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Using first‐principles calculations, two C4N monolayers with a zigzag buckled (ZB) structure are proposed. The ZB C4N monolayers contain raised‐C (raised‐N) atoms with sp3 hybridization, different from the traditional 2D graphene‐like carbon nitride materials with sp2 hybridization. Interestingly, the band structures of the ZB C4N monolayers exhibit quasi‐1D Dirac nodal line resulting from the corresponding quasi‐1D structure of the zigzag carbon chains, which is essentially different from the conventional ring‐shaped nodal line. The quasi‐1D Dirac nodal line exhibits the following features: i) gapless Dirac points, ii) varying Fermi velocity, and iii) a slightly curved band along the high‐symmetry path. All these features are successfully explained by the proposed tight‐binding model that includes interactions up to the third nearest neighbor. The Fermi velocity of the 2D system can reach 105 m s−1, which is promising for applications in high‐speed electronic devices. The topological flat band structure of the corresponding 1D system determined by the Zak phase and band inversion is edge‐dependent, which is a weak topological state and can be explained by the 2D Su‐Schrieffer‐Heeger (SSH) model. The quasi‐1D Dirac Fermions and SSH edge states make the ZB C4N monolayers promising for nanoelectronics applications. [ABSTRACT FROM AUTHOR]

We investigate in detail the transference of quantum states in a disordered channel. We consider a one-dimensional tight-binding model consisting of a source S connected to a receiver R throughout a disordered channel. The disorder distribution contains a single tunable spatial correlation length. We demonstrate that the disorder correlation length plays a relevant role within the localization properties of the channel. The hopping parameter between the sites S and R and the channel are also adjustable parameters. We investigate the possibility of transference of quantum states along this quantum channel model and describe the optimal conditions for the occurrence of a high fidelity process. [ABSTRACT FROM AUTHOR]

A derivation of a tight-binding model from Schrödinger formalism for various topologies of position-based semiconductor qubits is presented in the case of static and time-dependent electric fields. The simplistic tight-binding model enables the description of single-electron devices at a large integration scale. The case of two electrostatically Wannier qubits (also known as position-based qubits) in a Schrödinger model is presented with omission of spin degrees of freedom. The concept of programmable quantum matter can be implemented in the chain of coupled semiconductor quantum dots. Highly integrated and developed cryogenic CMOS nanostructures can be mapped to coupled quantum dots, the connectivity of which can be controlled by a voltage applied across the transistor gates as well as using an external magnetic field. Using the anti-correlation principle arising from the Coulomb repulsion interaction between electrons, one can implement classical and quantum inverters (Classical/Quantum Swap Gate) and many other logical gates. The anti-correlation will be weakened due to the fact that the quantumness of the physical process brings about the coexistence of correlation and anti-correlation at the same time. One of the central results presented in this work relies on the appearance of dissipation-like processes and effective potential renormalization building effective barriers in both semiconductors and in superconductors between not bended nanowire regions both in classical and in quantum regimes. The presence of non-straight wire regions is also expressed by the geometrical dissipative quantum Aharonov–Bohm effect in superconductors/semiconductors when one obtains a complex value vector potential-like field. The existence of a Coulomb interaction provides a base for the physical description of an electrostatic Q-Swap gate with any topology using open-loop nanowires, with programmable functionality. We observe strong localization of the wavepacket due to nanowire bending. Therefore, it is not always necessary to build a barrier between two nanowires to obtain two quantum dot systems. On the other hand, the results can be mapped to the problem of an electron in curved space, so they can be expressed with a programmable position-dependent metric embedded in Schrödinger's equation. The semiconductor quantum dot system is capable of mimicking curved space, providing a bridge between fundamental and applied science in the implementation of single-electron devices. [ABSTRACT FROM AUTHOR]

This study investigates low‐frequency plasmons and single‐particle excitations (SPEs) in monolayer and bilayer graphene with various stacking configurations. The dynamics of wave propagation under different time‐dependent perturbation scenarios are elucidated using the random‐phase approximation dielectric function and tight‐binding Hamiltonian. The modulation of coherent excitations, particularly affecting plasmon waves, provides insights into the spatial and temporal dynamics on graphene sheets. A 2D acoustic plasmon mode is observed in monolayer graphene under extrinsic doping effects, while in bilayer graphene, it is accompanied by higher frequency optical plasmons. The predicted dynamic behavior, indicative of plasmon resonance, SPEs, and Landau damping with respect to stacking and doping effects, can be detected through ultrafast coherent dynamics observed via nanoimaging and nanospectroscopy techniques. [ABSTRACT FROM AUTHOR]

Multiaxial magnetic anisotropy (MA) refers to the phenomenon that multiple axes of the magnetic crystal correspond to different energy minima. Compared with the common uniaxial magnetic anisotropy, multiaxial MA facilitates novel forms of applications in spintronics. Here, by combining the first-principles-based spin Hamiltonian and tight-binding (TB) method, we reveal the microscopic origins, instead of the common phenomenological understanding, of biaxial MA and triaxial MA. In the example system of NiO, it is found that the multiple minima result from the fourth-order and the sixth-order single ion interactions, while the difference between [110] and [ 1 1 ¯ 0 ] directions originates from a second-order bond-dependent anisotropic pair interaction (i.e., the so-called Gamma interaction). Moreover, through the application of a newly developed general spin dependent TB approach, it is revealed that the triaxial MA arises from the special spin-orbital entangled Hund term, which is different from the orbital-independent Hund term in the usual Slater Koster TB method. Our work thus not only leads to a thorough understanding of the multiaxial MA in NiO, but also establishes a methodology that can be widely used to explore the microscopic origins of MA in different magnets. [ABSTRACT FROM AUTHOR]

Background and Objectives: Progress in the development of pulsed radiation sources with high energy density makes it possible to study the nonlinear response of condensed matter to the disturbing influence of high-intensity electromagnetic fields. To understand the processes occurring in this case, adequate models are needed that qualitatively and quantitatively reproduce the characteristics of the materials under study. In this area, graphene is considered one of the most promising materials due to the specificity of its band structure. The purpose of the work is to present and test a new model based on the quantum kinetic equation, free from restrictions on such parameters as the frequency and strength of the electric field of the disturbing influence. Materials and Method: The approach used in the work is based on the quantum kinetic equation for the distribution function of charge carriers in the state space. It makes it possible, in the one-electron approximation, to nonperturbatively reproduce the ultrafast dynamics of carriers in an external classical electric field. The system under consideration is specified by the electron dispersion law. The approach was developed and implemented for the pseudo-relativistic approximation of massless fermions, successfully used in describing the features of graphene. However, by its definition, this approximation quite accurately reproduces the real dispersion law only in the low-energy region in the vicinity of the Dirac points. Therefore, the direct use of this version of the model to describe processes in which electronic states with high excitation energies are known to participate raises questions about the accuracy of the results obtained. The problem can be resolved by moving to an exact definition of the dispersion law through the parameters of the tight-binding model of nearest neighbors in the crystal lattice of the graphene. The presented work proposes an implementation option for such a procedure and verifies the results obtained. A generalization of the formalism for a two-level system with a massless Hamiltonian of general form is used, which universally defines the explicit form of the quantum kinetic equation and expressions for macroscopic observable parameters. Results: A computational model based on the exact tight-binding model Hamiltonian has been determined, which strictly takes into account the real law of graphene dispersion in reciprocal space. The new model has been verified. For this purpose, the results of its use are compared with the results of a similar model based on the massless fermion approximation. Under conditions of limiting the parameters of the perturbing influence, ensuring the generation of excited states with only low energies in the immediate vicinity of the Dirac points, an exact coincidence has been demonstrated both at the stage of determining the values of the distribution function and for the observed parameters. It has been shown that going beyond the applicability limits of the massless fermion approximation is accompanied by the appearance of qualitative and quantitative differences in the results obtained. Conclusion: The results of the work provide new opportunities for studying the behavior of graphene under extreme conditions of strong high-frequency fields, modeling and searching for new nonlinear effects, and accurately reproducing the ultrafast quantum dynamics of its electrons for states with high energy values.

Herein, via first‐principle calculations and theoretical analysis, a new Dirac semimetal carbon system called C32, which is composed of pentagonal, hexagonal, heptagonal, and octagonal carbon rings is systematically investigated. The stability of C32 is verified by calculating the phonon dispersion, elastic constants, etc., and an appropriate pathway for experimental synthesis is proposed. Besides, it is discovered that the system holds the quadruple rotation and inversion symmetry, resulting in the emergence of eight twisted Dirac cones (D1 and D2) with a highly anisotropic Fermi velocity from 3.83 × 105 to 8.96 × 105 m s−1 along different k directions. To substantiate the semimetallic nature of C32, its nontrivial topological properties are confirmed through the presence of topologically protected edge states, and the nonzero ℤ2 topological invariant. More importantly, by introducing biaxial strain, it is uncovered that Dirac cones can gradually evolve into a nodal line, and the perfect nodal line can be obtained when the biaxial strain is 13.3%. Furthermore, by constructing the tight‐binding model, the appearance of the Dirac cone is perfectly repeated and its evolution into the nodal line under biaxial strain is explained. [ABSTRACT FROM AUTHOR]

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena. [ABSTRACT FROM AUTHOR]

We examine the impact of temperature (T) on the Seebeck coefficient S, i.e., the T dependence of S for a single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band, where the coefficient is obtained from a ratio of the thermal conductivity to the electrical conductivity. The present paper demonstrates theoretically the novel result of large anisotropy in the Seebeck coefficient components of three-dimensional Dirac electrons in a molecular conductor. The conductor exhibits a nodal line with the energy variation around the chemical potential and provides the density of states (DOS) with a minimum. Using a threedimensional tight-binding (TB) model in the presence of both impurity and electron–phonon (e–p) scatterings, we study the Seebeck coefficient Sy for the molecular stacking and the most conducting direction. The impact of T on Sy exhibits a sign change, where Sy > 0 with a maximum at high temperatures and Sy < 0 with a minimum at low temperatures. The T dependence of Sy suggests that the contribution from the conduction (valence) band is dominant at low (high) temperatures. Further, it is shown that the the Seebeck coefficient components for perpendicular directions Sx and Sz are much smaller than Sy and present no sign change, in contrast to Sy. These results are analyzed in terms of the spectral conductivity as a function of the energy ϵ close to the chemical potential μ. [ABSTRACT FROM AUTHOR]

In the realm of electronics, the performance of Silicon Trigate Rectangular Nanowires (Si-TRNW) and the structural characteristics of <001> orientation using tight-binding models have been analyzed. The fast algorithm based on the tight-binding model for Trigate Silicon nanowires yielded a remarkable ION/IOFF ratio of 1.49 × 1010 and leakage current (ILeak or IOFF) of 3.7 × 10−17μA. Furthermore, a maximum conduction band energy level (Ecmax) of −0.003 eV and a Subthreshold Slope (SS) of 120 mV has been obtained for a channel length of 15 nm. At an energy level of 3 eV, a high Transmission coefficient, T(ε), of 4 has been attained using the E-k dispersion method. This analysis also involved the calculation of three ∆ valleys pertinent to the channel's effectiveness in <001> orientation, with proximity nearer to 1 m0. The Schrodinger-Poisson equation has been analyzed with the Ballistic transport along the [001] z-direction in channel potential. A comparative assessment has been also performed between the lateral dimensions of rectangular nanowires with equal energy levels, utilizing both the tight-binding model and Density Functional Theory (DFT) techniques. In some high-frequency applications, a high transmission coefficient is beneficial to maximize the amount of energy or information that gets transmitted. Reducing leakage current would offer a technological pathway for performance improvement of high-frequency applications. The high ON-current (ION) has been obtained through the DFT approach between source and drain terminals is particularly desirable for applications demanding for fast switching speeds and high-performance computing. The strengths of both methods in hybrid approaches is a common strategy to achieve simulations that are both accurate and efficient. Notably, the nanowires subjected to hydrostatic strain, exhibiting enhanced mobility and exceptional electrostatic integrity, emerged as pivotal components for forthcoming technology nodes. This research augments the potential feasibility of strain-based Si nanowires, even at the 3 nm scale, in subsequent technological advancements. [ABSTRACT FROM AUTHOR]

The optical properties and Landau quantisations in twisted bilayer graphene are investigated using a generalised tight-binding model that takes into account all interlayer and intralayer atomic interactions in the Moire superlattice. The system is a zero-gap semiconductor with double-degenerate Dirac-cone structures, and saddle-point energy dispersions appear at low energies for small twisting angles. The magnetic quantisation phenomena in this system are rich and unique, with Landau-level subgroups specified owing to specific Moire zone folding through modulation of the stacking angles. The Landau-level spectrum shows hybridised characteristics associated with those in monolayer, as well as AA and AB stackings. The detailed analysis explores the complex relations among the different sublattices on the same and different graphene layers. [ABSTRACT FROM AUTHOR]

In this paper, we study the electrical conductance of a molecular bridge consisting of a graphyne ring with the chemical formula C18H6 connected to two cumulene electrodes using the tightbinding model. We then compare its conductance to a similar system in which the graphyne ring has been replaced by a benzene molecule. To do this, we first obtain the structural characteristics of the studied rings using density functional theory, and then use the method of matching levels, to obtain the tight-binding parameters, i.e., the on-site and hopping energies for the benzene and graphyne rings. Using these parameters, we study the electrical conductance for these two molecules, the benzene and the graphyne rings. We conclude that when these two molecules are in the same position between two cumulene electrodes, they exhibit the same electrical properties. However, in the graphyne ring, a phase transition from metal to semiconductor or vice versa can be created with less energy than in a benzene ring. [ABSTRACT FROM AUTHOR]

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.

Abstract The acoustic response of defect‐based acoustic interferometer‐like designs, known as Coupled Resonator Acoustic Waveguides (CRAWs), in 2D phononic crystals (PnCs) is reported. The PnC is composed of steel cylinders arranged in a square lattice within a water matrix with defects induced by selectively removing cylinders to create Mach‐Zehnder‐like (MZ) defect‐based interferometers. Two defect‐based acoustic interferometers of MZ‐type are fabricated, one with arms oriented horizontally and another one with arms oriented diagonally, and their transmission features are experimentally characterized using ultrasonic spectroscopy. The experimental data are compared with finite element method (FEM) simulations and with tight‐binding (TB) calculations in which each defect is treated as a resonator coupled to its neighboring ones. Significantly, the results exhibit excellent agreement indicating the reliability of the proposed approach. This comprehensive match is of paramount importance for accurately predicting and optimizing resonant modes supported by defect arrays, thus enabling the tailoring of phononic structures and defect‐based waveguides to meet specific requirements. This successful implementation of FEM and TB calculations in investigating CRAWs systems within PnCs paves the way for designing advanced acoustic devices with desired functionalities for various practical applications, demonstrating the application of solid‐state electronics principles to underwater acoustic devices description.

Keldysh nonequilibrium diagram technique is used for a detailed description of electron transport through a system of tightly bound spatially separated localized states. Particular attention is paid to the predictive ability of the effective theory, for which the number of free parameters in the second-quantized Hamiltonian is reduced. The employed formalism in a variant of tight-binding model rigorously treats multi-electron tunneling effects and the discreteness of the energy spectra in low-dimensional structures. The model is also extended with Coulomb interaction of moderate strength. Proposed algorithm for calculating electric currents and occupation numbers of localized states in presence of weak Coulomb repulsion is implemented in software and tested on a model system of two consecutive three-level quantum dots. Electron transfer proceeds both sequentially between the dots and in parallel within each quantum dot. The calculated IV-curve and current stability diagram are intuitively explained using coordination energy diagrams. The model qualitatively reproduces typical effects in interference-based nanoelectronics: resonant tunneling, negative differential resistance, population inversion in a multi-level system. The impact of moderate Coulomb correlations on current stability diagram is examined. This demonstrates the capability of extended tight-binding model to incorporate weak Coulomb interaction into the description of electronic transport via discrete quantum states. [ABSTRACT FROM AUTHOR]

The electronic and transport properties of the zigzag and armchair borophene nanoribbons β12 with different edge geometries using the multi-band tight-binding model and Landauer Butticker formalism were investigated by the mode matching model. Our results show that nanoribbons with different edge geometries show different electronic behaviors from metal phase to semiconductor according to and under thermal gradient or voltage poetical produce electrical current from nano ampere to microampere (most of them have ohmic behavior). Also, vacancy defects with controlling energy gaps could change the phase from metal to semiconductor or from semiconductor to metal in different edge geometries. Moreover, vacancy defects could control the values of electrical currents. Finally, the edge geometries; and defect engineering with application thermal gradient or electrostatic potential could control the electronic and transport properties and convert borophene nanoribbons into a good candidate for application in nano-electronic devices.

We examine the impact of temperature (T) on the Seebeck coefficient S, i.e., the T dependence of S for a single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band, where the coefficient is obtained from a ratio of the thermal conductivity to the electrical conductivity. The present paper demonstrates theoretically the novel result of large anisotropy in the Seebeck coefficient components of three-dimensional Dirac electrons in a molecular conductor. The conductor exhibits a nodal line with the energy variation around the chemical potential and provides the density of states (DOS) with a minimum. Using a threedimensional tight-binding (TB) model in the presence of both impurity and electron–phonon (e–p) scatterings, we study the Seebeck coefficient Sy for the molecular stacking and the most conducting direction. The impact of T on Sy exhibits a sign change, where Sy > 0 with a maximum at high temperatures and Sy < 0 with a minimum at low temperatures. The T dependence of Sy suggests that the contribution from the conduction (valence) band is dominant at low (high) temperatures. Further, it is shown that the the Seebeck coefficient components for perpendicular directions Sx and Sz are much smaller than Sy and present no sign change, in contrast to Sy. These results are analyzed in terms of the spectral conductivity as a function of the energy ϵ close to the chemical potential μ.

This investigation was originally designed to verify that the tight-binding approach utilizes an amalgamation of estimated wave functions to compute the electrical band structure. Utilizing computational tools has become essential, especially for challenging and dull problems in physics. Computer programs, in general, once utilized in the approved manner, allow physical problems to be solved and explained rapidly and efficiently at the same time. The case then is to comprehend how to swap from the abstract equations to the computer program, i.e., codes. In this research, valid and numerical strategies are utilized to examine the electrical characteristics of 2D crystals through fluctuating geometries and magnetic fields. Certainty in the mathematical model is based upon those assessments of the two procedures utilizing the dispersal relationship and density of states. The numerical strategies become the importance as the examined systems goes into more complex to be investigated precisely. Throughout this study, it is confirmed that the tight-binding model utilizes a superposition of estimated wave functions to estimate the electrical band structure. This model was showed to a four-sided network and a hexagonal network to confirm the characteristics of electrons as they move over the graphene network. Particularly, this setup provides a way of investigating energy-reliant transport in graphene. The outcomes of this investigation are significant since the energy dependance of transport in mesoscopic graphene is the core of numerous odd transportation occurrences. Also, the conductance for the four-sided framework is considered utilizing the mathematical approaches and shows the accurate appearances for the quantum Hall effect.

Dispersion associated with the complex band structure of a periodic potential can be used to explain single-electron wave packet tunneling through a finite-sized tunnel barrier. The imaginary k-space dispersion in a tunnel barrier may be viewed as a filter that controls the arrival time, shape, and group velocity of a transmitted wave packet. This k-space filter can be designed to increase or decrease the group velocity of the transmitted pulse and a transmitted peak-pulse probability arrival time can be engineered to occur before or after that of an electron wave packet propagating in the absence of the tunnel barrier.

It has recently been demonstrated how the nitrogen dopant concentration in graphene can be controlled spatially on the nano-meter scale using a molecular mask. This technique may be used to create ballistic electron optics-like structures of high/low doping regions; for example, to focus electron beams, harnessing the quantum wave nature of the electronic propagation. Here, we employ large-scale Greens function transport calculations based on a tight-binding approach. We first benchmark different tight-binding models of nitrogen in graphene with parameters based on density functional theory (DFT) and the virtual crystal approximation (VCA). Then, we study theoretically how the random distribution within the masked regions and the discreteness of the nitrogen scattering centers impact the transport behavior of sharp n − p and n − n ′ interfaces formed by different, realistic nitrogen concentrations. We investigate how constrictions for the current can be realized by patterned high/low doping regions with experimentally feasible nitrogen concentrations. The constrictions can guide the electronic current, while the quantized conductance is significantly washed out due to the nitrogen scattering. The implications for device design is that a p − n junction with nitrogen corrugation should still be viable for current focusing. Furthermore, a guiding channel with less nitrogen in the conducting canal preserves more features of quantized conductance and, therefore, its low-noise regime. [ABSTRACT FROM AUTHOR]

Herein, the spin‐polarized edge‐state transport properties in L‐shaped zigzag MoS2$\left(\text{MoS}\right)_{2}$ nanodevice (L-zMoS2ND$\left(\text{L�?zMoS}\right)_{2} \text{ND}$) are investigated based on tight‐binding model, Green's function method, and ballistic transport theory. The spin conductance and spin polarization are calculated by considering external exchange field and electric field. It is shown in the results that the spin conductance is closely related to the configuration of atomic non‐consistence on the edge of L-zMoS2ND$\left(\text{L�?zMoS}\right)_{2} \text{ND}$. Meanwhile, the spin conductance is determined by the spin channel opening on the edge, which can be modulated by external fields. The configuration characteristic and external fields give rise to effects of sublattice mismatch and spin mismatch on the edge channels, respectively. As a consequence, mismatch effects are actually employed to modulate the spin channel on the edge of L-zMoS2ND$\left(\text{L�?zMoS}\right)_{2} \text{ND}$, and 100% spin polarization is realized selectively. Moreover, the corresponding local density of states distributions are plotted to reveal the modulation of the spin‐resolved edge‐state and the spin‐filtering effects in the real space. These spin‐polarized edge‐state transport properties in L-zMoS2ND$\left(\text{L�?zMoS}\right)_{2} \text{ND}$ can have potential application in various kinds of spin valves and spin filters in nanocircuits. [ABSTRACT FROM AUTHOR]

Single-component molecular conductors exhibit a strong connection to the Dirac electron system. The formation of Dirac cones in single-component molecular conductors relies on (1) the crossing of HOMO and LUMO bands and (2) the presence of nodes in the HOMO–LUMO couplings. In this study, we investigated the possibility of Dirac cone formation in two single-component molecular conductors derived from nickel complexes with extended tetrathiafulvalenedithiolate ligands, [Ni(tmdt)2] and [Ni(btdt)2], using tight-biding models and first-principles density-functional theory (DFT) calculations. The tight-binding model predicts the emergence of Dirac cones in both systems, which is associated with the stretcher bond type molecular arrangement. The DFT calculations also indicate the formation of Dirac cones in both systems. In the case of [Ni(btdt)2], the DFT calculations, employing a vdW-DF2 functional, reveal the formation of Dirac cones near the Fermi level in the nonmagnetic state after structural optimization. Furthermore, the DFT calculations, by utilizing the range-separated hybrid functional, confirm the antiferromagnetic stability in [Ni(btdt)2], as observed experimentally. [ABSTRACT FROM AUTHOR]

ABSTRACT: The discovery of graphene has led to the devotion of intensive efforts, theoretical and experimental, to produce two-dimensional (2D) materials that can be used for developing functional materials and devices. This work provides a brief review of the recent developments in the lattice models of 2D Dirac materials and their relevant real material counterparts that are crucial for understanding the origins of 2D Dirac cones in electronic band structures as well as their material design and device applications. We focus on the roles of lattice symmetry, atomic orbital hybridization, and spin–orbit coupling in the presence of a Dirac cone. A number of lattice models, such as honeycomb, kagome, ruby, star, Cairo, and line-centered honeycomb, with different symmetries are reviewed based on the tight-binding approach. Inorganic and organic 2D materials, theoretically proposed or experimentally synthesized to satisfy these 2D Dirac lattice models, are summarized.

The process of synthesis of CuAu nanoclusters from a high-temperature gas phase was simulated. The molecular dynamics method was used. 91124 Cu and Au atoms were used as the initial configuration. The atoms were arranged randomly in space, the average distance between them was 30 Bohr radii. The set of parameters was chosen in such a way as to simulate the conditions of the inert gas condensation. This system was cooled with a thermal energy removal rate of 108 K/s. Based on the data obtained, conclusions were drawn about the main stages of the evolution of the model system. It is shown that the initial stage of synthesis consists of five different stages, which gradually lead to the formation of primary spherical nanoparticles of the CuAu binary alloy. At the final stage, the eventual transformation of the formed primary nanoparticles takes place. The initial atomic atmosphere almost completely disappears and spherical binary nanoparticles are formed, a characteristic feature of which is the displacement of gold atoms to the surface.

The article considers the process of formation of binary Cu-Au nanoclusters with different target composition from a high-temperature gaseous medium. The molecular dynamics method was used. The main attention was paid to studying formation of the crystal structure in such clusters and determination its type. It is shown that an increase in the percentage of gold atoms in the primary gaseous medium significantly affects the formation of the internal structure of simulated nanoparticles. With a relatively small increase in the proportion of gold atoms, there is a complete disappearance of clusters with the fcc structure. The formation of nanoparticles with, as a rule, five-particle symmetry is observed. In this case, the Dh configuration prevails. If both precursors are evaporated at the same rate, then an increase in the percentage of gold atoms in the gas mixture leads to the fact that CuAu clusters are often unable to form any clearly distinguishable crystalline form, due to which approximately every fourth cluster was fixed in the amorphous state. We concluded that the cause of this phenomenon may be the separation of atoms of different types, which is typical for binary nanoparticles of the studied chemical composition.

We present a tight-binding (TB) model for describing the electronic properties of the free-standing χ3 and β12 borophenes via the Slater–Koster approach. This model is constructed through s, px, py, and pz orbitals for each boron atom. The optimal Hamiltonian plus the overlap matrix are calculated by fitting the results of the TB model and density functional theory calculations using the least-squares method and the Levenberg–Marquardt nonlinear fitting algorithm. Considering three nearest-neighbors and a non-orthogonal basis set, this TB model accurately describes energy bands around high-symmetry k-points. [ABSTRACT FROM AUTHOR]

The study of topological semimetals has been extended to more general topological nodal systems such as metamaterials and artificial periodic structures. Among various nodal structures, triply degenerate nodal line (TDNL) is rare and, hence, has received little attention. In this work, we have proposed a simple tight-binding (TB) model, which hosts a topological non-trivial TDNL. This TDNL not only has the drumhead surface states (DSSs) as usual nodal line systems but also has surface states that form a contracted-drumhead shape. The shape and area of this contracted drumhead can be tuned by the hopping parameters of the model. This provides an effective way to modulate surface states and their density of states, which can be important in future applications of topological nodal systems.

The symmetry of twisted bilayer graphene (tBG) has been extensively studied in the continuum model but somewhat overlooked in the tight-binding (TB) framework. In contrast to the continuum model, which requires operators for both sublattice and layer spaces, the TB framework relies solely on operators in real space. This paper begins by discussing the symmetries of the TB Hamiltonian and the single-valley TB Hamiltonian of tBG. Subsequently, the band structures with specific irreducible representations (irreps) are obtained by diagonalizing the irrep-dependent Hamiltonian constructed through projection operators. We also investigate the impact of symmetry on intervalley coupling and the influence of a non-zero mass term on the $C_{2z}T$ symmetry of the single-valley Hamiltonian. To understand the irrep change as the wavevector moves inside the Brillouin zone and the irrep change after considering the intervalley coupling or introducing a non-zero mass term at a fixed wavevector, we derive two kinds of compatibility relationships. The methodology presented here can be applied to other layered materials because the basis functions we employ are generic and unique to twisted bilayers.

Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other methods for inducing somewhat localized states in elementary lattice models have been historically much less studied. Here we show how edge states can emerge within a simple two-leg ladder of coupled harmonic oscillators, where it is important to include interactions beyond those at the nearest neighbor range. Remarkably, depending upon the interplay between the coupling strength along the rungs of the ladder and the next-nearest neighbor coupling strength along one side of the ladder, edge states can indeed appear at particular energies. In a wonderful manifestation of a type of bulk-edge correspondence, these edge state energies correspond to the quantum number for which additional stationary points appear in the continuum bandstructure of the equivalent problem studied with periodic boundary conditions. Our theoretical results are relevant to a swathe of classical or quantum lattice model simulators, such that the proposed edge states may be useful for applications including waveguiding in metamaterials and quantum transport.

Computational modules were developed to numerically determine electronic band structures, berry curvatures, Chern numbers, localization lengths, and critical exponents for tight- binding and related models. These modules were applied to a variety tight-binding and related models including the Hofstadter Model, Anderson Model, and the Chalker- Coddington model. When analytic solutions were available, numeric energy bands agreed with analytic solutions to within machine precision. In addition Chern numbers for well known models were reproduced, and localization lengths and critical exponents agreed with values in the literature.

Despite the simplified fabrication process and desirable microstructural stability, the limited charge transport properties of block copolymers and double-cable conjugated polymers hinder the overall performance of single-component photovoltaic devices. Based on the key distinction in the donor (D)-acceptor (A) bonding patterns between single-component and bulk heterojunction (BHJ) devices, rationalizing the difference between the transport mechanisms is crucial to understanding the structure-property correlation. Herein, the barrier formed between the D-A covalent bond that hinders electron transport in a series of single-component photovoltaic devices is investigated. The electron transport in block copolymer-based devices is strongly dependent on the electric field. However, these devices demonstrate exceptional advantages with respect to the charge transport properties, involving high stability to compositional variations, improved film uniformity, and device reproducibility. This work not only illustrates the specific charge transport behavior in block copolymer-based devices but also clarifies the enormous commercial viability of large-area single-component organic solar cells (SCOSCs). [ABSTRACT FROM AUTHOR]

The framework of the tight-binding model and Green's function formalism have been derived to investigate the electronic properties of few-layer T-graphene nanoribbons (TGNRs) with different edges including zigzag, bearded, and armchair TGNR (zTGNR, bTGNR, and aTGNR) and the results are compared with those of monolayers. It was observed that single-layer zTGNRs and bTGNRs with metallic properties retain this characteristic as the number of layers increases. In addition, by virtue of their mirror symmetry, aTGNR monolayers exhibit metallic and semiconducting properties by even and odd widths, respectively. When layers are added, symmetric aTGNRs display metallic behavior, while asymmetric aTGNRs display metallic and semiconducting characteristics, depending on the layer stacking. It is also found that the band structure of symmetric aTGNRs and metallic few-layer asymmetric aTGNRs contain Dirac points which increase with increasing their width and layers. [ABSTRACT FROM AUTHOR]

Using the Landauer–Buttiker formalism and the nonorthogonal tight-binding Hamiltonian with NTBM parametrization, the electron transmission and conductivity of metal armchair-type nanotubes of subnanometer diameter are studied. We consider the effect of various structural defects (Stone–Wales defect, monovacancy, replacing a nitrogen atom) and radicals adsorbed on the nanotube surface (H, O, OH, COOH) on the electronic characteristics of carbon nanotubes (CNTs). It is found that structural defects and adsorbates have different effects on their conductivity. In this case, two competing processes are observed. On the one hand, this is a weakening of the conductive properties of CNTs due to the increase in the number of scattering centers, and, on the other hand, the increase in conductivity due to structural relaxation processes. [ABSTRACT FROM AUTHOR]

The topological properties of the square–hexagon lattice are studied when the time‐reversal (TR) symmetry is broken. Based on the Chern number and spin Chern number, the topological trivial and nontrivial phases can be determined. When the spin‐dependent and ‐independent staggered potentials are taken into consideration, rich phase diagrams are obtained. A number of topological nontrivial phases, including the TR‐symmetry‐broken quantum spin Hall phase and quantum anomalous Hall (QAH) phase, can be achieved by tuning the spin‐dependent staggered potential. When the spin‐independent staggered potential is varied, it is possible to observe the topological phase transition from the metal phase to the QAH phase. The evolutions of the bulk bandgap and spin spectrum gap are also presented together. To support the identification of the topological phases, helical and chiral edge states are given numerically. Moreover, the corresponding density distribution and spin polarization are analyzed and discussed. [ABSTRACT FROM AUTHOR]

The electronic properties of Carbon based nanomaterials have been attracted the attention of the scientific community for decades. The structural details of these systems are of fundamental importance to describing their properties. With the objective of offering a fundamental review that allows entry into research areas related to nanoscience, this work is dedicated to investigating the electronic properties of one-dimensional physical systems in a systematic and pedagogical way. We use a simple Tight - Binding model to obtain the band structure of these systems and describe their electronic behavior. At first, we describe the methodology used, demonstrating its simplicity for understanding introductory concepts in nanoscience. Then, we determine the energy band of a linear chain of atoms, considering only one site per unit cell. In order to offer an extrapolation of this system, we apply our model to Graphene and Boron Nitride nanoribbons, which can be interpreted as the interpenetration of linear chains, displaying N sites per unit cell. Finally, despite the simplicity of the proposed model, we demonstrate that the presented calculations show consistency with more robust formalisms, such as the DFT. [ABSTRACT FROM AUTHOR]

We applied a one-dimensional tight-binding model to the study electron transport in a ferromagnetic metal-insulatorferromagnetic metal junction. We included a small external magnetic field perpendicular to the one-dimensional chain as a Zeeman Effect on electron spins. We obtained the transmission and reflection probabilities of an electron across the junction and used them to calculate its tunneling magnetoresistance. We found that the magnetoresistance ratio increases with the insulating gap of the insulator. The variation of the insulator thickness gives an oscillating behavior of the ratio. Our theoretical model predicts the right trend of the magnetoresistance on the thickness, and also indicates that at a certain thickness the maximum magnetoresistance ratio occurs.

• This study conducted the bandgap modulation of bilayer two-dimensional binary materials at high symmetry stackings. • We present the general trend of bandgap modulation through the tight-binding model. • It is found computationally that the bandgap modulation mechanism can be utilized to control the transmission characteristics of devices constructed from bilayer 2D materials. The interlayer interactions in layered two-dimensional materials, which are formed by Van der Waals forces, significantly influence the control of electronic and transport properties. The manipulation of the stacking order can modulate these interlayer interactions by altering the atomic arrangement in different layers. In this study, we conducted a systematic examination of the bandgap modulation of bilayer two-dimensional binary materials at high symmetry stackings. A general trend of bandgap modulation has been proposed through a tight-binding model and corroborated by density functional calculations. The mechanisms of bandgap modulation can be leveraged to control the transport properties of devices built with bilayer two-dimensional binary materials. Our research findings offer valuable insights for the control of bandgap in layered two-dimensional materials and their application in transport devices. [ABSTRACT FROM AUTHOR]

Abstract Despite the simplified fabrication process and desirable microstructural stability, the limited charge transport properties of block copolymers and double‐cable conjugated polymers hinder the overall performance of single‐component photovoltaic devices. Based on the key distinction in the donor (D)–acceptor (A) bonding patterns between single‐component and bulk heterojunction (BHJ) devices, rationalizing the difference between the transport mechanisms is crucial to understanding the structure–property correlation. Herein, the barrier formed between the D–A covalent bond that hinders electron transport in a series of single‐component photovoltaic devices is investigated. The electron transport in block copolymer‐based devices is strongly dependent on the electric field. However, these devices demonstrate exceptional advantages with respect to the charge transport properties, involving high stability to compositional variations, improved film uniformity, and device reproducibility. This work not only illustrates the specific charge transport behavior in block copolymer‐based devices but also clarifies the enormous commercial viability of large‐area single‐component organic solar cells (SCOSCs).

The flourishment of non-Hermitian topology has promoted the development of skin effect, a well-known feature of the non-Hermitian systems, by which the bulk states evolve from extended to localized toward boundaries. However, in previous works, the scenarios are usually delicately designed with intricate parameters to explore the skin effects. In this work, we propose a simple paradigm to implement tunable non-Hermitian skin effects in one and two-dimensional Su-Schrieffer-Heeger (SSH)-like tight-binding models. Skin modes with distinct dimensions can be predicted irrespective of the non-Hermitian systems are topological or not. They also have no relations with the coupling values, but only are dependent on the scaling factors of non-reciprocal hopping terms. Furthermore, by engineering the hopping configurations, the skin modes could be predicted at expected edges or corners, featuring skin effects hierarchical. These tunable non-Hermitian skin effects and higher-dimensional non-Hermitian skin effects can be exploited to guide waves into targeted regions and may have useful applications when realized in metamaterials.

A tight-binding theoretical model which describes the vibration properties of a new type of mechanical metamaterial, the coupled-resonator phononic metamaterial (CRPM), is developed. This metamaterial, composed of mechanical resonators coupled through finite phononic crystals, exhibits spectral properties analogue to those of crystalline atomic systems. The CRPMs obey a quantum tight-binding model when a normal mode frequency of the resonators lies within a bandgap of the finite phononic crystals. Analytical expressions for the dispersion relation and group velocity are obtained. The results suggest that almost any material described by the tight-binding model, of solid-state physics, can be emulated with CRPMs. [ABSTRACT FROM AUTHOR]

In this work, we investigated the effects of the magnetic field on the electronic properties, thermal conductivity and heat capacity of biased bilayer boron phosphide (2L-BP) with B = B and B = P stacking types, using the tight-binding model. The magnetic field splits the density of states (DOS) peaks and significantly changes the DOS peak positions. Both bias voltage and magnetic field decrease the band gap in a linear pattern until it reaches zero and semiconductor-metallic transition occurs. The thermal properties of 2L-BP reduce to zero in the low-temperature range TZ due to the nonzero band gap, and above the TZ region, the thermal properties increase with increasing the temperature. In the presence of the stronger external fields, the thermal properties have higher intensity with more sensitivity to the magnetic field. The thermal properties of 2L-BP with B = B stacking type are larger than that of B = P stacking type, and both cases are more sensitive to the magnetic field than the bias voltage. [ABSTRACT FROM AUTHOR]

Tight-binding models represent one of the basic approaches for studying the topological states of a matter. In the given account, we consider a tight-binding model set by a matrix Hamiltonian over 2D Brillouin zone. The corresponding multiband energy spectrum gives rise to non-Abelian gauge construction formed by the non-Abelian Berry connection A μ . The main gauge invariant quantities in such cases are the eigenvalues of Wilson loops. The purpose followed is the search for any special (on top of general) properties of Wilson loops for 2D tight-binding models which impose certain restrictions on the structure of its eigenvalues. The non-Abelian Berry connection is shown to be pure gauge with point-like singularities. The corresponding curvature tensor F μ ν = ∂ μ A ν − ∂ ν A μ + i [ A μ , A ν ] vanishes throughout the Brillouin zone except the isolated points where F μ ν is singular. Combining such behavior of F μ ν with non-Abelian Stokes theorem allows to avoid the path-ordering procedure in calculating the Wilson loops. In this approach, we show that Wilson loops are endowed by the group structure isomorphic to the fundamental group of the Brillouin zone. The latter is the Abelian group Z × Z forcing the set of eigenvalues of Wilson loops to comprise of two fixed phases associated with the two primitive elements (generators) of Z × Z. [ABSTRACT FROM AUTHOR]