
Superconductivity is a quantum state where electrical resistance vanishes and magnetic fields are expelled.Superconductivity is when certain materials, upon strong cooling, become perfect conductors of electricity: current can flow in them forever without losing energy. Imagine a slide down which a sled glides without friction—it would slide endlessly. Similarly, electrons in a superconductor move without resistance.
The discovery of superconductivity occurred in 1911, when Heike Kamerlingh Onnes measured the disappearance of resistance in mercury at 4.2 K. In 1933, Walther Meissner and Robert Ochsenfeld discovered that a superconductor expels a magnetic field. The Ginzburg–Landau theory (1950) phenomenologically described superconductivity based on an order parameter. The microscopic BCS theory (1957) explained electron pairing via phonons. In 1986, Georg Bednorz and Alex Müller discovered high-temperature superconductivity in ceramics, giving rise to a new class of materials.
The key principle is the formation of Cooper pairs and their Bose condensation. Electrons with opposite spins and momenta attract through virtual phonon exchange, overcoming Coulomb repulsion. The condensate wave function is described by a macroscopic order parameter, and its coherence leads to supercurrent. The BCS theory provides an expression for the critical temperature, where the Debye frequency and electron-phonon coupling potential are important. The electrodynamics of superconductors is described by the London equations, which explain the Meissner effect and perfect conductivity by linking supercurrent to fields. Superconductivity is a macroscopic manifestation of quantum mechanics, where the Schrödinger equation for the Cooper pair condensate describes a single wave function.
If you set a current in a superconducting ring, it will circulate for years without decaying—like water in a river that never stops.
| G | variable | Electrical conductance of a mesoscopic conductor — conductance siemens |
| T(E) | variable | Transmission probability for an electron at energy E — transmission probability |
| E | variable | Energy of the electron — energy joule |
| e | constant | Magnitude of the charge of an electron — elementary charge = 1.602176634e-19 coulomb |
| h | constant | Planck constant, fundamental quantum of action — planck constant = 6.62607015e-34 joule second |
| \sum | operator | Sum over all transmission channels or energy levels — summation |
| σ_total | variable | total conductivity — electrical conductivity siemens per metre |
| σ_cond | variable | conductivity from condensed (coherent) carriers — electrical conductivity siemens per metre |
| σ_fluct | variable | conductivity from fluctuating (incoherent) carriers — electrical conductivity siemens per metre |


















