We describe investigations of the largely unexplored field of mesoscopic type-I superconductors. Micromagnetometry and 3D Ginzburg-Landau simulations of our single crystal $\beta$-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.

• Received 18 May 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.197003