Type II/1 Superconductivity and C4KHg

The possibility of type I superconductivity in C₄KHg was discussed above. In this case a first-order transition is observed at H_c rather than a second-order one at H_c2. There is also the possibility of a first-order transition at the lower critical field, H_c1, even in type II superconductors.[11] There are materials which, as the applied field is swept up, exhibit first a first-order transition at H_c1 and then a second-order transition at H_c2, as explained below. These superconductors are called ``type II/1'' to distinguish them from the more commonly encountered ``type II/2'' variety which have second-order transitions both at H_c1 and H_c2.[252] According to Auer and Ullmaier, who studied type II/1 superconductivity in TaN and NbN films, ``type II/1 superconductivity is a general phenomenon for all low-kappa type-II superconductors''.[11] If this statement is correct, the numbers in Table suggest that type II/1 superconductivity should occur for a sizable range of angles in C₄KHg, especially close to T_c .

Type II/1 transitions occur in materials which have attractive interactions among vortices for large intervortex separations. (Of course the intervortex interactions must be repulsive at small separations, or else the vortices will coalesce into macroscopic normal regions, and the material will be type I rather than type II/1.) When this is the case, there will be an intervortex separation d₀ which minimizes the interaction energy. If the vortex-interaction energy terms dominate the condensation energy in the total free energy, then once one vortex has been nucleated, the sample can reduce its energy by admitting more flux until the average vortex separation is d₀. The result is that in type II/1 superconductors there is a discontinuity in the magnetization at H_c1, which corresponds to a first-order transition.[11]

Since type II/1 behavior impacts upon the beginning of the field sweep and not the region near H_c2, it cannot affect the measurement of the upper critical field directly. The influence of type II/1 behavior on the measurement of H_c2(theta) must come through its effect on the shape of the field sweeps, just like the indirect influence of the demagnetization. The shape of the transition could be significantly changed by a first-order transition, and this could bias the data analysis procedure enough to influence H_c2(theta). There is no definite evidence for type II/1 superconductivity in C₄KHg, but its presence seems likely according to the Auer-Ullmaier analysis.[11] The presence or absence of a first-order transition could undoubtedly be resolved with magnetization measurements if a 1 K SQUID magnetometer were available.