Multi-orbital Tight-binding Model 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.

Stability of electronical properties of Antimony antidot nanostructure in the presence and in the absence of substrate

Using the multi-orbital (sp3) tight-binding (TB) model, we have obtained the band structure of the Antimony monolayer with a hexagonal array of holes. These structures are named Antimony antidot lattice (AAL). In our tight-binding model, the interaction of the nearest and next-nearest neighbors of atoms has been considered. Our numerical results present that band structures of the system depend on the size of embedded holes in the Antimony monolayer as points of the antidot lattice. Also, we have shown that AALs with a large radius of holes are almost conductors with tiny energy gaps. Besides, we have represented that spin–orbit coupling magnificently affects the band gap for Antimony antidot lattice in the different ranges of hole radius. Moreover, we have investigated the effect of distance between holes of AALs on the band structure and energy gap. Also, the variations of the band gap of Antimony antidot by changing the inserted strain on it have been investigated. Furthermore taking into account the effect of strain, we have compared the band structure and energy gap of antidot lattice (Highlightslayer with hole) and ideal sheet (monolayer without hole).Finally, the effect of substrate on the electronical properties of Antimony monolayer with holes (Antidot) and without holes (ideal sheet) is analyzed.

Energy spectrum and light absorption of arsenene quantum dots

As a close relative of phosphorene, puckered arsenene is stable and has been demonstrated experimentally as a promising two-dimensional semiconductor material. By means of a multi-orbital tight-binding model, we investigate theoretically the energy spectrum and magneto-optical properties of circular and rectangular arsenene quantum dots (AQDs). The tight-binding parameters are obtained by reproducing accurately the electron energy bands of puckered arsenene from the first-principle calculation. For both AQDs, the density of states (DOS), probability distribution and inverse participation ratio (IPR) of eigenstates, and optical absorption spectrum are calculated numerically. It is found that edge states of AQDs fill up the bulk band gap of puckered arsenene and are only localized near the armchair edges of AQDs. These features differ greatly from those in quantum dots made of graphene or phosphorene. The band edges of arsenene monolayer can be located roughly from the IPR and DOS spectrum. The light absorptivity of both AQDs under zero magnetic field depends strongly on the polarization direction of incident light. The position and intensity of absorption peaks can be tuned by the shape of quantum dots and the applied magnetic field. The anisotropy ratio of light absorption can be reduced by one order of magnitude under a magnetic field of tens of Tesla.

Particle-hole symmetry broken solutions in graphene nanoribbons: A multi-orbital, mean-field perspective

Mean-field theories have since long predicted edge magnetism in graphene nanoribbons, where the order parameter is given by the local magnetization. However, signatures of edge magnetism appears elusive in the experiments, suggesting another class of solutions. We employ a self-consistent mean field approximation within a multi-orbital tight-binding model and obtain particle-hole symmetry broken solutions, where the local filling plays the role of the order parameter. Unlike the magnetic edge solutions, these are topologically non-trivial and show zero local magnetization. A small and a large doping regime are studied, and a free energy minimum for finite hole doping is encountered, which may serve as an explanation for the absence of experimental evidence for magnetic edge states in zigzag graphene nanoribbons. The electronic interaction may increase the finite \(d\)-orbital occupation, which leads to a change of the effective Coulomb interaction of the dominant \(p_z\)-orbitals. Our findings indicate that the non-magnetic solution for finite hole doping becomes energetically preferred, compared to the magnetic phases at half-filling, once thermal fluctuations or unintentional doping from the substrate are considered. This result persists even in the presence of the \(d\)-orbitals and the Coulomb interaction therein.

Floquet anomalous Hall effect in ferromagnetic multiorbital tight-binding models

In this work, we study the band structures and intrinsic anomalous Hall conductivity (AHC) of the ferromagnetic multiorbital tight-binding (TB) model derived from the transition metal compound Sr2RuO4 under periodic driving of monochromatic polarized light. Within the framework of the Floquet theory, we adopt the continued fraction technique to attain the effective Hamiltonian valid in the weak-driving and low-frequency regimes, and the related Green’s functions which are further employed for the transport calculations based on the Kubo formalism. The high-frequency circularly and linearly polarized light has limited impacts on the band structures, while the low-frequency light with the photon energy smaller than the bandwidth of the system opens up bandgaps at the edges of the Floquet–Brillouin zone since the transitions between Floquet sidebands become significant. For intrinsic AHC, the left-handed circularly polarized (LCP) light plays a distinct role on AHC compared to the right-handed circularly polarized (RCP) light. Furthermore, it reveals that the roles of LCP and RCP light can be interchanged by altering the incident plane of light. Finally, the intrinsic AHC with the interplay between the short-range disorder and circularly polarized light is also investigated.

Decoding the DC and optical conductivities of disordered MoS2 films: an inverse problem

To calculate the conductivity of a material having full knowledge of its composition is a reasonably simple task. To do the same in reverse, i.e. to find information about the composition of a device from its conductivity response alone, is very challenging and even more so in the presence of disorder. An inversion methodology capable of decoding the information contained in the conductivity response of disordered structures has been recently proposed but despite claims of generality and robustness, the method has only been used with 2D systems possessing relatively simple electronic structures. Here we put these claims to the test and generalise the inversion method to the case of monolayer MoS2, a material whose electronic structure is far more complex and elaborate. Starting from the spectral function that describes the DC conductivity of a disordered sample of a single layered MoS2 containing a small concentration of randomly dispersed vacancies, we are able to invert the signal and find the exact composition of defects with an impressive degree of accuracy. Remarkably, equally accurate results are obtained with the optical conductivity. This is indicative of a methodology that is indeed suitable to extract composition information from different 2D materials, regardless of their electronic structure complexity. Calculated conductivity results were used as a proxy for their experimental counterpart and were obtained with an efficient quantum transport code (KITE) based on a real-space multi-orbital tight-binding model with parameters generated by density functional theory.

Influence of electric and magnetic fields andσ-edge bands on the electronic and optical spectra of graphene nanoribbons

The unusual electronic and optical properties of armchair and zigzag graphene nanoribbons (GNRs) subject to in-plane transverse electric and perpendicular magnetic fields have been systematically investigated. Our calculations were carried out within the generalized multi-orbital tight-binding model based on a Hamiltonian which takes into account hopping integrals among the (s, $p_x$, $p_y$, $p_z$) atomic orbitals as well as the external electric and magnetic fields. The electronic structure consists of $\pi$ bands arising from the $p_z$ orbital and $\sigma$ bands originating from the (s, $p_x$, $p_y$) orbitals. The energy bands and optical spectra are diversified by both the nature of the edge of the nanoribbon and strength of the external fields. Armchair GNRs display a width-dependent energy gap in addition to low-energy $\sigma$ bands while the zigzag system has the unfilled flat band with $\pi$ edge states at zero energy and partially filled wide-range $\sigma$ bands. An applied in-plane electric field leads to the splitting of energy bands and shifted Fermi level, thereby enriching the inter-band and intra-band optical conductivities. The interplay between an external magnetic field and the edge geometry gives rise to extraordinary quantized Landau levels and special optical spectra.

Multi-orbital tight binding model for the electronic and optical properties of armchair graphene nanoribbons in the presence of a periodic potential

The influences of an external electric field with uniform or modulated potential on the electronic and optical properties of armchair graphene nanoribbons (GNRs) are explored using the multi-orbital tight-binding Hamiltonian. The interplay between an electric field and interaction between (s, p x , p y , p z ) orbitals remarkably enriches the main features of band structures and absorption spectra. The applied electric field can notably alter the energy dispersions of π and σ bands, leading to the deformation of band-edge states, open and close of a band gap, and modification of the Fermi energy. The vertical optical excitations happen among the π bands, while their available channels depend on the Fermi level which is controlled by the σ-edge bands and a finite potential. With the rich and unique properties, GNRs are suitable candidates for applications in the fields of photodetectors, nanoelectronics, and spintronics. The calculated results are expected to be examined by the angle-resolved photoemission spectroscopies and optical spectroscopies.

Maximally localized Wannier functions for describing a topological phase transition in stanene

Starting from first-principles calculations on pristine stanene and using maximally localized Wannier functions (MLWFs), we analyze the different phases of the system when it is driven to a topological phase transition. The transition is achieved by a continuous parameter represented by an external electric field ${\mathcal{E}}_{z}$ as a generic inversion-symmetry-breaking term. We also compare the results with those of a multiorbital tight-binding (TB) model for stanene, whose hopping integrals are determined by Slater-Koster parameters. The system is in a topological (trivial) phase for ${\mathcal{E}}_{z}<{\mathcal{E}}_{c}$ (${\mathcal{E}}_{z}>{\mathcal{E}}_{c}$). We obtain that the critical field is ${\mathcal{E}}_{c}\ensuremath{\simeq}0.69\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ for the more realistic MLWF compared to ${\mathcal{E}}_{c}\ensuremath{\simeq}0.15\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ in the TB model. This suggests a larger stability of the topological phase of stanene when deposited on inert substrates.

Thermoelectric power generation efficiency of zigzag monolayer nanoribbon of bismuth

The thermoelectric power generation efficiency of a bismuth monolayer nanoribbon has been studied theoretically. We calculate the conductance of such a structure using the multi-orbital tight-binding model and also recursive Green’s function method, in the presence of a substrate and on-site potential. For the case of the substrate-supported bismuth nanoribbon and by proper selection of on-site potential, a boxcar shape conductance in terms of energy has been obtained. Using the Landauer–Büttiker formalism in the non-linear response regime, we calculate heat and charge currents at low temperatures. By calculation of the electrical output power and power conversion thermoelectric efficiency, we have illustrated that such a structure can operate at high thermoelectric efficiency and also a considerable power generation rate.

Multi-orbital tight binding model for cavity-polariton lattices

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.

Spin-orbit coupling-induced band inversion and spin Chern insulator phase in plumbene and stanene

Z2 topology in two-dimensional group IVA materials has been explained by the band orders due to the crystal field splitting at the Γ point in the Brillouin zone, while spin-orbit coupling (SOC) was considered just to open a band gap. By using a multi-orbital tight-binding model, we show that the SOC induces band inversion between the conduction and valence bands at the Γ point in plumbene, which also is the case in stanene when the SOC strength increases. As a result of the band inversion, plumbene becomes a spin Chern insulator with a spin Chern number CS = 2 and, as the SOC strength increases, stanene undergoes a topological phase transition from a Z2 topological insulator to a spin Chern insulator with CS = 2. Under a staggered AB-sublattice potential, plumbene undergoes a phase transition from the spin Chern insulator with CS = 2 to a Z2 topological insulator with CS = 1.

Electronic transmission in the lateral heterostructure of semiconducting and metallic transition-metal dichalcogenide monolayers

We investigate the electronic transport property of lateral heterojunctions of semiconducting and metallic transition-metal dichalcogenide monolayers, MoSe2 and NbSe2, respectively. We calculate the electronic transmission probability by using a multiorbital tight-binding model based on the first-principles band structure. The transmission probability depends on the spin and valley degrees of freedom. This dependence qualitatively changes by the interface structure. The heterostructure with a zigzag interface preserves the spin and the valley of electrons in the transmission process. On the other hand, the armchair interface enables conduction electrons to transmit with changing the valley and increases the conductance in the hole-doped junctions due to the valley-flip transmission. We also discuss the spin and valley polarizations of electronic current in the heterojunctions.

Second highest occupied molecular orbital effects on the valence band structure of organic semiconductors

We investigate the electronic states of organic semiconductors with herringbone structures using the multi-orbital tight-binding model for highest and second highest occupied molecular orbitals (HOMOs and SHOMOs) to elucidate the effect of SHOMOs on the valence-band state. We diagonalize the Hamiltonian analytically and derive the valence band width considering hybridization of HOMO and SHOMO. It is shown that the SHOMO effect is enhanced in the condition where the sum of the intermolecular transfer integrals of HOMO-SHOMO in the sublattice and the sum between the sublattices is respectively so large that their product is not negligible compared to the energy difference between HOMO and SHOMO. We also investigate acene, phenacene and thienoacene using density functional theory. It is shown that [1]benzothieno[3,2-b][1]benzothiophene(BTBT) based materials satisfy this condition, and SHOMO contributes significantly. It implies that the origins of the high-mobility of BTBT based materials can be ascribed to the light effective mass due to the contribution of SHOMO.

Influence of edge magnetization and electric fields on zigzag silicene, germanene and stanene nanoribbons

Using a multi-orbital tight-binding model, we have studied the edge states of zigzag silicene, germanene, and stanene nanoribbons (ZSiNRs, ZGeNRs and ZSnNRs, respectively) in the presence of the Coulomb interaction and a vertical electric field. The resulting edge states have non-linear energy dispersions due to multi-orbital effects, and the nanoribbons show induced magnetization at the edges. Owing to this non-linear dispersion, ZSiNRs, ZGeNRs and ZSnNRs may not provide superior performance in field effect transistors, as has been proposed from single-orbital tight-binding model calculations. We propose an effective low-energy model that describes the edge states of ZSiNRs, ZGeNRs, and ZSnNRs. We demonstrate that the edge states of ZGeNR and ZSnNR show anti-crossing of bands with opposite spins, even if only out-of-plane edge magnetization is present. The ability to tune the spin polarizations of the edge states by applying an electric field points to future opportunities to fabricate silicene, germanene and stanene nanoribbons as spintronics devices.

An accurate and compact tight-binding model for GeS

In this work we calculate the bands structure for the GeS monolayer from a multi-orbital tight-binding model, where the effect of s-p mixing are considered in slater-Koster equations. The model parameters are adjusting and optimising compared with the band structure obtained by density-functional theory calculation based on the hybrid HSE06 functional. It reproduces the conduction and valence bands as well as the orbital compositions. The anisotropic effective masses and Fermi velocities are identified directly from the anisotropy bands structure.

Topological phases in Bi/Sb planar and buckled honeycomb monolayers

We investigate topological phases in two-dimensional Bi/Sb honeycomb crystals considering planar and buckled structures, both freestanding and deposited on a substrate. We use the multi-orbital tight-binding model and compare results with density functional theory calculations. We distinguish topological phases by calculating topological invariants, analyzing edge states properties of systems in a ribbon geometry and studying their entanglement spectra. We show that coupling to the substrate induces transition to the Z2 topological insulator phase. It is observed that topological crystalline insulator (TCI) phase, found in planar crystals, exhibits an additional pair of edge states in both energy spectrum and entanglement spectrum. Transport calculations for TCI phase suggest robust quantized conductance even in the presence of crystal symmetry-breaking disorder.

Entanglement entropy and entanglement spectrum of Bi1−xSbx (1 1 1) bilayers

We study topological properties of Bi1−xSbx bilayers in the (1 1 1) plane using entanglement measures. Electronic structures are investigated within multi-orbital tight-binding model and structural stability is confirmed through first-principles calculations. The topologically non-trivial nature of the bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum. We consider topological phase transitions driven by a composition change x, an applied external electric field in Bi bilayers and strain in Sb bilayers. Composition- and strain-induced phase transitions reveal a finite discontinuity in the entanglement entropy. This quantity remains a continuous function of the electric field strength, but shows a finite discontinuity in the first derivative. We relate the difference in behavior of the entanglement entropy to the breaking of inversion symmetry in the last case.

Charge Density Waves and the Hidden Nesting of Purple Bronze K_{0.9}Mo_{6}O_{17}.

We introduce the first multiorbital effective tight-binding model to describe the effect of electron-electron interactions in this system. Upon fixing all the effective hopping parameters in the normal state against an abinitio band structure, and with only the overall scale of the interactions as the sole adjustable parameter, we find that a self-consistent Hartree-Fock solution reproduces extremely well the experimental behavior of the charge density wave (CDW) order parameter in the full range 0<T<T_{c}, as well as the precise reciprocal space locations of the partial gap opening and Fermi arc development. The interaction strengths extracted from fitting to the experimental CDW gap are consistent with those derived from an independent Stoner-type analysis.

Stability of topological properties of bismuth (1 1 1) bilayer

We investigate the electronic and transport properties of the bismuth (1 1 1) bilayer in the context of the stability of its topological properties against different perturbations. The effects of spin–orbit coupling variations, geometry relaxation and interaction with a substrate are considered. The transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within the multi-orbital tight-binding model and density functional theory methods. A band inversion process in the bismuth (1 1 1) infinite bilayer and an evolution of the edge state dispersion in ribbons as a function of spin–orbit coupling strength are analyzed. A significant change in the orbital composition of the conduction and valence bands is observed during a topological phase transition. The topological edge states are shown to be weakly affected by the effect of ribbon geometry relaxation. The interaction with a substrate is considered for narrow ribbons on top of another bismuth (1 1 1) bilayer. This corresponds to a weakly interacting case and the effect is similar to an external perpendicular electric field. Robust quantized conductance is observed when the Fermi energy lies within the energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, scattering is possible between the channels lying close in the k-space. When the energy of the edge states overlaps the valence states, no topological protection is observed.