Electron—phonon coupling constant

These equations must be solved numerically. In our first calculations [46] the value of to was taken as 0.3 eV, the value obtained from an ab initio calculation of the energy of a pair of Gs as a function of the distance between them [47] for a separation of 3.4 A. The electron-phonon coupling constant a, the derivative of t with respect to displacement, was obtained as 0.6 eV/A from the results of [47]. Subsequently, when a value of to other than 0.3 eV was used a was scaled accordingly. Although to and a values depend on the particular pair of neighboring bases, the calculations were simplified by using the same value for all pairs of bases. The value of the elastic constant K was taken as 0.85 eVIA, derived [46] from the measured value of the sound velocity in DNA. 

Fig. 58. Composition dependence of the density of states N(E ) at the Fermi level ( ) of Y Lui-xl I C calculated by CPA, experimental data for the Sommerfeld parameter /n end the phenomenologically extracted values of the electron-phonon coupling constant Ae. ph (in this article usually written as Apt,), using eq. (9).

Fig. 3. Electron-phonon coupling constants for the monoanions of acene-edge-type hydrocarbons.

Fig. 5. Electron-phonon coupling constants /lumo as a function of the number of carbon atoms.

We are now able to estimate Tc for the hydrocarbon monoanions by using the approximate solution of the Eliashberg equation [20]. On the basis of the calculated BCS electron-phonon coupling constants [21], we estimate Tc s using McMillan s formula [22,23]. McMillan s formula was derived from a three-dimensional formalism, while the electron carriers in acene-edge-type molecules form a quasi-two-dimensional system. But we believe that McMillan s formula is still available for qualitative discussions. For A < 1.5, this is available for an approximate solution to the Eliashberg equations... 

Electron-phonon coupling constant (meV) Electron-phonon coupling constant (meV)... 

Fig. 6. Electron-phonon coupling constants in the monoanions of coronene and corannulene.

For a contact with E2g phonon modes in Fig. 7(a) the nonlinearity of the I — V curves due to electron-phonon interaction can be estimated from the dV/dl curves by about 10%. This is comparable with the nonlinearity observed for non-SC diborides [33] with small electron-phonon coupling constant A pc < 0.1. The reason for the relatively low nonlinearity of the I — V curves and the small intensity of the main E2g phonon modes in the spectra for MgE>2 contacts can be due to the fact that an anomalous strong interaction is characteristic for a restricted group of phonons with sufficiently small wave vector [9], whereas in PCS, the large angle scattering is increased. 

This study has been motivated by the recent discovery and investigations of a new family of superconductors metal-intercalated chloronitrides. For example, the compound Liu.48(THF)yHfNCl has arelatively high value of Tc 25K [l]-[5]. The mechanism of superconductivity for these materials had remained a puzzle. Indeed, according to theoretical calculations [6] the electron-phonon interaction is not sufficient to provide the observed value of Tc. Analysis of the data on heat capacity [2], based on the dependence 7 (1 + A), see [7], has led to a similar conclusion (7 is the Sommerfeld constant, A is the electron-phonon coupling constant). 

Here K is the stiffness constant. The values of the parameters generally used in Eq. (2.5) are given in Table 2.2. These values lead to a = 4.2 eV/A and the electron-phonon coupling constant k = 0.19. However using Eq. (2.5), the value of Ao comes out to be only 0.53 eV which is considerably smaller than the experimental value of 0.7 eV. Eq. (2.5) is approximate because the electron-electron interactions have been neglected. Also the optical absorption experiments do not give a reliable value of the gap because the absorption can occur by processes other than electronic excitation. 

D The Electron-Phonon Interaction and the Electron-Phonon Coupling Constant... 

A is tlie dimensionless electron-phonon coupling constant characteristic of the metal. We may write it in terms of the matrix elements for this problem as... 

More recently the amplitude mode model, which is a solid state approach to the problem, has been developed. Chains are assumed to be infinitely long, but each chain is thought to have a different overall electron-phonon coupling constant A. More precisely, A may even include other interaction processes which renormalize the phonon frequencies. The latter and the Raman intensities are obtained from... 

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