The edge effect on magnetic critical fields in high-temperature superconductors – numerical approach

It is well-known that the superconducting phase in type-II superconductors first appears near surfaces as magnetic field drops below the so-called “third critical field” . Every textbook on superconductivity mentions the fact that , where is the second critical field that corresponds to the appearance of superconductivity in the bulk. However, it is not easy to provide reference to a work where has been directly calculated, except for a couple of papers where an estimation for is found using the variational method. Here we provide a clear numerical algorithm (including MATLAB code) for calculation of the third critical filed that might be of methodological worth for both students studying superconductivity and numerical methods in quantum mechanics.