Magnetization measurements and Ginzburg-Landau simulations of micron-size β-tin samples: evidence for an unusual critical behavior of mesoscopic type-I superconductors

We describe investigations of the largely unexplored field of mesoscopic type-I superconductors. Micromagnetometry and 3D Ginzburg-Landau simulations of our single crystal β-tin samples in this regime reveal size- and temperature-dependent supercritical fields whose behavior is radically different from the bulk critical field H(c)(B). We find that complete suppression of the intermediate state in medium-size samples can result in a surprising reduction of the critical field significantly below H(c)(B). We also reveal an evolution of the superconducting-to-normal phase transition from the expected irreversible first order at low temperatures through the previously unobserved reversible first-order to a second-order transition close to T(c), where the critical field can be many times larger than H(c)(B). Finally, we have identified striking correlations between the mesoscopic H(c3) for nucleation of surface superconductivity and the thermodynamic H(c) near T(c). All these observations are entirely unexpected in the conventional type-I picture.