9420920 Cox This project addresses two pressing theoretical questions in the area of superconducitivity. First, what is the origin of superconductivity in the heavy fermion materials? Second, can the odd-in-time reversal Cooper pair really be found in a physical system? To address these questions, superconductivity in the heavy fermion materials will be studied using a variety of techniques based upon the primary assumption that it arises from odd-in-time-reversal Cooper pairs whose microscopic origin is in the two-channel Kondo model using a variety of techniques. Effects of doping, disorder, and symmetry breaking fields will be studied as well. Several phenomenological approaches will also be attempted. This study should answer definitely whether the two-channel Kondo model is a viable candidate for a comprehensive theory of heavy fermion superconductivity and whether odd-in-time-reversal pairing may have a solid basis in these materials. %%% In this work a variety of theoretical techniques is used to study a class of materials known as heavy fermion materials. In some ways these materials act as if the electrons have a much larger mass than an isolated electron. These materials are of special interest because at low temperatures they superconduct in a way that cannot be understood using the traditional theory of superconductivity. Here a particular model will be studied to see if it agrees with the known properties of heavy fermion superconductors. Understanding superconductivity in these materials should contribute to the theory of superconductivity in high temperature superconductors, with the ultimate goal of being able to design materials which are superconducting at higher and higher temperatures. ***
