Superconductivity

Superconductivity refers to a specific set of physical properties found in certain materials known as superconductors. In these materials, electrical resistance vanishes completely, and any magnetic field inside the material is pushed out. Unlike ordinary metals, where resistance slowly decreases as the temperature drops toward absolute zero, a superconductor has a distinct critical temperature. Below that temperature, resistance falls abruptly to zero. A current started in a loop of superconducting wire will continue to flow forever without any power source. This phenomenon was first observed in 1911 by the Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity can only be explained by quantum mechanics. A key feature is the Meissner effect, where the magnetic field inside the superconductor is completely canceled as it enters the superconducting state. This effect shows that superconductivity is not simply a classical idealization of perfect conductivity. In 1986, certain cuprate-perovskite ceramic materials were found to have a critical temperature above 35 K (−238 °C). Shortly after, Ching-Wu Chu discovered that replacing lanthanum with yttrium—creating YBCO—raised the critical temperature to 92 K (−181 °C). This was significant because liquid nitrogen could then be used as a refrigerant. Such a high transition temperature is impossible for a conventional superconductor, so these materials are called high-temperature superconductors. Liquid nitrogen, a cheap coolant, boils at 77 K (−196 °C), so superconductivity above that temperature makes many experiments and applications much more practical than those requiring lower temperatures. **History**

Superconductivity was first discovered in solid mercury on April 8, 1911, by Heike Kamerlingh Onnes. He was studying the resistance of mercury at cryogenic temperatures using newly produced liquid helium as a refrigerant. At 4.2 K, the resistance suddenly disappeared. In the same experiment, he also observed the superfluid transition of helium at 2.2 K, though he did not recognize its significance. The exact date and circumstances of the discovery were only reconstructed a century later when Onnes's notebook was found. Over the following decades, superconductivity was found in other materials: tin and lead in 1913 (at 3.8 K and 7 K, respectively), and niobium nitride in 1941 (at 16 K). Considerable effort went into understanding how and why superconductivity works. A major step came in 1933, when Meissner and Ochsenfeld discovered that superconductors expel applied magnetic fields—the Meissner effect. In 1935, Fritz and Heinz London showed that this effect results from minimizing the electromagnetic free energy carried by the superconducting current. **London constitutive equations**

The first theoretical model for superconductivity was entirely classical, summarized by the London constitutive equations. Proposed by the brothers Fritz and Heinz London in 1935, shortly after the discovery of magnetic field expulsion, these equations successfully explain the Meissner effect, where a material exponentially expels all internal magnetic fields as it becomes superconducting. Using the London equation, one can calculate how the magnetic field inside a superconductor varies with distance from the surface. The two London constitutive equations for a superconductor are:

∂j/∂t = (ne²/m) E, ∇ × j = −(ne²/m) B

The first equation follows from Newton's second law for superconducting electrons. **Conventional theories (1950s)**

In the 1950s, theoretical condensed matter physicists developed an understanding of "conventional" superconductivity through two theories: the phenomenological Ginzburg–Landau theory (1950) and the microscopic BCS theory (1957). In 1950, Landau and Ginzburg devised the phenomenological Ginzburg–Landau theory. This theory combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation and was highly successful in explaining the macroscopic properties of superconductors. Notably, Abrikosov showed that the Ginzburg–Landau theory predicts two categories of superconductors, now called Type I and Type II. Abrikosov and Ginzburg received the 2003 Nobel Prize for this work (Landau had won the 1962 Nobel Prize for other work and died in 1968). The four-dimensional extension of the Ginzburg–Landau theory, the Coleman-Weinberg model, is important in quantum field theory and cosmology.