Superconductivity

Superconductivity and the associated Meissner effect are introduced, indicating that superconductors are perfect diamagnetics. Condensation energy is deduced. The London analysis showing how superconductors exclude flux is presented. The BCS microscopic theory is recapitulated: Cooper pairs of electrons are the constituents of the Bose condensate that carries the non-dissipative current. The binding energy of pairs (energy gap below the Fermi sea) is deduced and related to their size and the critical temperature. Dependence of the energy gap on temperature is shown consistent with BCS theory. The Ginzberg–Landau analysis and the spontaneous symmetry breaking in the condensate phase are recounted. Quantization of trapped magnetic flux is shown to be related to superconductor topology. Type-II superconductors are treated. Finally Josephson effects show unambiguously that the condensate is a macroscopic quantum state. Josephson applications are enumerated, including a new voltage standard, SQUIDs and preliminary versions of qubits (transmons) for quantum computing.