Phonon Mechanism for Superconductivity

Many of the properties of the BCS superconductor are consequences of the formation of an energy gap Eg in the electron energy band at the Fermi energy ey when the temperature is reduced below Tc. The magnitude of this gap and Te are related by EglkaTc) 4 where ks is Boltzman s constant. This energy gap arises from an effective attractive interaction between paired elec- 

Theoretically and experimentally the transition from a normal metal to superconductor is preceded (above Tc) by a rapid rise in the conductivity (13, 332), termed paraconductivity or superconducting fluctuations. The temperature dependence of the paraconductivity depends upon the system being one-, two-, or three-dimensional (392). 

There has been considerable theoretical discussion concerning the role of the Peierls soft phonon mode with wavevector 2kp in the indirect coupling of electrons into pairs to form the superconducting state in a one-dimensional metal. It has been suggested that this phonon could lead to an anomalously large attractive indirect electron-electron interaction (6, 97, 392). In contrast, some theoretical work shows that phonons of energy less than ksTc (such as the soft phonon mode near the Peierls transition) tend to suppress the superconducting transition (6, 333,348). Further theoretical and experimental work is necessary to fully resolve this point. 

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