The Ginzburg-Landau Theory of Type II superconductors in magnetic field

Abstract

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg - Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor - normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high $T_c$ materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg - Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose - Einstein condensate.

60 pages, 15 figures, accepted for publication in Review of Modern Physics

References in corpus (10)

• Upper critical fields well above 100 T for the superconductor SmFeAsO${}_{0.85}$F${}_{0.15}$ with T${}_c$ = 46 K
• Direct observation of the flux-line vortex glass phase in a type II superconductor
• Peak effect and dynamic melting of vortex matter in NbSe${}_2$ crystals
• Dynamic ordering of driven vortex matter in the peak effect regime of amorphous MoGe films and 2H-NbSe2 crystals
• Thermal fluctuations and vortex melting in the classical superconductor Nb3Sn from high-resolution specific-heat measurements
• Flux Line Lattice Melting and the Formation of a Coherent Quasiparticle Bloch State in the Ultraclean URu${}_2$Si${}_2$ Superconductor
• Exploring metastability via the third harmonic measurements in single crystals of $2H$-$NbS{e}_2$ showing anomalous Peak effect
• Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of $YN{i}_2{B}_{2}C$ and $LuN{i}_2{B}_{2}C$
• Dynamics of vortex glass phase in strongly type II superconductors
• An Improved Nonperturbative Method for Studying Two-dimensional Vortex Liquids

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