Fundamental inversion problem for the magnetic-force microscopy of superconductors

A fundamental inversion problem for the magnetic-force microscopy (MFM) of a semi-infinite superconductor in the Meissner state is formulated. Under certain assumptions on the MFM tip and superconductor geometry, a unique layer-dependent penetration depth $\ensuremath{\lambda}(z)$ can be recovered from one-dimensional force measurements. This development opens new possibilities for the nondestructive evaluation of superconducting crystals and films. Some of the implications of the detailed knowledge of the temperature dependence of the penetration depth at low temperature on the superconducting pairing state are noted.