AN APPROACH BASED ON LANDAUER–BÜTTIKER FORMALISM TO COMPUTE THE ELECTRONIC LOCALIZED STATES AT SURFACE BOUNDARIES

2019 ◽  
Vol 27 (06) ◽  
pp. 1950164
Author(s):  
ADEL BELAYADI
Keyword(s):  
Tight Binding ◽  
Three Dimensional ◽  
Surface States ◽  
Relaxation Effect ◽  
Matching Theory ◽  
Localized States ◽  
Hamiltonian Matrix ◽  
Inhomogeneous System ◽  
Tight Binding Approximation ◽  
Characteristic Features

In this contribution, we provide a theoretical model to study the effect of different cutting edges on the appearance of localized electronic states. The system under study is a three-dimensional atomic chain that ends with an open cut forming a semi-infinite structured layer in the (1 0 0), (1 1 0) and (1 1 1) directions. We investigate the surface electronic characteristics of the monoatomic chain of a simple cube (sc), orthorhombic (orth), and tetragonal (tetr) structures. We have adopted in our approach the tight-binding approximation to build up the surface Hamiltonian matrix. Additionally, the number of secular equation, at the surface, has been determined by using phase field matching theory (FPMT). In fact, the Hamiltonian system obtained from different cutting orientations provides an inhomogeneous system. To solve the surface eigenvalue problem, we integrate the calculation of the scattering reflection probabilities as given in Landauer–Büttiker formalism. Next, based on the computed scattering probabilities, we build up the surface core states which provide the surface Hamiltonian matrix which can be solved numerically. Our model calculation has been applied to the following elements: (i) fluorite (F), manganese (Mn), polonium (Po), bromine (Br), indium (I), tin (Sn), and protactinium (Pa). The results emphasize the influence of cutting direction on the electronic characteristic of surface and on the scale of energy values. We report the appearance of new electronic curves that characterize the surface states. Those surface states are localized down, within, and above the bulk spectrum. They also provide different characteristic features, of the metals under study, in a given cutting orientation. Furthermore, we have integrated the calculation of non-structured cuts on the outer layers. The relaxation effect on the surface is a standard process which leads to stabilize the changes in the internal energy until the equilibrium. The spacing geometry caused by the relaxation on the surface could be determined by using the molecular dynamic algorithm. We account in this case the lift of degeneracy and the rise of additional localized branches within and outside the bulk range.

Computing the surface electronic states on the (100), (110) and (111) surfaces of FCC monatomic crystals

2021 ◽  
pp. 2150066
Author(s):  
Boualem Bourahla ◽  
Adel Belayadi
Keyword(s):  
Tight Binding ◽  
Relaxation Effect ◽  
Localized States ◽  
Quantum Scattering ◽  
Hamiltonian Matrix ◽  
Face Centered Cubic ◽  
Surface Band ◽  
Text Type ◽  
Scattering Coefficients ◽  
The Impact

In this study, we carry out a simulation of the surface band structures for face-centered cubic (fcc) leads that end up in (100), (110) and (111) surfaces. The surface Hamiltonian matrix is constructed from tight-binding approach and the secular equations of the surface eigenvalue problem. The solution of the problem is performed by integrating the Landauer–Büttiker formalism (LBF) in the phase field matching approach (PFMA). The LBF provides the quantum scattering properties and the PFMA connects the bulk modes to those of the surface based on the quantum scattering coefficients. The combination of these methods allows calculating the electronic bands in the three directions mentioned above. We report the results of ordered slabs for Ag, described as [Formula: see text]-like orbital and Ni given as [Formula: see text]-type orbitals. To show the impact of expanding the crystal wavefunction, we reveal the calculation of the localized states for Rh, Cu, Pt given as [Formula: see text]-type orbitals as first calculation then [Formula: see text]-coupling orbitals as second calculation. The results of the nonordered slabs are applied to Pd and Ir. Cutting the crystals affects the internal energy of the surface atoms, which will be subject to a relaxation effect until equilibrium is achieved.

Luminescent Amorphous Silicon Layers

1997 ◽  
Vol 486 ◽  
Author(s):  
G. Allan ◽  
C. Delerue ◽  
M. Lannoo
Keyword(s):  
Electronic Structure ◽  
Amorphous Silicon ◽  
Radiative Recombination ◽  
Crystalline Silicon ◽  
Tight Binding ◽  
Blue Shift ◽  
Localized States ◽  
Structure Model ◽  
Radiative Recombination Rate ◽  
Tight Binding Approximation

AbstractThe electronic structure of amorphous silicon layers has been calculated within the empirical tight binding approximation using the Wooten-Winer-Weaire atomic structure model. We predict an important blue shift due to the confinement for layer thickness below 3 nm and we compare with crystalline silicon layers. The radiative recombination rate is enhanced by the disorder and the confinement but remains quite small. The comparison of our results with experimental results shows that the density of defects and localized states in the studied samples must be quite small.

Topological phases of a three-dimensional topological insulator with structure inversion asymmetry

2015 ◽  
Vol 29 (06) ◽  
pp. 1550034 ◽  
Author(s):  
Xiaoyong Guo ◽  
Zaijun Wang ◽  
Qiang Zheng ◽  
Jie Peng
Keyword(s):  
Phase Diagram ◽  
Topological Insulator ◽  
Tight Binding ◽  
Three Dimensional ◽  
Surface States ◽  
Topological Phases ◽  
Zeeman Field ◽  
Surface Modes ◽  
Inversion Asymmetry ◽  
Structure Inversion

We investigate the topological phases of a three-dimensional (3D) topological insulator (TI) without the top–bottom inversion symmetry. We calculate the momentum depended spin Chern number to extract the phase diagram. Various phases are found and we address the dependence of phase boundaries on the strength of inversion asymmetry. Opposite to the quasi-two-dimensional thin film TI, in our 3D system the TI state is stabilized by the structure inversion asymmetry (SIA). With a strong SIA the 3D TI phase can exist even under a large Zeeman field. In a tight-binding form, the surface modes are discussed to confirm with the phase diagram. Particularly we find that the SIA cannot destroy the surface states but open a gap on its spectrum.

LOCALIZED ELECTRONIC SURFACE STATES IN METALLIC STRUCTURES

2018 ◽  
Vol 25 (05) ◽  
pp. 1850101 ◽  
Author(s):  
A. BELAYADI ◽  
B. BOURAHLA ◽  
F. MEKIDECHE-CHAFA
Keyword(s):  
Interatomic Potential ◽  
Atomic Orbital ◽  
Tight Binding ◽  
Surface States ◽  
Localized States ◽  
High Symmetry ◽  
Metallic Structures ◽  
Text Type ◽  
Type Orbital ◽  
Electronic Surface

We present theoretical models to study the localized electronic surface states in metallic structures. The materials under study have been chosen with different types of cubic meshes, fcc, sc and bcc. The calculation method used is closely related to the Linear Combination of Atomic Orbitals (LCAO) in the tight-binding method. We consider three cases: each of the atoms is described by a single atomic orbital of [Formula: see text]-, [Formula: see text]- and [Formula: see text]-type orbitals. In order to solve the rectangular secular equations of the systems under study, the phase field matching method is involved. In particular, we apply our approach to calculate the localized electronic surface states of some metals: (i) Chromium and Silver having, respectively, bcc and fcc structure and described as [Formula: see text]-type orbital. (ii) Nickel with sc crystallization and described by [Formula: see text]-type orbital. (iii) Palladium (Pd) given in fcc crystallization and described by [Formula: see text]-type orbital. The obtained results illustrate spatial edge effects between the bulk modes and the localized electronic states of the metallic surfaces over the three orientations of high symmetry path. We observe many localized states above and below the bulk band range. In addition, the relaxation effect on the surface layer has been investigated to compute the localized electronic surface state in this case and illustrate the lift of the degeneracy compared to the first calculations based on an ordered surface. The spacing geometry caused by the relaxation on the surface has been determined by using the Molecular dynamic algorithm and Morse interatomic potential.

Electronic Structure of Amorphous Silicon

1997 ◽  
Vol 491 ◽  
Author(s):  
G. Allan ◽  
C. Delerue ◽  
M. Lannoo
Keyword(s):  
Electronic Structure ◽  
Amorphous Silicon ◽  
Tight Binding ◽  
Localized States ◽  
Band Offset ◽  
Valence Band Offset ◽  
Tight Binding Approximation ◽  
Exponential Tails ◽  
Si Model ◽  
Hydrogenated Amorphous

ABSTRACTThe electronic structure of a continuous network model of tetrahedrally bonded amorphous silicon (a-Si) and of a model hydrogenated amorphous silicon (a-Si:H) that we have built from the a-Si model are calculated in the tight binding approximation. The band edges near the gap are characterized by exponential tails of localized states induced mainly by the variations in bond angles. The spatial localization of the states is compared between a-Si and a-Si:H. Valence band offset between the amorphous and the crystalline phases is calculated.

Surface-state energies and wave functions in layered organic conductors

2020 ◽  
Vol 75 (11) ◽  
pp. 987-998
Author(s):  
Danica Krstovska ◽  
Aleksandar Skeparovski
Keyword(s):  
Magnetic Field ◽  
Surface State ◽  
Tight Binding ◽  
Surface States ◽  
Organic Conductors ◽  
Wave Functions ◽  
Energy Dispersion ◽  
Quantization Rule ◽  
Tight Binding Approximation ◽  
Dispersion Law

AbstractWe have calculated and analyzed the surface-state energies and wave functions in quasi-two dimensional (Q2D) organic conductors in a magnetic field parallel to the surface. Two different forms for the electron energy spectrum are used in order to obtain more information on the elementary properties of surface states in these conductors. In addition, two mathematical approaches are implemented that include the eigenvalue and eigenstate problem as well as the quantization rule. We find significant differences in calculations of the surface-state energies arising from the specific form of the energy dispersion law. This is correlated with the different conditions needed to calculate the surface-state energies, magnetic field resonant values and the surface wave functions. The calculations reveal that the value of the coordinate of the electron orbit must be different for each state in order to numerically calculate the surface energies for one energy dispersion law, but it has the same value for each state for the other energy dispersion law. This allows to determine more accurately the geometric characteristics of the electron skipping trajectories in Q2D organic conductors. The possible reasons for differences associated with implementation of two distinct energy spectra are discussed. By comparing and analyzing the results we find that, when the energy dispersion law obtained within the tight-binding approximation is used the results are more relevant and reflect the Q2D nature of the organic conductors. This might be very important for studying the unique properties of these conductors and their wider application in organic electronics.

Empirical Tight-Binding Applied to Silicon Nanoclusters

1997 ◽  
Vol 491 ◽  
Author(s):  
G. Allan ◽  
C. Delerue ◽  
M. Lannoo
Keyword(s):  
Band Structure ◽  
Nearest Neighbor ◽  
Good Description ◽  
Tight Binding ◽  
Localized States ◽  
Basis Set ◽  
Band Structure Calculation ◽  
Minimal Basis ◽  
Tight Binding Approximation ◽  
Bulk Band

ABSTRACTThe calculation of the electronic structure of silicon nanostructures is used to discuss the accuracy of results obtained by the tight-binding method. We first show that the level of refinement of the tight-binding approximation must be adapted to the calculated property. For example, an accurate description of both the valence and conduction bands which can be achieved with a 3rd-nearest neighbor approximation is necessary to calculate the variation of the gap energy with the silicon crystallite size. The sp3s* model which gives a bad description of the conduction band underestimates the confinement energy but can give good results when it is used to determine the variation of the crystallite band gap with pressure. To study Si-III (BC-8) nanocrystallites, we show that a good description of the bulk band structure can be obtained with non-orthogonal tight-binding but due to the large number of nearest neighbors one must take analytical variations of the parameter with interatomic distances. The parameters involved in these expressions can be easily fitted to the bulk band structures using the k-point symmetry without requiring the use of group theory. Finally we discuss the effect of increasing the size of the minimal-basis set and we show that it would be possible to get the values of the tight-binding parameters from a first-principles localized states band structure calculation avoiding the fit to the energy dispersion curves.

Optical and Electronic Properties of GaAs/AlAs Random Superlattices

1993 ◽  
Vol 325 ◽  
Author(s):  
E.G. Wang ◽  
J.H. Xu ◽  
W.P. Su ◽  
C.S. Ting
Keyword(s):  
Electronic Properties ◽  
Tight Binding ◽  
Three Dimensional ◽  
Localized States ◽  
Level Crossing ◽  
State Splitting ◽  
Optical And Electronic Properties ◽  
Short Period ◽  
Layer Disorder ◽  
Good Agreement

AbstractThe optical and electronic properties of three-dimensional (3D) random GaAs/AlAs superlattices (SLs) has been studied by using a tight-binding Hamiltonian with secondneighbor interactions. We calculate three completely disordered sequences with the probability of GaAs layers being 30%, 50%, and 70%. The higher the GaAs composition, the narrower the indirect gap. An energy-level crossing is found at the bottom of conduction band, which originates from the M-state splitting induced by layer disorder. The localized states over two - four monolayers play an important role in the absorption edge of random SL. The highest absorption intensity of the band-edge transitions in our random models is about eight times stronger than that of short period ordered GaAs/AlAs SL. Our results are in good agreement with some recent photoluminescence measurements.

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