Tight-binding Picture Research Articles

Dirac fermions in monolayer blue phosphorus: A multi-orbital tight-binding investigation

This work is a theoretical investigation of the energy dispersion bands of blue phosphorus (buk-P) system within the multi-orbital tight-binding (MOTB) approach. The aim is to corroborate the presence of Dirac fermions, as observed in a recent experimental study. The existence of the Dirac cone at the high-symmetry K point primarily arises from the contributions of elemental phosphorus (P) s, px, and py atomic orbitals. Note that the Fermi velocity of the monolayer buk-P system (vf≈ 2.2 × 106 m s−1) is approximately 3 times higher than that of graphene (G). This discovery classifies monolayer buk-P as a novel and scarce two-dimensional Dirac material. Furthermore, it has been reported that these Dirac fermions exhibit remarkable adaptability along the Γ–K region while preserving their degeneracy intact.Here, we quantitatively improve the overall tight-binding (TB) picture of the monolayer buk-P throughout the Brillouin zone (BZ) by engaging more neighboring interacting sites up to the fifth intra-layer nearest-neighbors (5NN). However, our models reproduce the computations based on the DFT approach and the experimental findings quite accurately.To the best of our knowledge, this work is the first to systematically investigate the presence of Dirac cone in monolayer buk-P system within the MOTB model. This rigorous analytical approach, along with the experimental observations and DFT computations, holds significant promise for exploring the intrinsic characteristics of Dirac materials beyond buk-P. Moreover, the observed electronic properties and high Fermi velocity make this material a highly promising candidate for future high-performance nano-electronic devices.

Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Maximally-localized Wannier functions (MLWFs) are broadly used to characterize the electronic structure of materials. Generally, one can construct MLWFs describing isolated bands (e.g. valence bands of insulators) or entangled bands (e.g. valence and conduction bands of insulators, or metals). Obtaining accurate and compact MLWFs often requires chemical intuition and trial and error, a challenging step even for experienced researchers and a roadblock for high-throughput calculations. Here, we present an automated approach, projectability-disentangled Wannier functions (PDWFs), that constructs MLWFs spanning the occupied bands and their complement for the empty states, providing a tight-binding picture of optimized atomic orbitals in crystals. Key to the algorithm is a projectability measure for each Bloch state onto atomic orbitals, determining if that state should be kept identically, discarded, or mixed into the disentanglement. We showcase the accuracy on a test set of 200 materials, and the reliability by constructing 21,737 Wannier Hamiltonians.

Biaxial strain modulated valence-band engineering in III-V digital alloys

Some III-V digital alloy avalanche photodiodes exhibit low excess noise. These alloys have low hole ionization coefficients due to presence of small 'minigaps', enhanced effective mass and large separation between light-hole and split-off bands in the valence band. In this letter, an explanation for the formation of the minigaps using a tight binding picture is provided. Furthermore, we demonstrate that decreasing substrate lattice constant can increase the minigap size and mass in the transport direction. This leads to reduced quantum tunneling and phonon scattering of the holes. Finally, we illustrate the band structure modification with substrate lattice constant for other III-V digital alloys.

Second-order topology and multidimensional topological transitions in sonic crystals

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization of generalized Berry phases of the bulk energy bands through the bulk-edge correspondence, a paradigm that can also be extended to acoustic and photonic systems. Recently, high-order topological insulators (HOTIs) are proposed and observed, where the bulk topological invariants result in gapped edge states and in-gap corner or hinge states, going beyond the conventional bulk-edge correspondence. However, the existing studies on HOTIs are restricted to tight-binding models which cannot describe the energy bands of conventional sonic/photonic crystals that are due to multiple Bragg scatterings. Here, we report theoretical prediction and experimental observation of acoustic second-order topological insulators (SOTI) in two-dimensional (2D) sonic crystals (SCs) beyond the tight-binding picture. We observe gapped edge states and degenerate in-gap corner states which manifest bulk-edge correspondence in a hierarchy of dimensions. Moreover, topological transitions in both the bulk and edge states can be realized by tuning the angle of the meta-atoms in each unit-cell, leading to various conversion among bulk, edge and corner states. The emergent properties of the acoustic SOTIs open up a new route for topological designs of robust localized acoustic modes as well as topological transfer of acoustic energy between 2D, 1D and 0D modes.

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions.

An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The accuracy of the method is benchmarked for a wide variety of systems and compared with other semiempirical methods. Along with excellent performance for the "target" properties, we also find lower errors for "off-target" properties such as barrier heights and molecular dipole moments. High computational efficiency along with the improved physics compared to its precursor GFN-xTB makes this method well-suited to explore the conformational space of molecular systems. Significant improvements are furthermore observed for various benchmark sets, which are prototypical for biomolecular systems in aqueous solution.

Realizing the Harper model with ultracold atoms in a ring lattice

We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the idealized tight-binding picture, we determine the optimal conditions necessary to realize the critical point where the spectrum becomes fractal, and identify the nature and cause of the departures from the discrete model predictions. We also show that even with a commensurate ring with a few lattice sites, the Aubry-Andr\'e localization transition can be realized. Localized states that behave like edge states with energies that reside in the band gaps can be generated by introducing a surprisingly small local perturbation within the ring. Spectrum oscillation arising from complex coupling can be implemented by uniform rotation of the ring, but with certain significant differences that are explained

Design of full-k-space flat bands in photonic crystals beyond the tight-binding picture.

Based on a band engineering method, we propose a theoretical prescription to create a full-k-space flat band in dielectric photonic crystals covering the whole Brillouin Zone. With wave functions distributed in air instead of in the dielectrics, such a flat band represents a unique mechanism for achieving flat dispersions beyond the tight-binding picture, which can enormously reduce the requirement of permittivity contrast in the system. Finally, we propose and numerically demonstrate a unique application based on the full-k-space coverage of the flat band: ultra-sensitive detection of small scatterers.

Numerical study of carbon nanotube field effect transistors in presence of carbon–carbon third nearest neighbor interactions

In this paper, for the first time, we have used a more precise Hamiltonian matrix based on first nearest neighbor (1NN) and third nearest neighbor (3NN) carbon–carbon interactions to simulate carbon nanotube field effect transistors (CNTFETs). By taking the interactions with more distant neighbors into account, an improvement in tight-binding picture is gained. A self-consistent solution of Schrodinger equation based on nonequilibrium Green's function (NEGF) formalism coupled to a two-dimensional Poisson's equation for treating the electrostatics of the device has been employed to simulate CNTFETs. A tight-binding Hamiltonian with an atomistic (pz orbitals) mode space basis in the ballistic limits has been used to describe the carbon nanotube (CNT) region. Simulations show that in the presence of 3NN, the energy bandgap of the CNT decreases and consequently the simulated device has lower threshold voltage compared to a simulated device with just 1NN. Short channel effects study demonstrates that neglecting 3NN underestimates the subthreshold swing and overestimates ON/OFF current ratio. All these investigations show that for simulating a CNTFET more precisely, the 3NN interactions can be taken into account in addition to the 1NN.

ELECTRONIC TRANSPORT IN METALLIC SYSTEMS AND GENERALIZED KINETIC EQUATIONS

This paper reviews some selected approaches to the description of transport properties, mainly electroconductivity, in crystalline and disordered metallic systems. A detailed qualitative theoretical formulation of the electron transport processes in metallic systems within a model approach is given. Generalized kinetic equations which were derived by the method of the nonequilibrium statistical operator are used. Tight-binding picture and modified tight-binding approximation (MTBA) were used for describing the electron subsystem and the electron-lattice interaction correspondingly. The low- and high-temperature behavior of the resistivity was discussed in detail. The main objects of discussion are nonmagnetic (or paramagnetic) transition metals and their disordered alloys. The choice of topics and the emphasis on concepts and model approach makes it a good method for a better understanding of the electrical conductivity of the transition metals and their disordered binary substitutional alloys, but the formalism developed can be applied (with suitable modification), in principle, to other systems. The approach we used and the results obtained complements the existent theories of the electrical conductivity in metallic systems. The present study extends the standard theoretical format and calculation procedures in the theories of electron transport in solids.

Role of structural electromagnetic resonances in a steerable left-handed antenna

We reformulate the problem of a steerable left-handed antenna reported by Matsuzawa et al. [IEICE Trans. Electron. E89-C, 1337 (2006)] from the view point of structural electromagnetic resonance of the unit structure. We show that there are two such resonances with different spatial symmetries in the relevant frequency range, which result in the formation of two electromagnetic bands with opposite signs of curvature at the Γ point of the Brillouin zone. We derive an expression of dispersion curves based on the tight-binding picture and show that the dispersion of the two bands is linear in the vicinity of the Γ point in the case of accidental degeneracy only if the symmetry of the two resonance states satisfies certain conditions. We also show that the refraction angle can be designed by changing the lattice constant of the arrayed unit structures, since the band width is modified due to the change in the electromagnetic transfer integral.

Observation of cavity structures in composite metamaterials

We investigated the cavity structure by the deformation of a unit cell of a Composite Metamaterial (CMM) structure. We considered different cavity structures with different resonance frequencies and Q-factors. We observed the Q-factor of the cavity resonance as 108 for a CMM based single cavity wherein the cavity structure is a closed ring structure. We investigated the reduced photon lifetime and observed that at the cavity resonance, the effective group velocity was reduced by a factor of 20 for a CMM based single cavity compared to the electromagnetic waves propagating in free space. Since the unit cells of metamaterials are much smaller than the operation wavelength, subwavelength localization is possible within these metamaterial cavity structures. We found that the electromagnetic field is localized into a region of /8, where is the cavity resonance wavelength. Subsequently, we brought two cavities together with an intercavity distance of two metamaterial unit cells and then investigated the transmission spectrum of CMM based interacting 2-cavity system. Finally, using the tight-binding picture we observed the normalized group velocity corresponding to the coupled cavity structure.

Energy-gap modulations of graphene ribbons under external fields: A theoretical study

Here, we address a theoretical study of electronic properties of carbon ribbons under the effect of external electric and magnetic fields. The Peierls approximation is used to incorporate the magnetic field within a tight-binding picture. A charge self-consistent calculation is adopted to analyze the gap modulations induced by the application of the external electric field and compared with simple models. We show that depending on the ribbon geometries and field intensities, a large variety of electronic situations may be achieved, suggesting possible mechanisms for gap engineering of such carbon nanomaterials.

Analysis of Three Coupled Defects in One-Dimensional PhotonicBandgap Structure

The mutual interaction of three different defects in photonic crystalsis studied theoretically. A theoretical model based on the classicalwave analogue of the tight-binding (TB) picture is applied to thestructure. We obtain analytic expressions for the eigenfrequencies andeigenmodes, from which the transmissions at resonance are derived.Based on this, a new type of the photonic quantum-well structure isinvestigated and its possible application is discussed. The TBpredictions are compared with the transfer matrix method simulationresults.

Surface-induced d-band anisotropy on Cu( [formula omitted

Reflectance difference spectroscopy (RDS) was used to study the surface-induced anisotropy of the electronic band structure on Cu(1 1 0) in the energy range between 3 and 5.5 eV. The spectral features in this energy range can be well reproduced by approximating surface dielectric anisotropy by the first derivative of the known bulk dielectric function. In contrast to the conventional ‘derivative model’, however, the different sensitivity to the relevant Cu d-bands to the surface anisotropy has to be respected. The results can be rationalized in a tight-binding picture relating the shift of the surface projected d-bands to the different atomic densities along the in-plane [0 0 1] and [ 1 ̄ 1 0 ] directions, respectively. As a confirmation, the temperature dependence of the RDS features was measured and found to be in good agreement with the thermal shifts of the associated optical transitions.

Tight-binding description of graphene

We investigate the tight-binding approximation for the dispersion of the $\ensuremath{\pi}$ and ${\ensuremath{\pi}}^{*}$ electronic bands in graphene and carbon nanotubes. The nearest-neighbor tight-binding approximation with a fixed ${\ensuremath{\gamma}}_{0}$ applies only to a very limited range of wave vectors. We derive an analytic expression for the tight-binding dispersion including up to third-nearest neighbors. Interaction with more distant neighbors qualitatively improves the tight-binding picture, as we show for graphene and three selected carbon nanotubes.

Coupled optical microcavities in one-dimensional photonic bandgap structures

We present a detailed theoretical and experimental study of the evanescent coupled optical microcavity modes in one-dimensional photonic bandgap structures. The coupled-cavity samples are fabricated by depositing alternating hydrogenated amorphous silicon nitride and silicon oxide layers. Splitting of the eigenmodes and formation of a defect band due to interaction between the neighbouring localized cavity modes are experimentally observed. Corresponding field patterns and the transmission spectra are obtained by using transfer matrix method (TMM)simulations. A theoretical model based on the classical wave analogue of the tight-binding (TB)picture is developed and applied to these structures. Experimental results are in good agreement with the predictions of the TB approximation and the TMM simulations.

Ferromagnetic zigzag chains and properties of the charge-ordered perovskite manganites

The low-temperature properties of the so-called ``charge-ordered'' state in 50% doped perovskite manganites are described from the viewpoint of the magnetic spin ordering. In these systems, the zigzag antiferromagnetic ordering, combined with the double exchange physics, effectively divides the whole sample into the one-dimensional ferromagnetic zigzag chains and results in the anisotropy of electronic properties. The electronic structure of one such chain is described by an effective $3\ifmmode\times\else\texttimes\fi{}3$ Hamiltonian in the basis of $\mathrm{Mn}{(3\mathrm{de}}_{g})$ orbitals. We treat this problem analytically and consider the following properties: (i) the nearest-neighbor magnetic interactions; (ii) the distribution of the $\mathrm{Mn}{(3\mathrm{de}}_{g})$ and $\mathrm{Mn}(4p)$ states near the Fermi level, and their contribution to the optical conductivity and the resonant x-ray scattering near the Mn K-absorption edge. We argue that the anisotropy of magnetic interactions in the double exchange limit, combined with the isotropic superexchange interactions, readily explains both the local and the global stability of the zigzag antiferromagnetic state. The twofold degeneracy of ${e}_{g}$ levels plays a very important role in the problem and explains the insulating behavior of the zigzag chain, as well as the appearance of the orbital ordering in the double exchange model. Importantly, however, the charge ordering itself is expected to play only a minor role and is incompatible with the ferromagnetic coupling within the chain. We also discuss possible effects of the Jahn-Teller distortion and compare the tight-binding picture with results of band-structure calculations in the local-spin-density approximation.

Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides

We have experimentally demonstrated the guiding, bending, and splitting of electromagnetic (EM) waves in highly confined waveguides built around three-dimensional layer-by-layer photonic crystals by removing a single rod. Full transmission of the EM waves was observed for straight and bended waveguides. We also investigated the power splitter structures in which the input EM power could be efficiently divided into the output waveguide ports. The experimental results, dispersion relation and photon lifetime, were analyzed with a theory based on the tight-binding photon picture. Our results provide an important tool for designing photonic crystal based optoelectronic components.

Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal

We report on measurements of delay time corresponding to evanescent coupled-cavity modes in three-dimensional photonic crystals. By creating a defect inside the crystal, photons are confined within a boxlike cavity of volume $\ensuremath{\sim}(\ensuremath{\lambda}{/2)}^{3}.$ It is observed that photon lifetime increases drastically and group velocity of photons tends towards zero at the waveguiding band edges of the periodic coupled cavities. Experimental results are well explained within the classical wave analog of the tight-binding picture. Observation of the extremely small group velocity and long photon lifetime at the coupled-cavity waveguide band edges have important potential applications.

Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals

A new type of waveguiding mechanism in three-dimensional photonic band-gap structures is demonstrated. Photons propagate through strongly localized defect cavities due to coupling between adjacent cavity modes. High transmission of the electromagnetic waves, nearly 100%, is observed for various waveguide structures even if the cavities are placed along an arbitrarily shaped path. The dispersion relation of the waveguiding band is obtained from transmission-phase measurements, and this relation is well explained within the tight-binding photon picture. The coupled-cavity waveguides may have practical importance for development of optoelectronic components and circuits.