A preface is supposed to alert potential readers to the contents and style of what lies within so they can decide whether to proceed further. Superconductivity is now a vast subject extending from the esoteric to the very practical; the people who study or work on it have different preparations, goals, and talents. No treatment can or should address all these dimensions.

Part I is devoted to the phenomenological aspects of superconductivity, e.g., London's and Pippard's electrodynamics, the Ginzburg–Landau theory and the Landau Fermi liquid theory. These theories allow a discussion of the effects of magnetic fields, interfaces and boundaries, fluctuations, and collective response (which may all be thought of as different manifestations of inhomogeneities).

Since there is currently much interest in unconventional (non-s-wave) superconductivity, we have included a discussion of the associated Ginzburg–Landau theory (which then has a multidimensional, complex order parameter). He is the only established example of an unconventional superfluid (triplet p-wave) and therefore our discussions of this substance are somewhat longer.

Part II is devoted to the microscopic theory of uniform superconductors: the theory of Bardeen, Cooper, and Schrieffer (BCS) and the Bogoliubov–Valatin canonical transformation, where the latter so greatly simplifies the discussion of excited states and finite temperature effects. Although not strictly a uniform-superconductor phenomenon, the theory of tunneling and the accompanying Josephson effects are also discussed in Part II.

We recall expressions (26.19) for the expectation value of the reduced Hamiltonian

Let us calculate the energy required to add an electron to the system in a state |k↓〉 assuming its companion state | –k↓〉 is empty. In order to do this we must: (i) account for the energy increase due to removing the amplitude of the pair associated with this wave vector k and (ii) add the energy of the lone electron introduced into the state | k〉. When we remove the bound pair from the ground state, according to (27.1) the energy of the system changes by an amount

(the factor 2 in the second term arises because the chosen pair state (k, – k) occurs twice since we have a double sum). Using Eq. (26.23) we may write the form (27.2) as

Adding to (27.3) the energy ξk of one (unbound) electron then yields the quasiparticle excitation energy,

where we used Eqs. (26.24) and (26.27). Thus the energy needed to add an electron in state k↓ is σk. If we calculate the energy required to remove an electron in a state – k↓ we also obtain σk. Note the minimum excitation energy is Ak; i.e., the excitation spectrum has an energy gap.

A system which is disturbed from its equilibrium state will relax toward equilibrium when the associated perturbation is removed. This relaxation process has two characteristic forms in general: (i) damped oscillations, or (ii) monotonic decay. In this section we will be concerned primarily with the latter type of decay (oscillatory responses of bulk superconductors will be discussed in Sec. 54 and are termed collective modes).

Thermodynamic systems have characteristic microscopic (rapid) relaxation times and the relaxation of the vast majority of their internal degrees of freedom proceeds on these time scales. There are two important exceptions: (i) modes involving degrees of freedom for which conservation laws exist; and (ii) additional modes involving a broken symmetry of the system. The conservation laws are those involving mass (or charge), energy (or entropy) and momentum (which, being a vector quantity, involves an equation for each component). For a liquid this leads to the existence of five low frequency (also called hydrodynamic) modes involving: a heat conduction mode (1), transverse viscous shear waves (2), and longitudinal sound (2). The number in parentheses denotes the number of such modes, there being five in all, corresponding to the five conservation laws. For a derivation of this mode structure see Landau and Lifshitz (1987) or Miyano and Ketterson (1979). Additional equations of motion exist when the system spontaneously breaks some symmetry, and we now list some examples.