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

Abstract

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 $T_c$, 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.

10 pages, 4 figures

References in corpus (7)

• Two-Dimensional Vortex Lattice Melting
• Theory of a Continuous H${}_{c2}$ Normal-to-Superconducting Transition
• Density-functional theory of freezing of vortex-liquid in quasi two-dimensional superconductors
• Continuous 3d Freezing Transition in Layered Superconductors
• Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors
• First order melting of vortex lattice in strongly type-II three dimensional superconductors
• Existence of the Abrikosov vortex state in two-dimensional type-II superconductors without pinning

Cited by in corpus (9)

• The Ginzburg-Landau Theory of Type II superconductors in magnetic field
• Imaging superconducting vortex core and lattice with the scanning tunneling microscope
• Melting of the vortex lattice in high $T_c$ superconductors
• Thermal fluctuations correction to magnetization and specific heat of vortex solids in type II superconductors
• Supercooled vortex liquid and quantitative theory of melting of the flux line lattice in type II superconductors
• Large Broadening of the Superconducting Transition by Fluctuations in a 3D Metal at High Magnetic Fields: The MgB${}_2$ case
• Vortex states in 2D superconductor at high magnetic field in a periodic pinning potential
• Partially-ordered vortex lattices in the high-field, low-temperature mixed state of quasi two-dimensional organic superconductors
• Irreversible Magnetization Deep in the Vortex-Liquid State of a 2D Superconductor at High Magnetic Fields