# Elements of solid state physics by J.P. Srivastava

By J.P. Srivastava

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This expression demonstrates explicitly the possibility of increasing Tc when sufficiently strong coupling of electrons with high-frequency phonon modes exist. A practical limit to Tc within a phonon mechanism is, however, set by problems with the structural stability of the crystal lattice. Below Tc the BCS theory predicts a small energy gap in the electron excitation spectrum near EF. Physically the energy gap is one half of the minimum value of energy necessary for destroying a Cooper pair and exciting the two electrons to the normal state.

2 London penetration depth The application of Maxwell’s equations to the second London equation leads to the equation describing the penetration of a magnetic field into a superconductor Copyright © 1998 IOP Publishing Ltd 12 The evolution of SC theories This equation can be used in principle to find the distributions of flux density within any superconducting body. One needs to apply to the solutions of this equation the boundary conditions which follow from the shape of the body. Let us use this equation to determine the distribution of the magnetic field inside a superconductor when it is placed in a uniform magnetic field.

Therefore for most superconducting alloys with a small electron mean path l the GL parameter is large and they are type II superconductors. For intermediate values of electronic mean free path the expression for the GL parameter can be given in the following convenient form where γ is the Sommerfeld specific heat constant, in erg cm–3 K–2, and ρ is the residual resistivity in Ω cm. On the basis of this relation, it was shown that the GL theory satisfactorily explains the change of surface energy in Ta—Nb and U—Mo alloys.