Theory

In 1950 Vitaly Ginzburg and Lev Landau introduced in their seminal work1 (which will be referred to as GL hereafter) the equations which have been known ever since as GinzburgLandau (GL) equations and which became among the most universal equations of modern physics. Ginzburg-Landau equations either in their original or modified form describe a wealth of phenomena and systems including superconductivity and superfluidity, nonlinear waves in active media, pat-

tern formation and liquid crystals and supersymmetric conformal field theories2. Ginzburg-Landau equations were one of the first nonlinear theories to demonstrate solutions in the form of topological singularities. Historically, GL theory was an extension of the Landau theory of second-order phase transitions3 onto the quantum phenomenon of superconductivity. It was based on the idea that the normal metal-superconducting state transition is, in the absence of a magnetic field, a thermodynamic second-order transition. An order parameter Ψ of the GL theory is an averaged wave function of superconducting electrons. Because of its (comparative) simplicity and physical transparency, GL theory has become one of the most universal and powerful tools in studies of superconductivity. In what follows, we briefly review the history and the content of GL theory and discuss its most standard applications.