Critical Fields and Critical Currents in MgB2

We review recent measurements of upper (Hc2) and lower (Hc1) critical fields in clean single crystals of MgB2, and their anisotropies between the two principal crystallographic directions. Such crystals are far into the "clean limit" of Type II superconductivity, and indeed for fields applied in the c-direction, the Ginzburg-Landau parameter k is only about 3, just large enough for Type II behaviour. Because m0Hc2 is so low, about 3 T for fields in the c-direction, MgB2 has to be modified for it to become useful for high-current applications. It should be possible to increase Hc2 by the introduction of strong electron scattering (but because of the electronic structure and the double gap that results, the scatterers will have to be chosen carefully). In addition, pinning defects on a scale of a few nm will have to be engineered in order to enhance the critical current density at high fields.