Size Effects in the Ginzburg-Landau Theory

The Ginzburg-Landau theory is analyzed in the case of small dimension superconductors, a couple of orders of magnitude above the coherence length, where the theory is still valid but quantum fluctuations become significant. In this regime, the potential around the expectation value is approximated to a quadratic behavior, and the ground-state derived from the Klein-Gordon solutions of the Higgs-like field. The ground-state energy is directly compared to the condensation energy, and used to extract new limits on the size of superconductors at zero Kelvin and near the critical temperature.