Theory of tamm surface states in approximation higher than tight-binding approximation

1960 ◽  
Vol 10 (4) ◽  
pp. 268-274 ◽  
Author(s):  
M. Tomášek ◽  
J. Koutecký
Keyword(s):  
Tight Binding ◽  
Surface States ◽  
Tight Binding Approximation

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.

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.

Tight-binding approximation for bulk and edge electronic states in graphene

2015 ◽  
Vol 93 (5) ◽  
pp. 580-584 ◽  
Author(s):  
Oana-Ancuta Dobrescu ◽  
M. Apostol
Keyword(s):  
Finite Differences ◽  
Tight Binding ◽  
Electronic States ◽  
Surface States ◽  
Graphene Sheets ◽  
Graphene Monolayer ◽  
Edge States ◽  
Tight Binding Approximation ◽  
Edge Elements ◽  
Edge Surface

The tight-binding approximation is employed here to investigate electronic bulk and edge (“surface”) states in semi-infinite graphene sheets and graphene monolayer ribbons with various edge terminations (zigzag, horseshoe, and armchair edges). It is shown that edge states do not exist for a uniform hopping (transfer) matrix. The problem is generalized to include edge elements of the hopping matrix distinct from the infinite-sheet (“bulk”) ones. In this case, semi-infinite graphene sheets with zigzag or horseshoe edges exhibit edge states, while semi-infinite graphene sheets with armchair edges do not. The energy of the edge states lies above the (zero) Fermi level. Similarly, symmetric graphene ribbons with zigzag or horseshoe edges exhibit edge states, while ribbons with asymmetric edges (zigzag and horseshoe) do not. It is also shown how to construct the “reflected” solutions (bulk states) for the intervening equations with finite differences both for semi-infinite sheets and ribbons.

Electronic bound states at the surface of a metal

1952 ◽  
Vol 48 (3) ◽  
pp. 457-469 ◽  
Author(s):  
G. R. Baldock
Keyword(s):  
Crystal Structures ◽  
Small Groups ◽  
Bound States ◽  
Tight Binding ◽  
Surface States ◽  
Tight Binding Approximation ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Lattice Geometry

AbstractThe conditions under which bound states associated with atoms in the surface of a metal may exist are investigated, using the tight-binding approximation. These states arise as a result of modifications in the parameters of certain atoms. The modifications required to produce (a) bound states associated with all the atoms in the surface (surface states) and (b) bound states associated with particular small groups of atoms are found for the simple cubic lattice. It is also shown that most of the simpler crystal structures do not exhibit surface states without such modifications; in the graphite and diamond lattices, however, surface states exist solely by virtue of the lattice geometry.

Electrical Transport Properties of Carbon Nanotube Metal-Semiconductor Heterojunction

2016 ◽  
Vol 15 (05n06) ◽  
pp. 1660009 ◽  
Author(s):  
Keka Talukdar ◽  
Anil Shantappa
Keyword(s):  
Electrical Transport ◽  
Nearest Neighbor ◽  
Electronic Devices ◽  
Tight Binding ◽  
Transmission Function ◽  
Topological Defects ◽  
Dynamics Simulation ◽  
Internal Stresses ◽  
Electrical Transport Properties ◽  
Tight Binding Approximation

Carbon nanotubes (CNTs) have been proved to have promising applicability in various fields of science and technology. Their fascinating mechanical, electrical, thermal, optical properties have caught the attention of today’s world. We have discussed here the great possibility of using CNTs in electronic devices. CNTs can be both metallic and semiconducting depending on their chirality. When two CNTs of different chirality are joined together via topological defects, they may acquire rectifying diode property. We have joined two tubes of different chiralities through circumferential Stone–Wales defects and calculated their density of states by nearest neighbor tight binding approximation. Transmission function is also calculated to analyze whether the junctions can be used as electronic devices. Different heterojunctions are modeled and analyzed in this study. Internal stresses in the heterojunctions are also calculated by molecular dynamics simulation.

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