Unusual temperature dependence of the upper critical field in superconducting heavy-fermion systems

A new formulation of the superconducting properties of heavy-fermion metals with potentially dramatic consequences for the critical field is proposed and analyzed. The new feature of the formulation consists of including the field dependence of the normal-state properties such as the magnetic susceptibility, electronic specific heat, and electronic scattering lifetime in the calculation of the superconducting critical field. These effects are important for heavy-fermion metals because (1) the characteristic energy of the low-temperature coherent state is low, so that an applied magnetic field can appreciably alter the normal-state properties, and (2) the large effective masses lead to low Fermi velocities and high orbital critical fields, so that a significant field dependence of the normal-state properties may occur below Hc2. A Greens-function description of the field dependence of the normal-state properties showing how they arise from field dependence of the self-energy and vertex functions in the periodic Anderson model is given. The effect of these field-dependent normal-state properties on the superconducting critical field is calculated using a generalization of standard theory. For certain values of the parameters, the calculations predict unusually steep critical-field curves and magnetic-field-induced superconductivity, qualitatively similar to recent experimental results.