Simple two-band model

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

Fig. 4. (a) Magnetic field dependence of the high- and low-temperature MR, respectively. The solid lines are calculated using a simple two-band model for (a) and the 2D weak localization theory for (b) (after Song et o/.[16]). 

In order to test the relative weight of the difficult L- D or D L excitations as compared to the others, a model calculation was recently performed on a H2 molecule ring introducing disorder by varying the intermolecular distances. The number of H2 molecules was 11, and a minimal STO-3G basis set was used for the calculation. In this way one obtains a simple two-band model with one completely filled and one unfilled band. 

Fig. 19. Schematic representation of the two hybridized bands (solid curves) for the simple two-band model. The unperturbed broad band is represented by the dashed curve and the f level by the dashed line. The wave vector k is measured in units of the zone boundary vector, and the energy is in units of the total bandwidth.

The upper band is qualitatively the same as the simple two-band model discussed in section 3.1.2, but the band mass at zero temperature is enhanced by roughly a factor of 5 for fi 0) = 13r], where /r(0) is the Fermi level as temperature T=0 (Liu 1987, 1988). This factor plus the correlation effect due to Uk could put the mass enhancement factor to within the measured range of 20-30. When there are many f levels and many broad bands as in a real LDA calculation, there should be a one-to-one correspondence between the model bands and the LDA bands at the Fermi level. On the other hand, until the f hole screening dynamics can be calculated from realistic band eigenvalues and eigenstates, the present theory should only be considered qualitative or at most semi-quantitative. The quantity /r(0) cannot be determined with certainty, and we will treat it as a parameter in the model calculation. 

Above 2 K, the temperature dependence of the zero-field resistivity of the microbundle measured by Langer et al. [9] was found to be governed by the temperature dependence of the carrier densities and well described by the simple two-band (STB) model derived by Klein [23] for electrons, , and hole, p, densities in semimetallic graphite ... 

Here 1 labels the electronic states of the SWCNT with the chiral index (p,0), which are described by a simple two-band k p model based on an effective mass approximation [4], p being equal to 3M + v with integer M and v = 0( 1) for metallic (semiconducting) SWCNTs. The energy bands in Eq.(3) are given by... 

To illustrate this behaviour we briefly discuss an example which may be relevant to CeCu2 Si2. Qualitatively the complex phase diagram of CeCu2Si2 can be described by a simple mean-field model for a conventional spin density wave ground state (competing with d-wave superconductivity within a two band model proposed by Dahm (2001)). The calculated phase diagram displayed in fig. 8 shows that a state with dxy symmetry can become stable within the SDW phase. This is in contrast to the pairing states with d 2 yi symmetry considered by Kato... 

Those results were further developed by a study due to Monkhorst and Kertesz (15) using a two-band model system within Hiickel methodology they recovered the (-l) j asymptotic decay of exchange in a half-filled band (metallic) situation of this model and established a simple relationship between bahd gap, band width and an (exponential) large-j behavior of the density matrix elements in the filled band (insulating) situation. 

Fig. 1.4. Bonding and anti-bonding states of an hetero-polar diatomic molecule, in a simple two-orbital model (left), and broadening of these states, leading to the formation of the valence and conduction bands in the crystal (right).

The Hamiltonian provides a suitable analytic form that can be fitted to the adiabatic surfaces obtained from quantum chemical calculations. As a simple example we take the butatriene molecule. In its neutral ground state it is a planar molecule with Dy, symmetry. The lowest two states of the radical cation, responsible for the first two bands in the photoelectron spectrum, are X2B2g and A1 By The vibronic coupling model Hamiltonian is set up using the ground-state... 

Temperature quenching of broad band emission is usually explained by a simple configuration coordinate model consisting of two parabolas that have been shifted with regard to each other (Fig. 6). This is called the Mott-Seitz model. Nonradiative return from the excited to the ground state is possible via the parabola crossover. Its rate can be described with an activation-energy formula Pnr = C where C is a constant of the order of 10 sec i and AE is the... 

The simple free electron model might suggest that the lowest energy orbital in any band is that with =0. Figure 8.9, however, illustrates two combinations of... 

In this connection, a calculation of the energy involved in the electron transfer from the semiconductor to the chemisorbate and vice versa is desirable. By the aid of the simple band model of semiconductors, Dowden (5) has tried to calculate this energy and to give a physical interpretation. Although his explanation was not complimented by a refined interpretation in which the space charge effects were considered, as was done especially by Weisz (24) and Hauffe (17), Dowden s viewpoint was valuable in two respects. In the first place it makes the importance of the... 

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