Applications of symmetries in superconductivity

Abstract

Superconductivity was discovered by Kamerlingh Onnes in 1911. It is characterized by two major properties: i) the electrical resistance exactly vanishes and ii) the magnetic field lines are expelled outside the superconducting body (Meissner effect). Both properties are potentially useful for many applications, in particular for storage and dissipationless transport of electrical energy. However, though superconductivity has been observed in many metals, it has been limited to low temperatures so far. Moreover, it cannot sustain too large external magnetic fields or current densities. Applications have thus been limited to quite specific, though significant areas (superconducting electromagnets used for Magnetic Resonance Imaging, for instance). On the fundamental research side, superconductivity has fascinated many physicists, in particular because it is a direct manifestation of quantum coherence on the macroscopic scale. The theories that have been invented to explain this phenomenon have then irrigated other areas including condensed matter, nuclear, and particle physics. The aim of these lecture notes is to highlight that the concept of symmetry has been essential in making these advances. Section 2 will present the phenomenological description of superconductivity. It will allow ascribing it to a spontaneous gauge symmetry breaking in the frame of the Landau theory of phase transitions. In Section 3, the microscopic theory of superconductivity will be introduced. Unconventional superconductors where an additional symmetry breaking takes place at the phase transition will be contrasted with conventional superconductors where only the gauge symmetry breaking takes place. Physical signatures that allow distinguishing conventional and unconventional superconductors will be discussed. Section 4 will conclude by presenting active fields of research in superconductivity where the concepts of symmetry are still being used. For the clarity of the presentation, strong simplifications will be made in the analysis and many aspects of the theory will be put aside. The reader may consult the textbooks [1–3] for further reading and references. A detailed presentation of the aspects related with symmetries can be found in Refs. [4, 5].