A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kind of fundamental structures are given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
In this paper we investigate the influence of the next-nearest-neighbor coupling of tight-binding model of graphene on the spectrum of plasmon excitations. The nearest-neighbor tight-binding model was previously used to calculate plasmon spectrum in the next paper [1]. We expand the previous results of the paper by the next-nearest-neighbor tight-binding model. Both methods are based on the numerical calculation of the dielectric function of graphene and loss function. Here we compare plasmon spectrum of the next-nearest and nearest-neighbor tight-binding models and find differences between pl…
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 derive an {\em ab initio} $π$-band tight-binding model for $AB$ stacked bilayer graphene based on maximally localized Wannier wave functions (MLWFs) centered on the carbon sites, finding that both intralayer and interlayer hopping is longer in range than assumed in commonly used phenomenological tight-binding models. Starting from this full tight-binding model, we derive two effective models that are intended to provide a convenient starting point for theories of $π$-band electronic properties by achieving accuracy over the full width of the $π$-bands, and especially at the Dirac points, in…
Wannier tight-binding models are effective models constructed from first-principles calculations. As such, they bridge a gap between the accuracy of first-principles calculations and the computational simplicity of effective models. In this work, we extend the existing methodology of creating Wannier tight-binding models from first-principles calculations by introducing the symmetrization post-processing step, which enables the production of Wannier-like models that respect the symmetries of the considered crystal. Furthermore, we implement automatic workflows, which allow for producing a larg…
We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions.
Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to obtain analytic expressions of dispersion relations and eigenvectors. Four different band-gaps are identified along with two distinct indirect band-gaps at the Harrison point. Multiple band-gaps in this model may give rise to exotic electronic properties.
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 studied boron nitride monolayer and bilayer band structures. For bilayers, the ground state energies of the different five stackings are computed using DFT in order to determine the most stable configuration. Also, the interlayer distance for the five different types of stacking in which boron-nitride bilayers can be found is determined. Using a minimal tight binding model for the band structures of boron nitride bilayers, the hopping parameters and the onsite energies have been extracted by fitting a tight binding empirical model to the DFT results.
In the empirical tight-binding approach we study the electronic states in spherical SiGe nanocrystals embedded in SiO2 matrix. The energy and valley structure is obtained as a function of Ge composition and nanocrystal size. The calculations show that the mixing of hot electrons in the nanocrystal with electrons in wide band gap matrix is possible and this mixing strongly depends on the Ge composition in the nanocrystal.
In this paper we employ a combined {\it ab initio} and tight-binding approach to obtain the electronic and optical properties of hydrogenated InN nanowires. We first discuss InN band structure for the wurtzite structure calculated at the LDA+U level and use this information to extract the parameters needed for an empirical tight-binging implementation. These parameters are then employed to calculate the electronic and optical properties of InN nanowires in a diameter range that would not be affordable by {\it ab initio} techniques. The reliability of the large nanowires results is assessed by …
We study magnon spectra at finite temperature in yttrium iron garnet from tight-binding model with nearest neighboring exchange interaction. The spin reduction due to thermal magnon excitation are taken into account via the mean field approximation to the local spin and found to be different at two sets of iron atoms. The resulting temperature dependence of the spin wave gap shows good agreement with experiment. We find only two magnon modes are relevant to ferromagnetic resonance.
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 propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.
Parameters of the nonorthogonal tight-binding model for hydrocarbons are derived based on a criterion of the best agreement between the calculated and experimental values of bond lengths and binding energies for different molecules CnHm. The results obtained can be used, e. g., to study the kinetics of hydrogen absorption by carbon nanostructures, to simulate the dynamics of hydrocarbon clusters like cubane C8H8, etc.
With the help of a tight-binding (TB) electronic-structure toy model we investigate the matching of parameters across hetero-interfaces . We demonstrate that the virtual crystal approximation, commonly employed for this purpose, may not respect underlying symmetries of the electronic structure. As an alternative approach we propose a method which is motivated by the matching of wave functions in continuous-space quantum mechanics. We show that this method obeys the required symmetries and can be applied in simple band to band transitions. Extension to multiple interfaces and to more sophistica…
A novel approach to investigate the electron transport of cis- and trans-polyacetylene chains in the single-electron approximation is presented by using microwave emulation measurements and tight-binding calculations. In the emulation we take into account the different electronic couplings due to the double bonds leading to coupled dimer chains. The relative coupling constants are adjusted by DFT calculations. For sufficiently long chains a transport band gap is observed if the double bonds are present, whereas for identical couplings no band gap opens. The band gap can be observed also in rel…
We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [T. Stauber et al. Phys. Rev. Lett. 120, 046801 (2018)] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous co…
We develop an analytical scattering formalism for computing the transmittance through periodic defect lines within the tight-binding model of graphene. We first illustrate the method with a relatively simple case, the pentagon-only defect line. Afterwards, more complex defect lines are treated, namely the zz(558) and the zz(5757) ones. The formalism developed, only uses simple tight-binding concepts, reducing the problem to matrix manipulations which can be easily worked out by any computational algebraic calculator.
In this work we present a tight-binding model that allows to describe with a minimal amount of parameters the band structure of exciton-polariton lattices. This model based on $s$ and $p$ non-orthogonal photonic orbitals faithfully reproduces experimental results reported for polariton graphene ribbons. We analyze in particular the influence of the non-orthogonality, the inter-orbitals interaction and the photonic spin-orbit coupling on the polarization and dispersion of bulk bands and edge states.
As one of the first proposed topologically protected states, the quantum spin Hall effect in graphene relies critically on the existence of a spin-dependent gap at the K/K' points of the Brillouin zone. Using a tight-binding formulation based on the method of invariants, we identify the origin of such an intrinsic gap as the three-center interaction between the pi-orbitals caused by spin-orbit interactions. This methodology incorporates all symmetry compliant interactions previously neglected and has wider applications for comparisons between first-principle calculations and the tight-binding …
We study the electronic and optical properties of strained single-layer SnC in the density functional theory (DFT) and tight-binding models. We extract the hopping parameters tight-binding Hamiltonian for monolayer SnC by considering the DFT results as a reference point. We also examine the phonon spectra in the scheme of DFT, and analyze the bonding character by using Mulliken bond population. Moreover, we show that the band gap modulation and transition from indirect to direct band gap in the compressive strained SnC. The applied tensile strain reduces the band gap and eventually the semicon…
Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal…
We present a microwave realization of finite tight-binding graphene-like structures. The structures are realized using discs with a high index of refraction. The discs are placed on a metallic surface while a second surface is adjusted atop the discs, such that the waves coupling the discs in the air are evanescent, leading to the tight-binding behavior. In reflection measurements the Dirac point and a linear increase close to the Dirac point is observed, if the measurement is performed inside the sample. Resonances due to edge states are found close to the Dirac point if the measurements are …
We present the symmetry labelling of all electron bands in graphene obtained by combining numerical band calculations and analytical analysis based on group theory. The latter was performed both in the framework of the (nearly) free electron model, or in the framework of the tight-binding model. The predictions about relative positions of the bands which can be made on the basis of each of the models just using the group theory (and additional simple qualitative arguments, if necessary) are complimentary.
We report about a mechanism for surface localization, present in finite defect-free polyatomic lattices described by a tight binding model. Numerical diagonalization and degenerated perturbation theory show that there is a minimum number of atoms within each unit cell in the lattice for which surface states may exist, provided the local energy of the surface atom is different from the rest in the unit cell. It is shown that the appearance of surface states is a second-order effect in the hopping parameter. Other kinds of surface states are identified in the two-dimensional case.
We propose an accurate tight-binding parametrization for the band structure of MoS$_2$ monolayers near the main energy gap. We introduce a generic and straightforward derivation for the band energies equations that could be employed for other monolayer dichalcogenides. A parametrization that includes spin-orbit coupling is also provided. The proposed set of model parameters reproduce both the correct orbital compositions and location of valence and conductance band in comparison with ab initio calculations. The model gives a suitable starting point for realistic large-scale atomistic electroni…
We generalize the quantum waveguide approach to Hückel or tight-binding models relevant to unsaturated $\p$ molecular devices. A Landauer-like formula for the current density through {\em internal} bonds is also derived which allows for defining a local conductance. The approach is employed to study internal circular currents in two-terminal rings. We show how to predict the occurrence and the nature of large vortex currents in coincidence with vanishingly small currents in the leads. We also prove a remarkably simple formula for the onset of a vortex regime.
The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalist tight-binding model. The obtained analytical results allow in creating interface between semiconductor quantum computer and superc…
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 investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derive…
A quantum-mechanical calculation of conductance in an open quantum dot is performed in the Landauer-Büttiker formalism using a tight binding Hamiltonian with direct Coulomb interaction. The charge distribution in the dot is calculated self-consistently as function of a gate potential, for various dot-leads couplings. The interaction is active only inside the dot, but not in the leads, its strength being an input parameter. Our calculations are complementary to the master-equation approach, go beyond the "orthodox theory", and account for the size, tunneling, and interaction effects in quantum …
Experiments on hexagonal graphene-like structures using microwave measuring techniques are presented. The lowest transverse-electric resonance of coupled dielectric disks sandwiched between two metallic plates establishes a tight-binding configuration. The nearest-neighbor coupling approximation is investigated in systems with few disks. Taking advantage of the high flexibility of the disks positions, consequences of the disorder introduced in the graphene lattice on the Dirac points are investigated. Using two different types of disks, a boron-nitride-like structure (a hexagonal lattice with …
We study the electronic properties of spherical quantum dot quantum well nanocrystals within a symmetry-based tight-binding model. In particular, the influence of a concentric monolayer of HgS embedded in a spherical CdS nanocrystal of diameter 52.7 A is analyzed as a function of its distance from the center. The electron and hole states around the energy gap show a strong localization in the HgS well and the neighboring inner (core) interface region. Important effects on the optical properties such as the absorption gap and the fine structure of the exciton spectrum are also reported.
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…
We propose atomic films of n-doped $γ$-InSe as a platform for intersubband optics in the infrared (IR) and far infrared (FIR) range, coupled to out-of-plane polarized light. Depending on the film thickness (number of layers) of the InSe film these transitions span from $\sim 0.7$ eV for bilayer to $\sim 0.05$ eV for 15-layer InSe. We use a hybrid $\mathbf{k} \cdot \mathbf{p}$ theory and tight-binding model, fully parametrized using density functional theory, to predict their oscillator strengths and thermal linewidths at room temperature.
The electronic and transport properties of an extended linear defect embedded in a zigzag nanoribbon of realistic width are studied, within a tight binding model approach. Our results suggest that such defect profoundly modify the properties of the nanoribbon, introducing new conductance quantization values and modifying the conductance quantization thresholds. The linear defect along the nanoribbon behaves as an effective third edge of the system, which shows a metallic behavior, giving rise to new conduction pathways that could be used in nanoscale circuitry as a quantum wire.
One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite conditions the site reflects electrons {\it absolutely and elastically} (high-frequency blockade states). The problem is treated both numerically and (in the case of narrow band) analytically. The results are compared with the free-electron 1D problem with vibrating $δ$-functional potential. Together with the blockade states the local and reflectionless states …
We present a method which computes many-electron energies and eigenfunctions by a full configuration interaction which uses a basis of atomistic tight-binding wave functions. This approach captures electron correlation as well as atomistic effects, and is well suited to solid state quantum dot systems containing few electrons, where valley physics and disorder contribute significantly to device behavior. Results are reported for a two-electron silicon double quantum dot as an example.
Analytical solutions describing quantum swap and Hadamard gate are given with the use of tight-binding approximation. Decoherence effects are described analytically for two interacting electrons confined by local potentials with use of tight-binding simplistic model and in Schroedinger formalism with omission of spin degree of freedom. The obtained results can be generalized for the case of N electrostatically interacting quantum bodies confined by local potentials (N-qubit) system representing any electrostatic quantum gate with N1/N-N1 inputs/outputs. The mathematical structure of system evo…
We consider the distribution of waiting times between non-interacting fermions on a tight-binding chain. We calculate the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off as predicted by scattering theory. In addition, we consider several quantum dot structures for which we can associate oscillations in the waiting time distributions to internal energy scales of the scatterers. A detailed comparison with scattering theory and generalized master equations is provided. We focus o…
We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial bandstructure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a non-trivial square root of a parent lattice Hamiltonian---in analogy to the passage from a Klein-Gordon equation to a Dirac equation. In the tight-binding setting, the square-root operation admits to induce spectral symmetries at the expense of broken crystal symmetries. As we illustrate in detail for a simple one-dimensional example, the emergent and inherited spectral…
We consider the tight-binding model with cubic symmetry that may be relevant for the description of a certain class of Weyl semimetals. We take into account elastic deformations of the semimetal through the modification of hopping parameters. This modification results in the appearance of emergent gauge field and the coordinate dependent anisotropic Fermi velocity. The latter may be interpreted as emergent gravitational field.
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.
We present a computationally efficient transferable single-band tight-binding model (SBTB) for spin polarized transport in heterostructures with an effort to capture the band structure effects. As an example, we apply it to study transport through Fe-MgO-Fe(100) magnetic tunnel junction devices. We propose a novel approach to extract suitable tight-binding parameters for a material by using the energy resolved transmission as the benchmark, which inherently has the bandstructure effects over the two dimensional transverse Brillouin zone. The SBTB parameters for each of the four symmetry bands …
First-principles calculations were performed to investigate the electronic structure of two-dimensional (2-D) Ge, Sn, and Pb without and with the presence of an external electric field in combination with spin-orbit coupling. Tight-binding calculations based on four orbitals per atom and an effective single orbital are presented to match with the results obtained from first-principles calculations. In particular, the electronic band structure and the band splitting are investigated with both models. Moreover, the simple $k\cdot p$ model is also considered in order to understand the band splitt…
Many commonly used nearest neighbor tight binding models for cubic semiconductors often result in inaccurate band structures when transferred to hexagonal polytypes. The resulting bandgaps are systematically too small, and in some cases calculations may erroneously predict a metal for the wurtzite polytype. We have calculated a set of $\rm spds^*$ tight binding parameters for the hexagonal phases of non-nitride III-V and group V semiconductors fit to experimental data and empirical pseudopotential calculations. Our fitting procedure constrains the parameters to be as close as possible to those…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. Béri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).
We study the relationship between the differential conductance and the local density of states in tight-binding tunnel junctions where the junction' geometry can be varied between the point-contact and the planar-contact limits. The conductances are found to differ significantly in these two limiting cases. We also examine how the matrix element influences the tunneling characteristics and produces contrast in a simple model of scanning tunneling microscope (STM). Some implications regarding the interpretation of STM spectroscopic data in the cuprates are discussed. The calculations are carrie…
The surface spin states for bismuth thin films were investigated using an $sp^3$ tight-binding model. The model explains the experimental observations using angle-resolved photoemission spectroscopy, including the Fermi surface, the band structure with Rashba spin splitting, and the quantum confinement in the energy band gap of the surface states. A large out-of-plane spin component also appears. The surface states penetrate inside the film to within approximately a few bilayers near the Brillouin-zone center, whereas they reach the center of the film near the Brillouin-zone boundary.
Electrons in tight-binding lattice driven by DC electric field dissipate their energy through on-site fermionic thermostats. Due to the translational invariance in the transport direction, the problem can be block-diagonalized. We solve this time-dependent quadratic problem and demonstrate that the problem has an oscillatory steady-state. The steady-state occupation number shows that the Fermi surface disappears for any damping from the thermostats and any finite electric field. Despite the lack of momentum scattering, the conductivity takes the same form as the semi-classical Ohmic expression…
The electronic structure of Bernal-stacked graphite subject to tilted magnetic fields is studied theoretically. The minimal nearest-neighbor tight-binding model with the Peierls substitution is employed to describe the structure of Landau levels. We show that while the orbital effect of the in-plane component of the magnetic field is negligible for massive Dirac fermions in the vicinity of the K point of the graphite Brillouin zone, at the H point it leads to the experimentally observable splitting of Landau levels, which grows approximately linearly with the in-plane field intensity.
By performing \emph{ab initio} calculations for one- to four-layer black phosphorus within the $GW$ approximation, we obtain a significant difference in the band gap ($\sim$1.5 eV), which is in line with recent experimental data. The results are analyzed in terms of the constructed four-band tight-binding model, which gives accurate descriptions of the mono- and bilayer band structure near the band gap, and reveal an important role of the interlayer hoppings, which are largely responsible for the obtained gap difference.
