Brillouin zone scattering

We use s, p, and d partial waves, 16 energy points on a semi circular contour, 135 special k-points in the l/12th section of the 2D Brillouin zone and 13 plane waves for the inter-layer scattering. The atomic wave functions were determined from the scalar relativistic Schrodinger equation, as described by D. D. Koelling and B. N. Harmon in J. Phys. C 10, 3107 (1977). 

By changing the scattering parameters we can tune in to electrons with a well-defined, constant momentum value along the c-axis. In the present case pc = 0.25 au i.e. the resulting measurement was on the boundary of the Brillouin zone, along the A-L direction. Now two structures are visible, both the ou and the k band. The dispersion of the ou band has not changed noticeably from that found for the T-M... 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

The resistivities of the magnetic borides DyB, H0B12, ErB, and TmB, have been carefully measured by Gabani et al. (1999) for good quality crystals with low room temperature resistivities (10-30 p 2 cm) compared to the early work. Near the antiferromagnetic transition temperatures Tn, the resistivities all show small increases in the form of humps and then rapid drops as the temperature is lowered. This behavior can be explained as an initial increase in the resistivity attributed to the appearance of superzone boundaries within the Brillouin zone, followed by a decrease due to a reduction in spin scattering (Taylor and Darby, 1972 Fournier and Gratz, 1993). 

This saturation is due to a reduced energy dependence of the electron collection efficiency at the metal/semiconductor interface (at large electron energy almost the entire Brillouin zone has available conduction band states) and enhanced inelastic hot electron scattering in the metal base layers. Besides a, the emitter current also increases with tunnel barrier bias voltage. The combination of both effects results in collector currents in the pA range at large VEb [132, 149],... 

The periodicity of the multilayer provides an additional scattering of the phonons and introduces an artificial Brillouin zone. This leads to a folding of the phonon dispersion curves at wave vectors n/L, where L is the multilayer spacing. 

The second-order Raman spectra from 1,700 to 3,300 cm are relatively weak and broad compared to the first order Raman spectra. There are many papers devoted to the second-order Raman processes in graphite [49, 59-62] and carbon nanotubes [8, 34, 63]. The interpretation of the spectral behavior of the second-order bands in terms of DR have been done [3, 64, 65]. The corresponding phonon is involved in an inter-valley scattering process of in-plane modes (LO or TO) around the K-points in the two-dimensional (2D) Brillouine zone (BZ, Fig. 7.4) [66, 67]. 

We shall see below that the transport properties above are consistent with the picture of Luttinger chains in (a - b) planes. The exponent a = 0.7 derived from the constant volume transverse data leads to K = 0.22. This value of allows in turn a prediction for the constant volume T-dependence for p . The only scattering process through which electron-electron collisions can contribute to resistivity in this 1-D electron gas occurs when the total momentum transfer is commensurate with a Brillouin zone wave vector. For the situation of a 1/4-filled 1-D band which is likely to apply to (TMTSFljPF as the dimerization can be forgotten in first approximation (A ,[Pg.254]

Different models have been used to derive the particle size from Raman spectra As an example, we shah briefly explain the phonon confinement model (PCM). The scattering of one photon by n phonons is governed by the momentum conservation. Only vibrations from the center of the Brillouin zone (BZC) should therefore be active in one phonon process (first-order Raman spectrum) and this is actually the case in large and flawless crystals, where... 

All vibrations are active in INS and, in principle, measurable. This stems from the mass of the neutron ca 1 unified atomic mass imit). When scattered the neutron transfers momentum to the atom and INS measurements are not limited to observation at the Brillouin zone centre, as are photon techniques. The measured INS intensities are, inter alia, proportional to the concentration of the elements in the sample. 

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