## Enigmas and solutions (1933-)

The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current. In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg.

Ginzburg-Landau theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968). Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

### BCS Theory

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature. Gor'kov was the first to derive the superconducting phase evolution equation $2eV=\hbar\frac{\partial \phi}{\partial t}$.

### Little and Parks effect

The Little-Parks effect was discovered in 1962 in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. The electrical resistance of such cylinders shows a periodic oscillation with the magnetic flux piercing the cylinder, the period being h/2e = 2.07×10−15 V·s. The explanation provided by Little and Parks is that the resistance oscillation reflects a more fundamental phenomenon, i.e. periodic oscillation of the superconducting critical temperature (Tc). This is the temperature at which the sample becomes superconducting. The LP effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the fluxoid rather than the flux which is quantized in superconductors. The LP effect demonstrates that vector-potential couples to an observable physical quantity, namely the superconducting critical temperature.

## Commercial activity

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse.

In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/2e, and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973.

In 1973 Nb3Ge found to have Tc of 23 K which remained the highest ambient pressure Tc until the discovery of the cuprate high temperature superconductors in 1986 (see below).

## High temperature superconductors

In 1986, Bednorz and Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987) and was the first of the high temperature superconductors. It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.

In March 2001 superconductivity of Magnesium diboride (MgB2) was announced.

As of March 2007, the current world record of superconductivity[1] is held by a ceramic superconductor doped with thallium, mercury, copper, barium, calcium and oxygen (Tc=138 K).[2] Also a patent has been applied for a material which becomes superconductive at an even higher temperature (up to 200 K).[3] Efforts by this same group are currently underway to resolve resistance transitions appearing near 218K. This structure type has not yet been identified and efforts to synthesize a 24-layer analog proved inconclusive.

In 2008 the oxypnictide or iron-based superconductors were discovered which led to a flurry of work in the hope that studying them would provide a theory of the cuprate superconductors.

## Historical publications

Onnes papers

• "The resistance of pure mercury at helium temperatures" Comm. Leiden. April 28, 1911.
• "The disappearance of the resistivity of mercury". Comm. Leiden. May 27, 1911.
• "On the sudden change in the rate at which the resistance of mercury disappears". Comm. Leiden. November 25, 1911.
• "The imitation of an ampere molecular current or a permanent magnet by means of a supraconductor". Comm. Leiden.

BCS theory

• J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)

Other papers

• W. Meissner and R. Oschenfeld, Naturwiss. 21, 787 (1933)
• F. London and H. London, Proc. R. Soc. London A149, 71 (1935)
• V.L. Ginzburg and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950)
• E.Maxwell, Phys. Rev. 78, 477 (1950)
• C.A. Reynolds et al., Phys. Rev. 78, 487 (1950)
• W. A. Little and R. D. Parks, Physical Review Letters, Vol.9, page 9, (1962).

Other books

• M. Tinkham, “Introduction to Superconductivity”, 2nd Ed., McGraw-Hill, NY, 1996.
• Matricon, Jean; Waysand, Georges; Glashausser, Charles; The Cold Wars: A History of Superconductivity, Rutgers University Press, 2003, ISBN 0813532957 ... how the Cold War influenced the research in superconductivity

Patents

• Tesla, Nikola, U.S. Patent 685,012 "Means for Increasing the Intensity of Electrical Oscillations", March 21, 1900.
source: wikipedia