Electron-phonon coupling parameter

Another interesting application of the total energy approach involves superconductivity. For conventional superconductors, the 1957 theory of Bardeen, Cooper and Schrieffer [26] has been subject to extensive tests and has emerged as one of the most successful theories in physics. However, because the superconducting transition temperature Tc depends exponentially on the electron-phonon coupling parameter X and the electron-electron Coulomb parameter p, it has been difficult to predict new superconductors. The sensitivity is further enhanced because the net attractive electron-electron pairing interaction is proportional to X-p, so when these parameters are comparable, they need to be determined with precision. 

Alternatively, the same interaction matrices form can be obtained exploiting the Ck,v (or DK/l) symmetry of the molecule, as described in Section 3. Of course, the main motivation of the present section is not the general structure of the interaction matrices, but rather the detailed information about the electron-phonon coupling parameters this information is important in view of future a priori elaboration of the coupling constants, instead of their estimation on the basis of semi-empirical approaches. 

Intramolecular vibrations strongly scatter electrons near the Femii-surfacc in doped fuUerenes. A simple expression for the electron-phonon coupling parameters for this case is derived and evaluated by quantum-chemical calculations. The observed superconducting transition temperatures and their variation with lattice constants can be understood on this basis. To test the ideas and calculations presented here, we predict that high frequency Hg modes acquire a width of about 20% of their frequency in superconductive foUerenes, and soften by about 5% compared to the insulating fuUerenes. 

C is the function of electron-phonon coupling parameters and n(co) is the number of phonons present of energy ko. For the absorption of phonons the square bracket is replaced by n(uj) and the sign changed before hco. 

Superconducting transition temperatures (T ), Debye temperatures (ffjy), density of states N(Ep) and electron-phonon coupling parameters of several amorphous alloys. 

Formally, a is the electron-phonon coupling parameter defined by eqn (2.38), but it is often convenient to regard it as a semiempirical parameter. Notice that a positive value of A corresponds to a reduction in the bond length, and vice versa. It is this term in that couples the electrons to the lattice, and corresponds to eqn (2.40) with / = 0. A plays the role of an order parameter, whereby a nonzero value indicates a broken symmetry. 

Concluding remarks 788 A = electron phonon coupling parameter... 

Fig. 10.13. vs. pressure for Lu up to 200 kbar. Solid circles are the data of fig. 10.12. Open circles systematically deviate from the curve (see text). The curve is a fit of eq. (10.1) to the data assuming a linear pressure-dependence of the electron-phonon coupling parameter A upon pressure. The upper scale shows the corresponding values of A. 

Ziman, 1972). From the low melting temperature one may infer that the average of the squared phonon frequencies M(w ) is appreciably smaller for a, a"... Ce than for Hf. This, in turn, will favor a larger electron-phonon coupling parameter A as seen from eq. (10.3). 

The electron-phonon coupling parameter A in La is of the order of 0.8-0.9 at normal pressure (Wiihl et al., 1973). The coupling parameter for Lu is expected to be small, possibly =0.3 (see section 2.5). The calculated values for the density of states are thus just equal for La and Lu. Apparently, the 4f character of La is not reflected in a particularly high density of states N Ef) as in a-Ce (section 3.2). One should however keep in mind that La is a complicated metal which also has strong d character. At present it is unknown to what extent the 5d and the 4f bands contribute to the density of states (see however Glotzel (1976)). 

Electron-phonon coupling parameters for rare-earth metals and their dihydrides. 

Electronic specific-heat coefficient, and acoustic and optic electron-phonon coupling parameters, and... 

Section III.D.l treats the multiphonon scattering in II-VI nanostructures and the dependence of the resonance enhancement on the excitation energy and temperature Section III.D.2 shows the determination of the size dependence of the electron-phonon coupling parameter. 

Shiang et al. [105] have developed a model which relates the electron-phonon coupling parameter S with the homogeneous linewidth Fq of the electronic excited state and the 2LO/LO intensity ratio. The result is a relatively strong dependence of the 2LO/LO ratio on S but only a weak dependence on To for short lifetimes 1/Fo and low values of S S < 1.5). Furthermore, they found that a decrease in the lifetime of the excited state leads to a decrease in the Raman intensities of the LO. 

A is the electron-phonon coupling parameter (see last section) the time constant is given by... 

The electron-phonon coupling parameters in Table I correspond to a reorganization energy of 360 cm" which corresponds to the accurately determined value for the CT absorption of the anthracene pyromellitic acid dianhydride 7C-molecular complex. It might be argued that this value is too small for the problem at hand. However, increasing this value would only strengthen the conclusions of ref. 18, vide supra. 

Here A-n is a transport electron-phonon coupling parameter. It is a number, typically 0.5-1 for many transition metals, and is closely related to the electron-phonon coupling parameter X.ei.ph that appears in the theory of superconductivity see Eqs. (25) and (26). The high-temperature version of Eq. (5) can then be written... 

---