Superconductivity electron-phonon interaction

Keywords point-contact spectroscopy, MgB2, two-band/gap superconductivity, electron-phonon interaction... 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

The gap in superconductivity between the fifth and sixth groups of the periodic table, discovered by Matthias,24 is seen to correspond to the transition from crest to trough superconductivity. It does not require for its explanation the assumption20- 25 that there are mechanisms of superconductivity other than the electron-phonon interaction. 

The theory of superconductivity based on the interaction of electrons and phonons was developed about thirty years ago. I 4 In this theory the electron-phonon interaction causes a clustering of electrons in momentum space such that the electrons move in phase with a phonon when the energy of this interaction is greater than the phonon energy hm. The theory is satisfactory in most respects. 

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. 

Shirai, M., Suzuki, N. and Motizuki, K., Microscopic Theory of Electron - Phonon Interaction and Superconductivity of BaPbj.jjB Og. Solid State Comm. 60(6) 489 (1986). 

Already in the seminal paper of Bednorz and Muller [1], the guide to look for systems with a high superconductive transition temperature (Tc), has been the presence of strong electron-phonon interactions. Such interaction has been known to exist in a wide class of perovskite type oxides. The authors mention [1] the vibronic Jahn-Teller polaron effect [2] in this context. They also emphasize the fact that the Cu2+-ion is a well-known Jahn-Teller system and this circumstance preserves significance in the physics of cuprate superconductors [3-7]. As a microscopic cause for ferroelectric ordering the interband vibronic hybridisation has been supposed [8-11] enlargening the view on perovskites as Jahn-Teller systems. 

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. 

The onset of electron-phonon interaction in the superconducting state is unusual in term of conventional electron-phonon interaction where one would expect that the phonon contribution is weakly dependent on the temperature [19], and increase at high T. Indeed, based on this naive expectation, this type of unconventional T dependence has been often used to rule out phonons. Here, however, we see clearly that this reasoning is not justified. Moreover, this type of unconventional enhancement of the electron phonon interaction below a characteristic temperature scale is actually expected for other systems such as spin-Peierls systems or charge density wave (CDW) systems. Thus, our results put an important constraint on the nature of the electron phonon interaction in these systems. 

For review of earlier results see Kulic M., (2000). Interplay of electron-phonon interaction and strong correlations the possible way to high-temperature superconductivity. Phys. Rep. 338 1-264. 

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 zero-approximation in expansion of I(V) in d/l is the ohmic current considered by Sharvin [5]. From the Sharvin s formula the characteristic size d of the contact can be determined in the ballistic limit. The second derivative of the first approximation in expansion of I(V) in d/l is directly proportional to the spectral function of electron-phonon interaction (PC EPI) gpc w) = apc (w) F (w) °f the specific point-contact transport both in the normal and in the superconducting states [1, 6, 7], This term is the basis of the canonical inelastic point-contact spectroscopy (PCS). Here, ot2pC (oj) is the average electron-phonon matrix element taking into account the kinematic restriction imposed by contact geometry and F (oj) is the phonon density of states. 

Light scattering is a useful tool for investigating a superconducting gap in the electronic energy spectrum because it is based on electron-phonon interaction and therefore is able to sensitively probe both phonon and electronic states. This idea and experimental studies have recently been developed for (BEDT-TTF)2I3 family superconductors [85,86]. The van-... 

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