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.
Using density functional theory calculations, we show that the binding strength of a graphene monolayer on Pd(111) can vary between physisorption and chemisorption depending on its orientation. By studying the interfacial charge transfer, we have identified a specific four-atom carbon cluster that is responsible for the local bonding of graphene to Pd(111). The areal density of such clusters varies with the in-plane orientation of graphene, causing the binding energy to change accordingly. Similar investigations can also apply to other metal substrates, and suggests that physical, chemical, an…
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…
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…
We propose a generalized Peierls substitution method in conjunction with the tight-binding model to explore the magnetic quantization and quantum Hall effect in twisted multilayer graphene under a magnetic field. The Bloch-basis tight-binding Hamiltonian is constructed for large twist angle while a simplified tight-binding model is employed for the magic angle. We investigate extensively the band structures, Landau levels (LLs), and quantum Hall conductivity (QHC) of twisted bilayer graphene and twisted double bilayer graphene, as well as their dependence on the twist angle. Comparison between…
We present a tight-binding parametrization for penta-graphene that correctly describes its electronic band structure and linear optical response. The set of parameters is validated by comparing to ab-initio density functional theory calculations for single-layer penta-graphene, showing a very good global agreement. We apply this parameterization to penta-graphene nanoribbons, achieving an adequate description of quantum-size effects. Additionally, a symmetry-based analysis of the energy band structure and the optical transitions involved in the absorption spectra is introduced, allowing for th…
We used the binding energy-bond-charge model to study the atomic bonding and electrical properties of the two-dimensional graphene/BN van der Waals heterostructure. We manipulated its atomic bonding and electrical properties by manufacturing defects. We discovered that this process yielded a band structure with a flat band, i.e., a horizontal band structure without dispersion at the Fermi level. Thus, our research is significant because it is the first report on this flat band of defect graphene/BN van der Waals heterostructures.
We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA- and AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9) meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calcu…
We present density functional theory calculations of the binding energies of one, two and three fluorine adatoms on the same side of monolayer graphene. We show that fluorine dimers on graphene in a spin-singlet state are stable against dissociation into isolated fluorine adatoms, suggesting that there is a tendency for fluorine adatoms on a single side of graphene to cluster. Our results suggest that fluorination develops by successive bonding of fluorine atoms to neighbouring carbon atoms on different sublattices, while the spins are arranged to reduce the total magnetisation of the ground s…
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.
The adsorption of an alkali-metal submonolayer on graphene occupying every third hexagon of the honeycomb lattice in a commensurate $(\sqrt{3}\times\sqrt{3})R30^\circ$ arrangement induces an energy gap in the spectrum of graphene. To exemplify this type of band gap, we present \textit{ab initio} density functional theory calculations of the electronic band structure of C$_6$Li. An examination of the lattice geometry of the compound system shows the possibility that the nearest-neighbor hopping amplitudes have alternating values constructed in a Kekulé-type structure. The band structure of the …
The interaction between graphene and copper (111) surface have been investigated using the molecular dynamics simulations. We have shown that it is possible to fit Lennard-Jones potential leading to the correct values of the binding energy and the binding distance and, at the same time, yielding experimentally observed Moiré superstructures. The dependencies of the binding energy, the binding distance and the graphene thickness on the parameters of the potential and the rotational angle are presented.
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…
Free standing silicene is predicted to display comparable electronic properties as graphene. However, the yet synthesized silicene-like structures have been only realized on different substrates which turned out to exhibit versatile crystallographic structures that are very different from the theoretically predicted buckled phase of freestanding silicene. This calls for a different approach where silicene is stabilized using very weakly interacting surfaces. We propose here a novel route by using graphene bilayer as a scaffold. The confinement between the flat graphene layers results in a plan…
We have investigated the effect of imperfect circular polarization on the angle-resolved photoemission spectroscopy signal, using graphene as a prototypical system that can be understood within tight-binding formalism. We found that perfect left- and right-circularly polarized lights give the same photoelectron intensity distribution around a constant energy contour of the graphene $π$ band. On the other hand, upon breaking the purity of the polarization, photoelectron intensity starts to show circular dichroism, which is enhanced with further increasing the imperfection. Our results predict t…
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…
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…
We have investigated ozone adsorption on graphene using the ab initio density functional theory method. Ozone molecules adsorb on graphene basal plane with binding energy of 0.25 eV, and the physisorbed molecule can chemically react with graphene to form an epoxide group and an oxygen molecule. The activation energy barrier from physisorption to chemisorption is 0.72 eV, and the chemisorbed state has the binding energy of 0.33 eV. These binding energies and energy barrier indicate that the ozone adsorption on graphene is gentle and reversible. Atomic layer deposition experiment on ozone treate…
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…
The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localised Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalised and hydroxylated gra…
Using micro-Raman spectroscopy and scanning tunneling microscopy, we study the relationship between structural distortion and electrical hole doping of graphene on a silicon dioxide substrate. The observed upshift of the Raman G band represents charge doping and not compressive strain. Two independent factors control the doping: (1) the degree of graphene coupling to the substrate, and (2) exposure to oxygen and moisture. Thermal annealing induces a pronounced structural distortion due to close coupling to SiO2 and activates the ability of diatomic oxygen to accept charge from graphene. Gas fl…
In this work we argue that it is important to make a proper choice of the unit cell within tight-binding theory if one aims to compute the optical matrix elements. By considering zigzag graphene nanoribbons, we demonstrate that the band structure is insensitive to the choice of the unit cell. However, if the chosen unit cell does not incorporate the symmetries of the system, wrong values of optical matrix elements are obtained, leading to the violation of well-known selection rules. This result holds irrespective of the formalism utilized for calculating the optical matrix elements.
A universal set of third--nearest neighbour tight--binding (TB) parameters is presented for calculation of the quasiparticle (QP) dispersion of $N$ stacked $sp^2$ graphene layers ($N=1... \infty$) with $AB$ stacking sequence. The QP bands are strongly renormalized by electron--electron interactions which results in a 20% increase of the nearest neighbour in--plane and out--of--plane TB parameters when compared to band structure from density functional theory. With the new set of TB parameters we determine the Fermi surface and evaluate exciton energies, charge carrier plasmon frequencies and t…
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.
X-ray photoelectron spectroscopy (XPS) combined with first principles modeling is a powerful tool for determining the chemical composition and electronic structure of novel materials. Of these, graphene is an especially important model system for understanding the properties of other carbon nanomaterials. Here, we calculate the carbon 1$\textit{s}$ core level binding energy of pristine graphene using two methods based on density functional theory total energy differences: a calculation with an explicit core-hole ($Δ$KS), and a novel all-electron extension of the delta self-consistent field ($Δ…
We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk spectral gap. However this gap is critical, requiring threshold deformations in excess of 20%, and only along preferred directions with respect to the underlying lattice. The gapless Dirac spectrum is robust for small and moderate deformations, and the gap appears as a consequence of the merging of the two inequivalent Dirac points, only under considerable de…
Non-Hermitian Tight-Binding Bands in Graphene: Optical Conductivity, Strain Effects, and Bernal Bilayer Extension
Key Laboratory of Extraordinary Bond Engineering and Advanced Materials Technology (EBEAM) of Chongqing, School of Materials Science and Engineering, Yangtze Normal University（重庆特殊键工程与先进材料技术重点实验室，长江师范学院材料科学与工程学院）
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…
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and accurate model of the systems is of vital importance for the further study. Here, we construct the symmetry-adapted localized Wannier functions and the corresponding $\textit{ab initio}$ minimal two-valley four-band effective tight-binding models for generic twisted graphene systems with small twist angle. Such two-valley model evades the Wannier obstruction caused…
We report on the adsorption dynamics of phospholipid membranes on graphene-coated substrates using the quartz crystal microbalance with dissipation monitoring (QCM-D) technique. We compare the lipid vescle interaction and membranne formation on gold and silicon dioxide QCM crystal surfaces with their graphene oxide (GO) and reduced (r)GO coated counterparts, and report on the different lipid structures obtained. We establish graphene derivative coatings as support surfaces with tuneable hydrophobicity for the formation of controllable lipid structures. One structure of interest formed are lipi…
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 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.
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.
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.
Methane, the primary constituent of natural gas, binds too weakly to nanostructured carbons to meet the targets set for on-board vehicular storage to be viable. We show, using density functional theory calculations, that replacing graphene by graphene oxide increases the adsorption energy of methane by 50%. This enhancement is sufficient to achieve the optimal binding strength. In order to gain insight into the sources of this increased binding, that could also be used to formulate design principles for novel storage materials, we consider a sequence of model systems, that progressively take u…
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…
Graphene is the extreme material for molecular sensory and hydrogen storage applications because of its two-dimensional geometry and unique structure-property relationship. In this Letter, hydrogenation of graphene is discussed in the extent of intercoupling between mechanical deformation and electronic configuration. Our first principles calculation reveals that the atomic structures, binding energies, mechanical and electronic properties of graphene are significantly modified by the hydrogenation and applied strain. Under an in-plane strain of 10 %, the binding energies of hydrogen on graphe…
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…
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 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…
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…
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…
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.
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.
Using the ab initio pseudopotential density functional method, we investigate the functionalization of halogen molecules into graphene-based nanostructures with zigzag and armchair edges. We find that halogen molecules adsorb through chemisorption on the zigzag edge carbon atoms with a binding energy of ~1-5 eV and their adsorption on a perfect zigzag edge is preferred, in sharp contrast to physisorption on the armchair edge and elsewhere where they adsorb with a binding energy of ~0.07 eV. We suggest that our findings would be utilized for an approach to the separation of zigzag graphene nano…
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…
