semiconductors using Harrison's tight-binding model to describe the electronic structure. Our results, which are essentially exact within the model, are found to be in much better agreement with experiment than previous perturbation-theory estimates. Efforts to improve the results by using more sophisticated variants of the tight-binding model were actually less successful. The results underline the importance of including quantities that are sensitive to the electronic wavefunctions, such as the effective charges, in the fit…
A dynamics of the precession of coupled atomic moments in the tight-binding (TB) approximation is presented. By implementing an angular penalty functional in the energy that captures the magnetic effective fields self-consistently, the motion of the orientation of the local magnetic moments is observed faster than the variation of their magnitudes. This allows the computation of the effective atomic magnetic fields that are found consistent with the Heisenberg's exchange interaction, by comparison with classical atomistic spin dynamics on Fe, Co and Ni magnetic clusters.
An application of the tight binding approximation is presented for the description of electronic structure and interatomic force in magnetic iron, both pure and containing hydrogen impurities. We assess the simple canonical d-band description in comparison to a non orthogonal model including s and d bands. The transferability of our models is tested against known properties including the segregation energies of hydrogen to vacancies and to surfaces of iron. In many cases agreement is remarkably good, opening up the way to quantum mechanical atomistic simulation of the effects of hydrogen on me…
Using density-functional theory and a tight-binding approach we investigate the physical origin of distinct favourable geometries of adsorbed hydrogen atoms in various graphyne structures, and the relation with electronic properties. In particular, H atoms are adsorbed in-plane for $α$-graphyne, and they assume an oblique configuration in all other graphynes, including 6,6,12-graphyne. The origin of different configurations is identified by means of a simple tight-binding model and it is controlled by the tuning of the hopping between sp$^2$-bonded C atoms and sp-bonded C atoms hybridized with…
We demonstrate for the first time a tight binding model for water incorporating polarizable anions. A novel aspect is that we adopt a "ground up" approach in that properties of the monomer and dimer only are fitted. Subsequently we make predictions of the structure and properties of hexamer clusters, ice-XI and liquid water. A particular feature, missing in current tight binding and semiempirical hamiltonians, is that we reproduce the almost two-fold increase in molecular dipole moment as clusters are built up towards the limit of bulk liquid. We concentrate on properties of liquid water which…
We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the completeness of the basis set of atomic orbitals, we are able to optimize the quality of the band structure interpolation over wide energy ranges including unoccupied states. This methodology is applied to the case of interlayer and image states, which appear several eV above the Fermi level in materials with large interstitial regions or surfaces such as graphite an…
We present a tight-binding potential for transition metals, carbon, and transition metal carbides, which has been optimized through a systematic fitting procedure. A minimal basis, including the s, p electrons of carbon and the d electrons of the transition metal, is used to obtain a transferable tight-binding model of the carbon-carbon, metal-metal and metal-carbon interactions applicable to binary systems. The Ni-C system is more specifically discussed. The successful validation of the potential for different atomic configurations indicates a good transferability of the model and makes it a …
We present a Mathematica program package MagneticTB, which can generate the tight-binding model for arbitrary magnetic space group. The only input parameters in MagneticTB are the (magnetic) space group number and the orbital information in each Wyckoff positions. Some useful functions including getting the matrix expression for symmetry operators, manipulating the energy band structure by parameters and interfacing with other software are also developed. MagneticTB can help to investigate the physical properties in both magnetic and non-magnetic system, especially for topological properties.
Tight-binding (TB) molecular dynamics (MD) has emerged as a powerful method for investigating the atomic-scale structure of materials --- in particular the interplay between structural and electronic properties --- bridging the gap between empirical methods which, while fast and efficient, lack transferability, and ab initio approaches which, because of excessive computational workload, suffer from limitations in size and run times. In this short review article, we examine several recent applications of TBMD in the area of defects in covalently-bonded semiconductors and the amorphous phases of…
We propose that we can realize "tight-binding photonic bands" in metallophotonic waveguide networks, where the photonic bound states localized around the crossings of a network form a tight-binding band. The formation of bound states at the crossings is distinct from the conventional bound states at defects or virtual bound states in photonic crystals, but comes from a photonic counterpart of the zero-point states in wave mechanics. Model calculations show that the low-lying photon dispersions are indeed described accurately by the tight-binding model. To exemplify how we can exploit the tight…
A simulated annealing (SA) approach is employed in the determination of different tight binding (TB) sets of parameters for the nitride semiconductors AlN, GaN and InN, as well their limitations and potentialities are also discussed. Two kinds of atomic basis set are considered: (\textit{i}) the orthogonal $sp^3s*$ with interaction up to second neighbors and (\textit{ii}) a $spd$ non-orthogonal set, with the Hamiltonian matrix elements calculated within the Extended Hückel Theory (EHT) prescriptions. For the non-orthogonal method, TB parameters are given for both zincblend and wurtzite crystal…
This article is a pedagogical introduction to density-functional tight-binding (DFTB) method. We derive it from the density-functional theory, give the details behind the tight-binding formalism, and give practical recipes for parametrization: how to calculate pseudo-atomic orbitals and matrix elements, and especially how to systematically fit the short-range repulsions. Our scope is neither to provide a historical review nor to make performance comparisons, but to give beginner's guide for this approximate, but in many ways invaluable, electronic structure simulation method--now freely availa…
The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We firstly study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tight-binding approximation. We prove that the cor…
Localized interface states in abrupt semiconductor heterojunctions are studied within a tight-binding model. The intention is to provide a microscopic foundation for the results of similar studies which were based upon the two-band model within the envelope function approximation. In a two-dimensional description, the tight-binding Hamiltonian is constructed such that the Dirac-like bulk spectrum of the two-band model is recovered in the continuum limit. Localized states in heterojunctions are shown to occur under conditions equivalent to those of the two-band model. In particular, shallow int…
In this article we have reproduced the tight binding $π$ band dispersion of graphene including upto third nearest neighbours and also calculated the partial density of states (due to $π$ band only) within the same model. The aim was to find out a set of parameters descending in order as distance towards third nearest neighbour increases compared to that of first and second nearest neighbours with respect to an atom at the origin. Here we have talked about two such sets of parameters by comparing the results with first principle band structure calculation.
It is shown that the current-perpendicular-to-plane giant magneto-resistance (CPP-GMR) oscillations, in the ballistic regime, are strongly correlated with those of the exchange coupling (J). Both the GMR and J are treated on equal footing within a rigorously solvable tight-binding single-band model. The strong correlation consists in sharing asymptotically the same period, determined by the spacer Fermi surface, and oscillating with varying spacer thickness predominantly in opposite phases.
