Elastic properties of the Abrikosov lattice near the upper critical field and peak effect in the critical current

Abrikosov vortices in type II superconductors under magnetic field form highly correlated configurations with well defined elasticity, like regular atomic solids. While in the London limit vortices can be considered as line-like objects, when the field approaches the upper critical field Hc2(T) the core structure becomes important for elastic properties. Taking into account the deformation of the shape of the current distribution leads to significant increase in the shear modulus of the vortex lattice compared to previous estimates. The elastic properties determine the response to vortex matter pinning. The modified value of the elastic modulus is used to support a recent theory of the discontinuous “peak effect” in the critical current. It is argued that the critical current of the vortex lattice decreases monotonously as a function of the magnetic field, jumping to a high value in the homogeneous amorphous phase.