scholarly journals Onsite matrix elements of the tight-binding Hamiltonian of a strained crystal: Application to silicon, germanium, and their alloys

2009 ◽  
Vol 79 (24) ◽  
Author(s):  
Y. M. Niquet ◽  
D. Rideau ◽  
C. Tavernier ◽  
H. Jaouen ◽  
X. Blase
Keyword(s):  
Silicon Germanium ◽  
Tight Binding ◽  
Matrix Elements ◽  
Strained Crystal

Tight Binding Modeling of Properties Related to Field Emission from Nanodiamond Clusters

2000 ◽  
Vol 621 ◽  
Author(s):  
Denis A. Areshkin ◽  
Olga A. Shenderova ◽  
Victor V. Zhirnov ◽  
Alexander F. Pal ◽  
John J. Hren ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Field Emission ◽  
Density Of States ◽  
Electron Affinity ◽  
Potential Distribution ◽  
Tight Binding ◽  
Matrix Elements ◽  
Energy States ◽  
Bulk Diamond ◽  
Modeling Of Properties

ABSTRACTThe electronic structure of nanodiamond clusters containing between 34 and 913 carbon atoms was calculated using a tight-binding Hamiltonian. All clusters had shapes represented by an octahedron with (111) facets with the top and the bottom vertices truncated to introduce (100) surfaces. The tight-binding Hamiltonian consisted of environment-dependent matrix elements, and C-H parameters fit to reproduce energy states of the cyclic C6 and methane. The calculations predict a density of states similar to bulk diamond for clusters with radii greater than ∼2.5nm, and insignificant differences in the potential distribution between the clusters and bulk diamond for radii greater than ∼1nm. Hydrogen passivated nanodiamond clusters are estimated to have an electron affinity of approximately -1.8 eV.

SYMMETRY AND ELECTRO-OPTICAL PROPERTIES OF NANOTUBES

2002 ◽  
Vol 01 (03n04) ◽  
pp. 313-325 ◽  
Author(s):  
M. DAMNJANOVIĆ ◽  
I. MILOŠEVIĆ ◽  
T. VUKOVIĆ ◽  
B. NIKOLIĆ ◽  
E. DOBARDŽIĆ
Keyword(s):  
Carbon Nanotubes ◽  
Optical Properties ◽  
Density Functional ◽  
Tight Binding ◽  
Optical Characteristics ◽  
Optical Transitions ◽  
Matrix Elements ◽  
Selection Rules ◽  
Single Wall Carbon ◽  
Quantum Numbers

The symmetry of single-wall carbon and inorganic tubes is reviewed. For the carbon nanotubes it is used to get the full set of quantum numbers, in the efficient precision (combined density functional and tight-binding methods) calculation of electronic bands and their complete assignation, to obtain the selection rules for optical transitions and the momenta matrix elements for the Bloch eigen-states. The optical characteristics are thoroughly found, and discussed.

THEORY OF BICRYSTAL c-AXIS TWIST JOSEPHSON JUNCTIONS

2001 ◽  
Vol 15 (24n25) ◽  
pp. 3164-3189 ◽  
Author(s):  
RICHARD A. KLEMM ◽  
KURT SCHARNBERG
Keyword(s):  
Fermi Surface ◽  
Experimental Error ◽  
High Temperature Superconductors ◽  
Twist Angle ◽  
Tight Binding ◽  
Momentum Dependence ◽  
Matrix Elements ◽  
Josephson Tunneling ◽  
Wave Symmetry ◽  
Tunneling Matrix Element

We calculate the critical current density [Formula: see text] for Josephson tunneling between identical high temperature superconductors twisted an angle (ϕ0) about the c-axis. Regardless of the shape of the two-dimensional Fermi surface and for very general tunneling matrix elements, an order parameter (OP) with general d-wave symmetry leads to [Formula: see text]. This general result is inconsistent with the data of Li et al. on Bi2Sr2CaCu2O8+δ (Bi2212), which showed [Formula: see text] to be independent of ϕ0. If the momentum parallel to the barrier is conserved in the tunneling process, [Formula: see text] should vary substantially with the twist angle (ϕ0) when the tight-binding Fermi surface appropriate for Bi2212 is taken into account, even if the OP is completely isotropic. We quantify the degree of momentum non-conservation necessary to render [Formula: see text] constant within experimental error for a variety of pair states by interpolating between the coherent and incoherent limits using five specific models to describe the momentum dependence of the tunneling matrix element squared. From the data of Li et al., we conclude that the c-axis tunneling in Bi2212 must be very nearly incoherent, and that the OP must have a non-vanishing Fermi surface average for T≤Tc.

Optical matrix elements in tight-binding approach of hydrogenated Si nanowires

2009 ◽  
Vol 40 (3) ◽  
pp. 456-458 ◽  
Author(s):  
A. Miranda ◽  
R. Vázquez ◽  
A. Díaz-Méndez ◽  
M. Cruz-Irisson
Keyword(s):  
Tight Binding ◽  
Matrix Elements ◽  
Si Nanowires

Optical matrix elements in tight-binding calculations

2001 ◽  
Vol 63 (20) ◽  
Author(s):  
Thomas Garm Pedersen ◽  
Kjeld Pedersen ◽  
Thomas Brun Kriestensen
Keyword(s):  
Tight Binding ◽  
Matrix Elements

Tight-binding model with intra-atomic matrix elements

1994 ◽  
Vol 49 (12) ◽  
pp. 8506-8509 ◽  
Author(s):  
James L. Mercer ◽  
M. Y. Chou
Keyword(s):  
Tight Binding ◽  
Tight Binding Model ◽  
Matrix Elements ◽  
Binding Model

INVERSE FORMULATION OF THE GREEN'S FUNCTION THEORY: EXACT SOLUTION FOR THE BETHE LATTICE

2001 ◽  
Vol 15 (21) ◽  
pp. 2935-2943 ◽  
Author(s):  
L. ŠAMAJ
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Bethe Lattice ◽  
Diagonal Matrix ◽  
Local Form ◽  
Matrix Elements ◽  
Factorization Property ◽  
Inverse Form

We study the tight-binding Hamiltonian H=∑j|j> ∊j<j| + ∑j,k |j>Vjk < k | defined on the Bethe lattice of an arbitrary coordination number; the hopping elements Vjk are nonzero (and constant) only for j,k being the nearest-neighbor sites and the energies ∊j are considered to be site-dependent. The Green's function (z-H)-1 problem is solved explicitly in the inverse form, with diagonal matrix elements {<j | (z-H)-1 | j >} as controlling (prescribed) variables. Namely: (i) the inverse profile relation, i.e. z-∊j versus diagonal matrix elements, is obtained in a local form; (ii) the off-diagonal matrix elements { <j | (z-H)-1 | k >} are shown to exhibit a simple factorization property in terms of the diagonal ones.

Third Neighbor Analytic Tight-Binding Solutions for Electronic Structure of Carbon Nanosystems

2010 ◽  
Vol 659 ◽  
pp. 197-202
Author(s):  
István László
Keyword(s):  
Electronic Structure ◽  
Tight Binding ◽  
Electronic Structure Calculations ◽  
Diagonal Matrix ◽  
Graphene Sheets ◽  
Matrix Elements ◽  
Structure Calculations

Third neighbor analytic tight-binding formulae were obtained for graphene sheets and nanotubes. After fitting the corresponding of-diagonal matrix elements can be used in numerical electronic structure calculations of nanotubes and corrugated graphene.

scholarly journals Theoretical Analysis of the Faraday Effect in Carbon Nanotubes with Arbitrary Chirality

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Abbas Zarifi
Keyword(s):  
Magnetic Field ◽  
Carbon Nanotubes ◽  
Faraday Effect ◽  
Axial Magnetic Field ◽  
Tight Binding ◽  
Nearest Neighbour ◽  
Matrix Elements ◽  
Binding Model ◽  
Weak Magnetic Fields ◽  
Close Form

Using tight-binding model with nearest neighbour interactions, the optical properties of carbon nanotubes under the influence of an external magnetic field are analyzed. First, dipole matrix elements for two cases of light polarized parallel as well as perpendicular to the nanotube axis are analyzed. A close form analytic expression for dipole matrix is obtained for carbon nanotubes with arbitrary chirality in the case of light polarized parallel to the nanotube axis. Then the diagonal and off-diagonal elements of the frequency-dependent susceptibility in the presence of an axial magnetic field are investigated. The off-diagonal elements are applied to calculate the interband Faraday rotation and the Verdet constant. These effects should be clearly detectable under realistic conditions using weak magnetic fields.

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