Schrieffer mechanism

The first forward step was taken by Leon Cooper, the slightly built graduate of the Bronx High School of Science in New York, a newly minted Ph.D. from Columbia, and the man Bardeen called the quantum mechanic from the East. Cooper had joined with Bardeen and Schrieffer at the University of Illinois to tackle the mystery of superconductivity. (Schrieffer, from the Massachusetts Institute of... 

As the mechanism of superconductivity in these doped fullerites was not clear, the greatest attention was directed to the standard mechanism of superconductivity. The conventional theory is based on the electron-phonon interaction and generalized in the Eliashberg equations which include the Bardeen, Cooper and Schrieffer (BCS) equation as a weak-coupling limit [78]. For real superconductors the ratio for the weak-coupling limit is close to the value of 3.52, and for stronger coupling materials it increases up to about 5.1... 

In this chapter we describe the consequences of electron-phonon coupling in the absence of electron-electron interactions. The celebrated model for studying this limit is the so-called Su-Schrieffer-Heeger model (Su et al. 1979, 1980), defined in Section 2.8.2. In the absence of lattice dynamics this model is known as the Peierls model. We begin by describing the predictions of this model, namely the Peierls mechanism for bond alternation in the ground state and bond defects in the excited states. Finally, we reintroduce lattice dynamics classically and briefly describe amplitude-breathers. 

The first detailed quantum-mechanical explanation of superconductivity was given by Bardeen, Cooper, and Schrieffer in 1957 [7] (commonly called the BCS theory). Since then various advances in the mathematics of the theory have been made, but the basic physical interpretation has not changed. In this theory conduction electrons of equal but opposite angular momentum fall as pairs into a lowest energy state which is separated from the first excited state by a temperature dependent gap in the spectrum of allowed energies. The existence of... 

The BCS theory, however, developed in 1957 by three physicists, John Bardeen, Leon Cooper, and Robert Schrieffer, does estabhsh a model for the mechanism behind superconductivity. Bardeen, Cooper, and Schrieffer received the Nobel Prize in physics in 1972 for their theory. It was known that the flux quantum was inversely proportional to twice the charge of an electron, and it had also been observed that different isotopes of the same superconducting element had different critical temperatures. Actually, the heavier the isotope, the lower the critical temperature is. The critical temperature, in K, of an isotope with an atomic mass, M, expressed in kg.moT can be predicted by the following equation ... 

In 1957, the American physicists J. Bardeen, L. N. Cooper, and J. R. Schrieffer (1957) developed a microscopic theory of superconductivity (the BCS theory), and were subsequently awarded the Nobel Prize in physics in 1972. The BCS theory is applicable to metals and alloys (conventional low-Tc superconductors). The Coulombic repulsion of electrons is thought to be overcome by a phonon-mediated mechanism, whereby two electrons with their spins aligned in opposite directions strongly attract each other (Cooper pairing). Cooper pairs condense to a remarkably stable macroscopic quantum state, described by identical wave functions (see Appendix E). 

Superconductivity in metals can be explained satisfactorily by BCS theory, first proposed by John Bardeen, Leon NeU Cooper, and John Roben Schrieffer in 1957. They received the Nobel Prize in Physics in 1972 for their work. BCS theory treats superconductivity using quantum mechanical effects, proposing that electrons with opposite spin can pair due to fundamental attractive forces between the electrons. At temperatures below Tc, the paired electrons resist energetic interference from other atoms and experience no resistance to flow. Superconductivity in ceramics has yet to be satisfactorily explained. 

Since it is apparent that the high temperature superconductivity of cuprates cannot be explained by the Bardeen-Cooper-Schrieffer (BCS) mechanism that explained the low temperature superconductors so beautifully, the role of the... 

The basic mechanism of superconductivity was accounted for in considerable detail by the theory of Bardeen, Cooper, and Schrieffer (BCS theory), which discusses the phenomenon in terms of the formation of Cooper pairs of electrons through an attractive interaction mediated by the lattice. Unlike individual electrons. 

Finally we mention the interesting new developments in this field. KRUM-HANSL and SCHRIEFFER have studied the dynamics and statistical mechanics of a one-dimensional model system whose displacement field Hamiltonian is strongly anharmonic [5.10]. The most important result is that the phonon representation commonly used in perturbation calculations is inadequate for discussing one important type of excitation which can occur in highly nonlinear systems. This excitation corresponds to domain-wall motion and is now called a soliton [5.11,12]. A qualitative discussion of solitons will be given in [1.35]. 

According to the BCS (Bardeen, Cooper and Schrieffer) theory, electrons form pairs below the critieal temperature T., stabilized by a decrease in energy A = kT. . Lattice vibrations, more precisely acoustic phonons, are mediators of the interaction. This interpretation is confirmed through different experimental observations when the transition temperature is low (T. < 30 0 K). For higher temperatures, and henee stronger interaetions, the mechanism of pair formation stated by BCS must be reexamined. Several proposals have been made but to date none have been impressive. The phase diagram in Figure 11.7 shows how superconductivity appears under extreme eonditions. 

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