Numerical and Analytical Calculations of the Superheating Field for a Superconducting Half-Space

Abstract

Superconductivity is observed in some materials that are cooled below a critical temperature T_C. In the superconducting state, the sample expels magnetic fields (a phenomenon called the Meissner effect). However, if the applied magnetic field is greater than a certain critical field H_C(T_C), superconductivity is destroyed and the sample becomes normal. In “semi-infinite” bulk samples (i.e. the sample is bounded on one side by a plane), superconductivity has been observed experimentally for magnetic fields larger than H_C These metastable “superheated” states exist for H_C < H < H_sh. Our task was to numerically calculate H_sh as a function of κ, where κ is the ratio of the penetration depth to the correlation length of the sample.