Effect of two length scales on the properties ofMgB2 for arbitrary applied magnetic field

Abstract

Experiments carried out on the intermetallic superconducting materialMgB2 have shown anomalous magnetic field dependence of upper critical field, small angleneutron scattering form factor, specific heat, critical current etc. Similarly, scanningtunnelling microscopy (STM) experiments on vortex structures have shown unusuallylarge vortex core size and two different magnetic and spatial field scales. Also,whereas the specific heat measurements and isotope shift experiments have shownBardeen–Cooper–Schrieffer-like (BCS-like) behaviour, the temperature dependences ofthe penetration depth experiments have shown non-BCS-like behaviour. Theseanomalous behaviours have been attributed to the multiband superconductivityof this material and the nature of the local spatial behaviour of the magneticinduction and the order parameter components having two length scales. Wereport an analytical investigation of the effect of two length scales on thetemperature and the applied magnetic field dependence of several properties ofMgB2, such as, the penetration depth, single vortex and vortex lattice structure, vortex coreradius, reversible magnetization, critical current, small angle neutron scattering form factorand the shear modulus of the vortex lattice within the framework of two-order parameterGinzburg–Landau theory. We solve the corresponding nonlinear Ginzburg–Landauequations numerically exactly using an iterative method for arbitrary applied fieldHc1 < H < Hc2, the Ginzburg–Landau parameter and vortex lattice symmetry. This enablesus to compute the local spatial behaviour of the magnetic induction and theorder parameters accurately for arbitrary applied field and a wide rangeof temperature. Comparison of the analytical results with experiments onMgB2 gives very good agreement.