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 shear modulus above $T_{m}$ decreases asymptotically to zero with increasing temperature. Despite the large phase fluctuations, the average positions of Bragg chains at fimite temperature correspond to a regular vortex lattice, slightly distorted with respect to the triangular Abrikosov lattice. It is also shown that a genuine long range phase coherence exists only at zero temperature; however, below the melting point the vortex state is very close to the triangular Abrikosov lattice. A study of the size dependence of the structure factor at finite temperature indicates the existence of quasi-long range order with $S(\overrightarrow{G}) \sim N^{\sigma}$, and $1/2<\sigma <1$, where superconducting crystallites of correlated Bragg chains grow only along pinning chains. This finding may suggest a very efficient way of generating pinning defects in quasi 2D superconductors. Our results for the melting temperature and for the entropy jump agree with the state of the art Monte Carlo simulations.Comment: 10 pages, 4 figure

Does the Streaming Instability exist within the Terminal Velocity Approximation?

Terminal velocity approximation is appropriate to study the dynamics of gas-dust mixture with solids tightly coupled to the gas. This work reconsiders its compatibility with physical processes giving rise to the resonant Streaming Instability in the low dust density limit. It is shown that the linearised equations have been commonly used to study the Streaming Instability within the terminal velocity approximation actually exceed the accuracy of this approximation. For that reason, the corresponding dispersion equation recovers the long wavelength branch of the resonant Streaming Instability caused by the stationary azimuthal drift of the dust. However, the latter must remain beyond the terminal velocity approximation by its physical definition. The refined equations for gas-dust dynamics in the terminal velocity approximation does not lead to the resonant Streaming Instability. The work additionally elucidates the physical processes responsible for the instability.Comment: 11 pages, no figures, no tables, accepted to Ap