Tight-binding dispersion

In order to determine the phonon dispersion of CuZn and FeaNi we made use of an expanded tight binding theory from Varma and Weber . In the framework of a second order perturbation theory the dynamical matrix splits in two parts. The short range part can be treated by a force constant model, while the T>2 arising from second order perturbation theory is given by... 

Here, u is the displacement of the /ith molecule from its equilibrium position and M the reduced mass of each molecular site. Second, the electron is described within the frame of the tight-binding approximation, where it is assumed that the effect of the potential at a given site of the one-dimensional chain is limited to its nearest neighbors. In that case, the energy dispersion of the electron is given by... 

Dispersion curve for tight-binding case E—U — tcos (kd) in one dimension first Brillouin zone. 

Although the symmetry of TM2X salts is triclinic, most physical features can be explained by taking an orthorhombic symmetry with the tight-binding energy dispersion written as... 

The tight-binding bandwidth, W, or band dispersion, is given by ... 

Fig. 4.6. Band dispersion in the tight binding model (a) for a symmetric (even) atomic wavefunction and (b) for an antisymmetric (odd) atomic wavefunction.

The electronic states for a given lattice configuration are given by the solution of fleiect- In the limit of equal bond lengths, we can use the result already obtained for the one-dimensional, tight binding model, Equation (4.22), to write down the result for the dispersion of the electron band as ... 

The STM observation of the Y Cs2 dimers and clusters is direct experimental evidence that Y Cs2 molecules exhibit the superatom feature. The observed interfullerene distance is 11.2 A, which is shorter than that of the simple Y C82-Y Cs2 van der Waals distance (11.4 A), suggesting that the interfullerene interaction is not a simple dispersion type of weak interaction but a relatively strong interaction. A large dipole moment of Y Cs2 also plays an important role in the tight binding between Y Cs2... 

In the tight-binding band approximation the analogous result for the dispersion relation can be written as... 

Numerical tight-binding band-structure calculations result in the approximative dispersion relation which is valid in the neighborhood of the FS [43]... 

Based on the extended Hiickel tight-binding method the 2D energy dispersion relation and FS of k-(ET)2Cu(NCS)2 [29, 155, 161, 162] and K-(ET)2l3 [147, 163] have also been calculated. Figure 2.19 shows the results. The band structures are very similar except for the degeneracy of the two upper bands along Z-M for K-(ET)2l3. In k-(ET)2Cu(NCS)2, due to the lack of a center of... 

The calculated tight-binding band structure based on the 20 K lattice parameters is shown in Fig. 4.44. Compared to other organic metals, unusually complicated dispersion relations are found which consist of ID and 3D energy bands. Perpendicular to c two ID FS sheets denoted by FSl and FS2 exist. Within the approximation used the doubly degenerate FSl is ideally... 

Tab. 11.1. Tight-binding parameters obtained from the least-square-error fit to LMTO band dispersions for the nine ll-VI semiconductors in the sp d basis with the A-B and B-B interactions. The first row lists the interatomic spacings in A, the next eight rows contain the onsite energies for all the orbitals, e.g. the row for dc t2) lists the entries for the t2cl orbital onsite energies for the cation. The subscript a denotes the anion. The last fifteen rows list the Slater Koster parameters. The last column shows the average value of the Slater Koster parameters multiplied by the square of the cation-anion distance, d. ...

Fig. 4.14. Dispersion relation for a one-dimensional s-band tight-binding model.

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