Abstract
The standard Ginzburg-Landau (GL) equations are only valid in the vicinity of the critical temperature. Based on the Eilenberger equations for a single band and s-wave superconductor, we derive a modified version of the standard GL equations to improve the applicability of the standard formalism at temperature away from the critical temperature. It is shown that in comparison with previous studies, our method is more convenient to calculate and our modified equations are also compatible with a dirty superconductor. To illustrate the usefulness of our formalism, we solve the modified equations numerically and give the magnetic field distribution in the mixed state at any temperature. The results show that the vortex lattice could be still observed even away from the critical temperature (e.g., T/Tc = 0.3).
Highlights
As is well known, the Ginzburg-Landau (GL) theory is an effective phenomenological theory to describe superconductivity [1]
Strictly speaking, the GL equations are only valid in the vicinity of the critical temperature [3]
A transformation of the Eilenberger equations from partial differential equations into ordinary differential equations enables the numerical study of the field distribution in the mixed state [6] [7]
Summary
The Ginzburg-Landau (GL) theory is an effective phenomenological theory to describe superconductivity [1]. A transformation of the Eilenberger equations from partial differential equations into ordinary differential equations enables the numerical study of the field distribution in the mixed state [6] [7]. All of these works are based on the microscopic theory, which is not convenient enough compared with the GL theory. We develop a more convenient approach to derive a set of modified GL equations from the Eilenberger equations, which are applicable to any finite temperature cases. To illustrate the validity of our formalism, we will solve the modified equations numerically and investigate the temperature dependence of the field distribution in the mixed state. We discuss the single band, s-wave superconductor, and we adopt the ansatz that the Fermi surface is a sphere
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