Nearest-neighbor Tight-binding Model Research Articles

Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge**Project supported by the National Natural Science Foundation of China (Grant Nos. 61475075 and 61170321).

Recently, an interesting family of quasiperiodic models with exact mobility edges (MEs) has been proposed (Phys. Rev. Lett. 114 146601 (2015)). It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended (localized) states in the real space to localized (extended) ones in the Fourier space. Therefore, it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively. Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.

On linear waveguides of zigzag honeycomb lattice

An analysis of the scalar linear waves in infinite honeycomb lattice strips with discrete Dirichlet and Neumann boundary conditions, as well as the periodic boundary condition, is presented for the zigzag orientation. The dispersion relations and the associated wave modes in these waveguides are provided in the paper; the former in terms of the Chebyshev polynomials. It is found that the localized propagating waves, addressed as surface wave modes, occur in case of certain boundary conditions only; for which the details are provided separately. The dispersion relations and wave modes for certain even and odd symmetry are also discussed in the paper, wherever applicable. Graphical illustrations of the dispersion curves for all waveguides are included. Applications include the transmission of phononic, electronic, magnetic, and photonic waves in nanostructures of carbon-like constituents. The analytical results are directly applicable for the out-of-plane phonons assuming only nearest-neighbor interactions in graphene nanoribbons on certain substrates, as well as the counterparts in the single orbital nearest neighbor tight-binding model for the electrons.

Third-Nearest-Neighbors Tight-Binding Description of Optical Response of Carbon Nanotubes: Effects of Chirality and Diameter

We have applied a third nearest-neighbor tight binding model to investigate the optical properties of CNTs in terms of radius, chirality and magnetic field. The optical spectrum of CNTs depends strongly on the radius and chirality in the infrared region in contrast to the middle energy region. The dependence of E22/E11 on the radius and chirality from optical peak positions and band structure is similar. In the infrared region, by applying the magnetic field, the optical peak splitting rates show well-expressed radius and chirality dependence and family behaviors.

Optimizing third-harmonic generation at terahertz frequencies in graphene

We model third-harmonic generation in doped monolayer graphene at terahertz frequencies by employing a nearest-neighbor tight-binding model in the length gauge. We show that for a given incident-field amplitude there is an optimum Fermi level that maximizes the emitted third-harmonic field. The optimum Fermi level depends very strongly on the incident-field amplitude as well as on the scattering time and increasing either enhances the third-harmonic response. We consider the general case of Fermi-level-independent scattering as well as three different scattering mechanisms that are Fermi-level dependent: phonon, long-range impurity, and short-range impurity scattering. For each case, we determine the optimal Fermi level as well as the amplitude of the optimized third-harmonic response for single-cycle incident fields with central frequencies of 1 THz and amplitudes in the range of 25--75 kV/cm. We find that although nonlinear processes beyond third order suppress third-harmonic generation, we still obtain third-harmonic amplitudes as large as 1.6% of the fundamental of the transmitted field.

The vacancy defect in graphene nano-ribbon field-effect transistor in the presence of an external perpendicular magnetic field

In this paper, we investigate effect of vacancy defect on graphene nano-ribbon field effect transistor (GNR-FET) in the presence of an external perpendicular magnetic field. Our simulation is based on Non-Equilibrium Green's Function (NEGF). The nearest neighbor tight-binding model based on pz orbital construct the device Hamiltonian. Also we calculate magnetoresistance (MR) for different position vacancies in presence B-field. We find an external B-field causes the conductance of the GNR increases, giving rise to the MR effect. The simulation results indicate in the presence of a small B-field the current is degraded because the vacancy defect act as scattering and the conductance decreases due to defects compared with the perfect nanoribbons and the MR is reduced but in the hall quantum regime the probability of being scattered by the vacancy reduced due to the electrons are more localized at edge states and this phenomena to enhance the MR ratio of the device. The results indicate that the defect near drain and near edge has the largest MR ratio in the presence of a small B-Field and in the hall quantum the defect near source has the largest MR ratio.

Nearest neighbor tight binding models with an exact mobility edge in one dimension.

We investigate localization properties in a family of deterministic (i.e., no disorder) nearest neighbor tight binding models with quasiperiodic on site modulation. We prove that this family is self-dual under a generalized duality transformation. The self-dual condition for this general model turns out to be a simple closed form function of the model parameters and energy. We introduce the typical density of states as an order parameter for localization in quasiperiodic systems. By direct calculations of the inverse participation ratio and the typical density of states we numerically verify that this self-dual line indeed defines a mobility edge in energy separating localized and extended states. Our model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry. We propose a realistic experimental scheme to realize our results in atomic optical lattices and photonic waveguides.

Inversion Symmetry and Wave-Function Nodal Lines of Dirac Electrons in Organic Conductor α-(BEDT-TTF)2I3

By examining the organic conductor α-(BEDT-TTF)2I3, which is described by a nearest neighbor tight-binding model, it is shown that, owing to inversion symmetry, each component of a wave function (WF) exhibits nodal lines (NLs) (i.e., lines in the two-dimensional Brillouin zone where the WF component vanishes). In the absence of any band crossing, each NL connects two time reversal invariant momenta (TRIMs) as partners. In the presence of a pair of Dirac points (band crossing), there are NLs that connect the pair of Dirac points via a TRIM without a partner. This second kind of NL leads to a discontinuous sign change for nonvanishing components of the WF. Such a property is the origin of the \(\pm\)π Berry phase accumulated on a contour integral encircling one Dirac point. The results are exemplified by the numerical calculation of WF components for the above conductor with a 3/4 filled band.

Chirality dependence of dipole matrix element of carbon nanotubes in axial magnetic field: A third neighbor tight binding approach

We have studied the electronic structure and dipole matrix element, D, of carbon nanotubes (CNTs) under magnetic field, using the third nearest neighbor tight binding model. It is shown that the 1NN and 3NN-TB band structures show differences such as the spacing and mixing of neighbor subbands. Applying the magnetic field leads to breaking the degeneracy behavior in the D transitions and creates new allowed transitions corresponding to the band modifications. It is found that |D| is proportional to the inverse tube radius and chiral angle. Our numerical results show that amount of filed induced splitting for the first optical peak is proportional to the magnetic field by the splitting rate ν11. It is shown that ν11 changes linearly and parabolicly with the chiral angle and radius, respectively.

Electrical design of InAs-Sb/GaSb superlattices for optical detectors using full bandstructure sp3s* tight-binding method and Bloch boundary conditions

InAs-Sb/GaSb type-II strain compensated superlattices (SLS) are currently being used in mid-wave and long-wave infrared photodetectors. The electronic bandstructure of InSb and GaSb shows very strong anisotropy and non-parabolicity close to the Γ-point for the conduction band (CB) minimum and the valence band (VB) maximum. Particularly around the energy range of 45–80 meV from band-edge we observe strong non-parabolicity in the CB and light hole VB. The band-edge dispersion determines the electrical properties of a material. When the bulk materials are combined to form a superlattice we need a model of bandstructure which takes into account the full bandstructure details of the constituents and also the strong interaction between the conduction band of InAs and valence bands of GaSb. There can also be contact potentials near the interface between two dissimilar superlattices which will not be captured unless a full bandstructure calculation is done. In this study, we have done a calculation using second nearest neighbor tight binding model in order to accurately reproduce the effective masses. The calculation of mini-band structure is done by finding the wavefunctions within one SL period subject to Bloch boundary conditions ψ(L)=ψ(0)eikL. We demonstrate in this paper how a calculation of carrier concentration as a function of the position of the Fermi level (EF) within bandgap(Eg) should be done in order to take into account the full bandstructure of broken-bandgap material systems. This calculation is key for determining electron transport particularly when we have an interface between two dissimilar superlattices.

ON THE VERDET CONSTANT AND FARADAY ROTATION FOR GRAPHENE-LIKE MATERIALS

We present a rigorous and rather self-contained analysis of the Verdet constant in graphene-like materials. We apply the gauge-invariant magnetic perturbation theory to a nearest-neighbor tight-binding model and obtain a relatively simple and exactly computable formula for the Verdet constant, at all temperatures and all frequencies of sufficiently large absolute value. Moreover, for the standard nearest-neighbor tight-binding model of graphene we show that the transverse component of the conductivity tensor has an asymptotic Taylor expansion in the external magnetic field where all the coefficients of even powers are zero.

Ferromagnetism in ABC-stacked trilayer graphene

In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electron-electron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in ABC-trilayer graphene is more robust than in monolayer, in bilayer, and in ABA-trilayer graphene. Although the screening reduces the ferromagnetic regime in ABC-trilayer graphene, the critical doping level remains one order of magnitude larger than in unscreened bilayer graphene.

Tight-binding description of Landau levels of graphite in tilted magnetic fields

The electronic structure of Bernal-stacked graphite subject to tilted magnetic fields is studied theoretically. The minimal nearest-neighbor tight-binding model with the Peierls substitution is employed to describe the structure of Landau levels. We show that, while the orbital effect of the in-plane component of the magnetic field is negligible for massive Dirac fermions in the vicinity of the K point of the graphite Brillouin zone, at the H point it leads to the experimentally observable splitting of Landau levels, which grows approximately linearly with the in-plane field intensity.

Analytical models of approximations for wave functions and energy dispersion in zigzag graphene nanoribbons

In this work, we present analytical solutions for the wave functions and energy dispersion of zigzag graphene nanoribbons. A nearest neighbor tight-binding model is employed to describe the electronic band structure of graphene nanoribbons. However, an exact analytical solution for the dispersion relation and the wave functions of zigzag nanoribbons cannot be obtained. We propose two approximations of the discrete energies, which are valid for a wide range of nanoribbon indices. Employing these models, selection rules for optical transitions and optical properties of zigzag graphene nanoribbons are studied.

Engineering enhanced thermoelectric properties in zigzag graphene nanoribbons

We theoretically investigate the thermoelectric properties of zigzag graphene nanoribbons in the presence of extended line defects, substrate impurities, and edge roughness along the nanoribbon’s length. A nearest-neighbor tight-binding model for the electronic structure and a fourth nearest-neighbor force constant model for the phonon bandstructure are used. For transport, we employ quantum mechanical non-equilibrium Green’s function simulations. Starting from the pristine zigzag nanoribbon structure that exhibits very poor thermoelectric performance, we demonstrate how after a series of engineering design steps the performance can be largely enhanced. Our results could be useful in the design of highly efficient nanostructured graphene nanoribbon–based thermoelectric devices.

ELECTRONIC STATES AND LOCAL DENSITY OF STATES NEAR GRAPHENE CORNER EDGE

We study that stability of edge localized states in semi-infinite graphene with a corner edge of the angles 60°, 90°, 120° and 150°. We adopt a nearest-neighbor tight-binding model to calculate the local density of states (LDOS) near each corner edge using Haydock's recursion method. The results of the LDOS indicate that the edge localized states stably exist near the 60°, 90°, and 150° corner, but locally disappear near the 120° corner. By constructing wave functions for a graphene ribbon with three 120° corners, we show that the local disappearance of the LDOS is caused by destructive interference of edge states and evanescent waves.

Performance Comparison of GaSb, Strained-Si, and InGaAs Double-Gate Ultrathin-Body n-FETs

Using a full-band and atomistic approach based on the nearest-neighbor tight-binding model and the nonequilibrium Green function formalism, (111)/(110) GaSb, (100)/(110) strained-Si, and (100)/(100) In0.53Ga0.47As n-type double-gate ultrathin-body field-effect transistors designed according to the ITRS specifications for 2020 are simulated in the ballistic limit of transport and with electron-phonon scattering. It is found that, at an equivalent oxide thickness of 0.59 nm, the GaSb device offers the highest ballistic ON-current at a fixed OFF-current, due to the projection to the Γ point of bands originating from the bulk L-valley and possessing a low transport effective mass. It is followed by the strained-Si FET and, finally, the In0.53Ga0.47As FET, the latter suffering from its small density of states in the channel despite very high electron velocities. However, when electron-phonon scattering is taken into account, the presence of multiple energy subbands, as in GaSb and strained Si, increases the probability of backscattering for electrons; thus, the current of these devices does not exceed that of the In0.53Ga0.47As FET by more than 13 %.

Nearly flat band with Chern numberC=2on the dice lattice

We point out the possibility of nearly flat band with Chern number C=2 on the dice lattice in a simple nearest-neighbor tightbinding model. This lattice can be naturally formed by three adjacent $(111)$ layers of cubic lattice, which may be realized in certain thin films or artificial heterostructures, such as SrTiO$_3$/SrIrO$_3$/SrTiO$_3$ trilayer heterostructure grown along $(111)$ direction. The flatness of two bands is protected by the bipartite nature of the lattice. Including the Rashba spin-orbit coupling on nearest-neighbor bonds separate the flat bands with others but maintains their flatness. Repulsive interaction will drive spontaneous ferromagnetism on the Kramer pair of flat bands and split them into two nearly flat bands with Chern number $C=\pm 2$. We thus propose that this may be a route to quantum anomalous Hall effect and further conjecture that partial filling of the C=2 band may realize exotic fractional quantum Hall effects.

Calculation of the chirality-dependent orbital magnetic anisotropy in doped semiconducting single-walled carbon nanotubes

We calculate the orbital magnetic anisotropy (Δ χ) of semiconducting single-walled carbon nanotubes at different carrier densities using a nearest-neighbor tight-binding model. Kataura plots of Δ χ exhibit 2 n + m family groupings and chiral index dependence at all carrier densities which are consistent with the trigonal warping effect. The diameter dependence of Δ χ varies strongly with carrier density. We fit our data with a symmetry-restricted model to obtain approximate analytic expressions for Δ χ as a function of nanotube chirality and carrier density. Our results illustrate the important role of doping on the magnetic properties of carbon nanotubes. Experimental studies of Δ χ should take these effects into account for accurate interpretation of their results.

Geometrical effects on the thermoelectric properties of ballistic graphene antidot lattices

The thermoelectric properties of graphene-based antidot lattices are theoretically investigated. A third nearest-neighbor tight-binding model and a fourth nearest-neighbor force constant model are employed to study the electronic and phononic band structures of graphene antidot lattices with circular, rectangular, hexagonal, and triangular antidot shapes. Ballistic transport models are used to evaluate transport coefficients. Methods to reduce the thermal conductance and to increase the thermoelectric power factor of such structures are studied. Our results indicate that triangular antidot lattices have the smallest thermal conductance due to longer boundaries and the smallest distance between the neighboring antidots. Among them, iso-triangular antidot lattices have also a large power factor and as a result a large figure of merit.

SPIN SPLITTING PROPERTIES IN GaSb Γ AND L/X-VALLEYS

The band structures of GaSb in the Γ-valley as well as L/X-valley are excellently reproduced with sp3d5s* nearest-neighbor tight-binding model. The electron spin splitting energy and the spin–orbit interaction coefficients in the Γ, L and X multi-valleys are calculated. In the Γ-valley, the results obtained are in good agreement with experimental report. We then further extend our calculations to the GaSb L- and X-valleys. We also present the results of the top three valence bands in the Γ-valley. Due to the small band offset and large difference of the density of states between Γ- and L-valleys, it is shown that even at zero electric field, there is still an explicit electron population in the L-valley. These results are important to the realization of spintronic device and the investigation of spin dynamics far away from equilibrium.