Superconductivity

Abstract

Superconductivity was discovered in 1911 by H. Kamerlingh Onnes (1911) in Leiden just three years after he first liquified helium, which made sufficiently low temperatures available. What he found was that the electrical resistance of some metals, such as lead, mercury, tin, and aluminum, disappeared completely in a narrow temperature range at a critical temperature T _c (typically a few Kelvin) specific to each metal. Twenty-two years later, Meissner and Ochsenfeld (1933) discovered that these superconductors were perfectly diamagnetic (the “Meissner effect” ) as well as perfectly conducting. These remarkable properties were neatly described by the phenomenological theory of F. and H. London (1935). Their model postulated a density of “superconducting electrons” n _s per unit volume, whose response to electromagnetic fields could be described by

$${{\bf{J}}_s} = - \left( {c/4\pi \lambda _L^2} \right){\bf{A}}$$

(with a specific “London gauge” choice for the vector potential). The time derivative of Eq. (1) implies that the superconducting electrons respond to an electric field E essentially as Drude free electrons with an infinitely long relaxation time. Combined with the Maxwell equations, this leads to a frequency-independent skin depth, called the London penetration depth:

$${\lambda _L} = {\left( {m{c^2}/4\pi {n_s}{e^2}} \right)^{1/2}}.$$

The curl of Eq. (1) (with Maxwell’s equations) implies the static flux expulsion of the Meissner effect, which cannot be interpreted in a classical way. Since λ _L was found experimentally to diverge at T _c roughly as [1 - (T/T _c )⁴]^−1/2, n _s was presumed to go continuously to zero at T _c , as in a second-order phase transition.