Electron-phonon interaction coupling

A AH < kT has important consequences. As the temperature is lowered to where AHg, kT, strong electron-phonon interactions must manifest themselves. Direct evidence for mode softening and strong electron-phonon coupling in the internal Ty < T < 250 K has been provided by measurements of the Mdssbauer recoiless fraction and the X-ray Debye-Waller factor as well as of muon-spin rotation Therefore, it would be... 

Fig. 4a-c. Models for electron hopping correlated by electrostatic electron-electron interactions plus strong electron-phonon interactions for a valence ratio Fe /Fe = 1 (a) small pola-rons, (b) diatomic polarons, (c) small polaron coupled to slower (only one phase shown) dimerization... 

Raman spectra indicate that phonons are coupled to electronic states in BaPb BijPj (53) and in Ba1.xKxBiOs (58). These studies do show a strong electron - phonon interaction is present in the superconducting phases, but do not prove that these modes are responsible for high Tc driven by a phonon - only mechanism. 

However, this ceases to hold when Gd contains also the self-energy part due to interactions. Using an approximate solution [13] for Gd for an electron-phonon interaction linear in the boson coordinates, one finds [11] that to lowest-order in the electron-phonon coupling aq 2, Ipc = Ipc + AIpc, with... 

The key to understand the anomalous behaviors in A vC,o is the electron-electron interaction, U, and the electron-phonon interaction, S. In A vCgo, the important interaction as U is the Coulomb repulsion between the flu electrons. The importance of U has been pointed out based on the results of the photoemission experiments [15]. Also, in AxC o, the important interaction as S is the coupling of the tlu electrons to the intramolecular phonons of the CRaman experiments [16], Nevertheless, a complete understanding of the anomalous behaviors in AxCgo has not been established yet. The reason is that the system with the orbital degree of freedom in which both U and S are important has not been known so far [17-20],... 

In this section, a model which gives the basis of the present study is introduced to investigate the electronic properties of A,Cfio [17]. First, the one-electron part of the Hamiltonian, which describes the itinerant motion of the flu electrons in terms of the electron transfer T, is given. Next, the electron-electron interaction U and the electron-phonon interaction S are examined U represents the Coulomb repulsion between the t u electrons and S represents the coupling of the fiu electrons to the intramolecular phonons of the Cdynamical aspect of S is pointed out. 

Following the analysis of Refs. [54,55,72], we now make use of the fact that the nuclear modes of the Hamiltonian Eq. (8) produce cumulative effects by their coupling to the electronic subsystem. From Eq. (9), the electron-phonon interaction can be absorbed into the following collective modes,... 

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. 

These are the essential phenomenological characteristics of superconductivity. The first significant step in a theoretical interpretation was taken in 1950 when H. Frohlich and J. Bardeen showed that electron-phonon interactions are capable of coupling two electrons together as if there is a direct attractive force between them. 

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). 

The electron-phonon interaction can take on two different forms, depending on the type of phonons involved. The interaction with optical phonons is intramolecular and of the form %e 0 = X E, q(nh where X is the coupling strength and < , is the phonon normal coordinate at molecule i. The interaction with acoustical phonons is through the hopping integrals, which are modulated by intermolecular motion. The hopping between two molecules at the crystal positions R, and R is ti = t + (V ) (uj - uf) + , so... 

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