Size Effects in the Ginzburg-Landau Theory

TL;DR

This paper investigates how the Ginzburg-Landau theory applies to small superconductors, incorporating quantum fluctuations, and derives new size limits based on ground-state energy comparisons.

Contribution

It extends the Ginzburg-Landau theory to small superconductors near quantum regimes, providing new size constraints and insights into quantum fluctuation effects.

Findings

Derived size limits for superconductors at zero Kelvin and near critical temperature.

Quantified the impact of quantum fluctuations on the Ginzburg-Landau potential.

Compared ground-state energy with condensation energy to establish new bounds.

Abstract

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.