Time-dependent Ginzburg-Landau theory with floating nucleation kernel; FIR conductivity in the Abrikosov vortex lattice

Why Vortex Lattice Melting Theory is Science Fiction

Five years ago the talk "The vortex lattice melting theory as example of science fiction" cond-mat/9811051 was presented. Nevertheless this theory predominates up to now and very many people devote oneself to it. It is explained in the present paper why the only first order phase transition observed on the way from the Abrikosov state in the normal state should be interpreted as phase coherence disappearance. The false concept of vortex lattice melting appeared because of some causes main of them are erroneous interpretation of direct observation of the Abrikosov state and the use by theorists…

Effect of Fluctuations on the NMR Relaxation Beyond the Abrikosov Vortex State

The effect of fluctuations on the nuclear magnetic resonance (NMR) relaxation rate, $W$, is studied in a complete phase diagram of a 2D superconductor above the upper critical field line $H_{c2}(T)$ . In the region of relatively high temperatures and low magnetic fields, the relaxation rate $W$ is determined by two competing effects. The first one is its decrease in result of suppression of quasi-particle density of states (DOS) due to formation of fluctuation Cooper pairs (FCP). The second one is a specific, purely quantum, relaxation process of the Maki-Thompson (MT) type, which for low fiel…

Finite size effects as the explanation of ``freezing'' in vortex liquids

We investigate the effect of thermal fluctuations on the (mean-field) Abrikosov phase. The lower critical dimension of the superconducting phase is three, indicating the absence of the Abrikosov phase for dimensions d<3. Within the d=3 vortex liquid, the phase correlation length along the magnetic field direction grows exponentially rapidly as the temperature is lowered. For a finite bulk system, there is a 3D-2D crossover effect when the phase correlation length becomes comparable to the sample thickness. Such a crossover effect takes place over a very narrow temperature interval and mimics t…

A Simple Analytical Model of Vortex Lattice Melting in 2D Superconductors

The melting of the Abrikosov vortex lattice in a 2D type-II superconductor at high magnetic fields is studied analytically within the framework of the phenomenological Ginzburg-Landau theory. It is shown that local phase fluctuations in the superconducting order parameter, associated with low energies sliding motions of Bragg chains along the principal crystallographic axes of the vortex lattice, lead to a weak first order 'melting' transition at a certain temperature $T_{m}$, well below the mean field $T_{c\text{}}$, where the shear modulus drops abruptly to a nonzero value. The residual shea…

The vortex lattice melting theory as example of science fiction

The concept of the transition of type II superconductor into the Abrikosov state as the appearance of long-range phase coherence is considered. It is shown that this transition should be first order in ideal (without disorder) superconductor. Such transition is indeed observed in bulk superconductors with weak disorder at a field Hc4 < Hc2. No experimental evidence of the vortex lattice melting exists now. It is shown that this popular concept has appeared on a consequence of an incorrect interpretation of the Abrikosov state and incorrect definition of the phase coherence. The absence of a sh…

Superconducting zero temperature phase transition in two dimensions and in the magnetic field

We derive the Ginzburg-Landau-Wilson theory for the superconducting phase transition in two dimensions and in the magnetic field. Without disorder the theory describes a fluctuation induced first-order quantum phase transition into the Abrikosov lattice. We propose a phenomenological criterion for determining the transition field and discuss the qualitative effects of disorder. Comparison with recent experiments on MoGe films is discussed.

First integrals of Ginzburg-Landau equations and stability criteria for vortex-free state in unconventional superconductors

The first integrals of the Ginzburg-Landau equations for a vortex-free state of superconductors with different mixed symmetries of the order parameter are found. The general boundary conditions for the order parameter at the ideal interface between the superconductor and vacuum are derived. Based on these integrals and boundary conditions, we analyze the stability criteria for vortex-free state in unconventional superconductors. The threshold field above which the Abrikosov vortices can enter the superconductor is found to be higher or equal to the thermodynamic critical field for all states u…

原子费米超流在球面上的近似涡旋晶格

Approximate vortex lattices of atomic Fermi superfluid on a spherical surface

研究原子费米超流在球面受有效单极场作用时的近似涡旋结构，通过吉金格-兰道理论两种方法构建序参量，探讨涡旋参数与平面情况的关联。

Magnetic field dependence of the electrical conductivity in V3Ge in the vicinity of Hc2

The phase transition from the Abrikosov state to the normal state with superconducting fluctuations observed below the second critical field and well-known as vortex lattice melting was one of the most popular problems in the nineties. This problem had became popular after the discovery of high-Tc superconductors because the fluctuation phenomena are much stronger in the HTSC than in the conventional superconductors. Most people are sure that this sharp transition was observed for the present only in HTSC and are ignorant that it was observed as far back as 1981, before the HTSC discovery. In …