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To enable an electron to scatter from the state to to the state the latter must be free (due to the Pauli exclusion principle). This is possible only in the vicinity of the Fermi surface which is represented in momentum space by a sphere of radius as shown in Fig. 5. Now we are ready to formulate the law of phonon-mediated interaction between electrons which forms the foundation of the BCS theory: Electrons with energies that differ from the Fermi energy by no more than are attracted to each other.

The zero-voltage The BCS model of superconductivity in metals 25 current flow resulting from the tunneling of Cooper pairs is known as the Josephson effect. Josephson also predicted that if a constant nonzero voltage V is maintained across the tunnel barrier, an alternating supercurrent will flow through the barrier in addition to the current produced by the tunneling of single electrons. The frequency v of the ac supercurrent is given by where is the electron charge, and is the Planck constant.

Nevertheless, in conventional superconductors, the residual losses which 26 HIGH-TEMPERATURE SUPERCONDUCTIVITY IN CUPRATES are determined by are small in comparison, for example, with those in superconductors. 7 Acoustic properties Let us consider the case in which pulsed ultrasound travels in a sample and is reflected at the surface. If the sample of length has two parallel surfaces on both sides, a train of echo pulses will be observed with a time interval of The height of successive echo pulses decreases exponentially with time From this information, one can obtain important physical quantities such as the sound velocity the attenuation coefficient and the elastic coefficient where is the mass density.