Superconductivity Frohlich theory

Two - particle energy correction correction to electron - electron correlation energy due to the phonon field. This non-adiabatic term represents full attractive contribution, and can be compared to the reduced form of Frohlich effective Hamiltonian which maximizes attractive contribution of electron - electron interaction and that can be either attractive or repulsive (interaction term of the BCS theory). For superconducting state transition at the non-adiabatic conditions, the two-particle correction is unimportant - see [2],... 

Superconductivity was first discovered in mercury by H. Kamerlingh Onnes in 1911 (329) and eluded attempts at explanation until, in 1957, Bardeen, Cooper, and Schrieffer formulated the BCS theory (29) based on an electron-lattice-electron interaction. This theory and two others [by W. A. Little (268) and H. Frohlich (152)] are briefly described a full review is beyond the scope of this article. Interest in this area has been heightened by the report of superconducting fluctuations in the one-dimensional organic material, tetrathio-fulvalenium tetracyanoquinodimethanide, (TTF)(TCNQ) (97). 

The BCS and Little models for superconductivity are both based on the formation of pairs of electrons with an effective attractive interaction due to phonons or excitons respectively. Recently, J. Bardeen (8,28) revived a model, originally presented by Frohlich in 1954 (152), as a possible explanation of the reported anomalous conductivity behavior of (TTF)(TCNQ) (97). This model predates the BCS theory and relies on the direct interaction between electrons and the one-dimensional lattice resulting in the formation of charge density waves. The model has also been applied to the one-dimensional metal K2Pt(CN)4Bro.3o(H20)s (72, 457). 

Results of the ab initio theory of the antiadiabatic state have shown that the Frohlich s effective attractive e-e interaction term represents correction to electron correlation energy in transition from adiabatic into antiadiabatic state due to e-p interactions. Analysis of this term has shown that increased electron correlation is a consequence of stabilization of the system in superconducting electronic ground state, but not the reason of its formation. 

At this stage the J-T approach to superconductivity is still problematic for basically two reasons first, the J-T approach is not formulated in the many-body form as is the Frdhlich Hamiltonian, and second, this approach is ignorant with respect to the COM problem. Note, however, that the Frohlich Hamiltonian and all theories based on it, including the BCS formulation, also suffer from the same omission. 

Although the problem of the correct derivation of the Frohlich Hamiltonian has been thoroughly discussed in the past, the much more important problem of the possibility of the creation of an energy gap by means of an effective attractive two-electron interaction was never re-examined, in spite of the fact that Frohlich, who first derived this effective two-electron Hamiltonian finally never accepted the two-particle Cooper-pair based theory and claimed that the superconductivity has to be of one-particle origin. 

Frohlich applied the unitary transformation on the Hamiltonian describing conductors, but his attempt to remove the degeneracy failed. Then he proposed the true many body treatment. Bardeen with Cooper and Schrieffer continued to fulfil Frohlich s idea, and with the full multiconfiguration method used on the Frohlich-transformed Hamiltonian, they attempted to remove the degeneracy. After 2-years of intensive work they had no positive solution. At the last moment Bardeen accepted the trial function proposed by Schrieffer, inconsistent with the particle conservation law, and leading to the concept of the Cooper pair based theory, known as BCS. Nevertheless, the solid-state Hamiltonian does not contain information of superconductivity, so that Frohlich as well as Bardeen in fact only calculated the correlation energy of conductors. 

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