Theory of Superconductivity
Based on lectures by the author, the fundamentals of the theory of superconductivity are stressed, to provide the reader with a framework for the literature in which detailed applications of the microscopic theory are made to specific probems. Recent developments are also considered.
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ABC ppbk absorption amplitude Bardeen BCS theory calculations Chapter coherence factors condensation conduction electrons contribution Coulomb interaction coupling defined density diamagnetic discussed eigenstates electromagnetic electron-phonon interaction energy gap energy-gap equation excitation energy excitation spectrum experimental expression Fermi gas Fermi sea Fermi surface fermions finds finite flux Fourier frequency gauge gauge-invariant given gives Gor'kov graphs Green's function ground Hamiltonian integral ISBN jellium London longitudinal magnetic field many-body matrix elements Meissner effect momentum normal metal nuclear spin number of electrons number of particles obtain occupation number operator P. W. Anderson pairing approximation pairing theory parameter Pauli principle perturbation phonon Phys poles problem properties quantization quantum quasi-particle relation result satisfy scattering self-energy shown in Figure single-particle spectral weight function super superconducting superfluid temperature tion transition transverse tunneling vanishes vector vertex function wave function zero
Page 298 - Le savant doit ordonner; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison.
Page 303 - ... the other electrons and the electrons also shield the ions involved in the vibrational motion. Pines and I derived an effective electron-electron interaction starting from a Hamiltonian in which phonon and Coulomb terms are included from the start. [1 7] As is the case for the Frohlich Hamiltonian, the matrix element for scattering of a pair of electrons near the Fermi surface from exchange of virtual phonons is negative (attractive) if the energy difference between the electron states involved...
Page 284 - ... formation of correlated pairs. In the wave function that results there are strong correlations between pairs of electrons with opposite spin and zero total momentum. These correlations are built from normal excitations near the Fermi surface and extend over spatial distances typically of the order of 10~4 cm. They can be constructed due to the large wave numbers available because of the exclusion principle. Thus with a small additional expenditure of kinetic energy there can be a greater gain...
Page 281 - ... in this enormous matrix, sub-matrices in which all single-particle states except for one pair of electrons remain unchanged. These two electrons can scatter via the electron-electron interaction to all states of the same total momentum. We may envisage the pair wending its way (so to speak) over all states unoccupied by other electrons. [The electron-electron interaction in which we are interested is both weak and slowly varying over the Fermi surface. This and the fact that the energy involved...
Page 268 - Fig. 1 which owing to its particular electrical properties can be called the state of superconductivity." He found this state could be destroyed by applying a sufficiently strong magnetic field, now called the critical field Hc. In April — June, 1914, Onnes discovered that a current, once induced in a closed loop of superconducting wire, persists for long periods without decay, as he later graphically demonstrated by carrying a loop of superconducting wire containing a persistent current from Leiden...
Page 286 - The y operators satisfy Fermi anti-commutation relations so that with them we obtain a complete orthonormal set of excitations in one-to-one correspondence with the excitations of the normal metal. We can sketch the following picture. In the ground state of the superconductor all the electrons are in singlet-pair correlated states of zero total momentum. In an m electron excited state the excited electrons are in "quasiparticle" states, very similar to the normal excitations and not strongly correlated...
Page 286 - ... very hard to scatter or to excite. Thus, one can identify two almost independent fluids. The correlated portion of the wave function has the properties of the superfluid : the resistance to change, the very small specific heat, whereas the excitations behave very much like normal electrons, and have an almost normal specific heat and resistance. When a steady electric field is applied to the metal the superfluid electrons short out the normal ones, but with higher frequency fields the resistive...
Page 286 - ... while the excitations behave very much like normal electrons, displaying an almost normal specific heat and resistance. When a steady electric field is applied to the metal, the superfluid electrons short out the normal ones, but with higher frequency fields the resistive properties of the excited electrons can be observed. [7...