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PrOs₄Sb₁₂ is the first known heavy fermion superconductor containing Pr. Many experiments show results indicating unconventional superconductivity in this system. Most notably, PrOs₄Sb₁₂ exhibits two superconducting transitions. The upper transition occurs at Tc₁ ≈ 1.89 K and the lower transition occurs at Tc₂ ≈ 1.72 K. There are many features of this system that are not understood and do not have a unifi ed consensus among researchers. Many issues remain unanswered, such as the origin of superconductivity, symmetry of the superconducting energy gap, and the nature of the two superconducting transitions. We present specific heat data for a single PrOs₄Sb₁₂ crystal. The data show two superconducting transitions. Variance in the lower superconducting transition (among various samples) suggests multiple superconducting phases. Power law dependence of the low temperature specific heat is indicative of asymmetric energy gap. Cuprates are unconventional high temperature superconductors. The theory on origin and characteristics of superconductivity in these systems is still a debated issue. Experiments indicate presence of a phase in these systems that occurs above the superconducting transition temperature which exhibits some common characteristics with the superconducting state. An important issue is the nature of this so-called "pseudogap" phase and its relationship to the superconducting state. We have developed an experimental apparatus and procedure for measuring the specific heat of a high temperature superconductor and demonstrated it by measuring the heat capacity of a YBCO high-Tc superconductor sample.

PrOs₄Sb₁₂ is the first known heavy fermion superconductor containing Pr. Many experiments show results indicating unconventional superconductivity in this system. Most notably, PrOs₄Sb₁₂ exhibits two superconducting transitions. The upper transition occurs at Tc₁ ≈ 1.89 K and the lower transition occurs at Tc₂ ≈ 1.72 K. There are many features of this system that are not understood and do not have a unifi ed consensus among researchers. Many issues remain unanswered, such as the origin of superconductivity, symmetry of the superconducting energy gap, and the nature of the two superconducting transitions. We present specific heat data for a single PrOs₄Sb₁₂ crystal. The data show two superconducting transitions. Variance in the lower superconducting transition (among various samples) suggests multiple superconducting phases. Power law dependence of the low temperature specific heat is indicative of asymmetric energy gap. Cuprates are unconventional high temperature superconductors. The theory on origin and characteristics of superconductivity in these systems is still a debated issue. Experiments indicate presence of a phase in these systems that occurs above the superconducting transition temperature which exhibits some common characteristics with the superconducting state. An important issue is the nature of this so-called "pseudogap" phase and its relationship to the superconducting state. We have developed an experimental apparatus and procedure for measuring the specific heat of a high temperature superconductor and demonstrated it by measuring the heat capacity of a YBCO high-Tc superconductor sample.

This thesis investigates the many extraordinary physical properties of the candidate p-wave ferromagnetic superconductors UCoGe and URhGe, and proposes theoretical predictions for p-wave superconductors yet to be discovered. In particular, we carry out angular dependent quantum field theoretical calculations of the thermodynamic H - T phase diagram known as the upper critical field, or more appropriately for ferromagnetic superconductors the upper critical induction, for various p-wave superconducting order parameter symmetries including: The axial Anderson-Brinkman-Morel(ABM) state, the chiral Scharnberg-Klemm (SK) state, and the completely broken symmetry polar state (CBS), as well as for some other states with partially broken symmetry (PBS) superconducting order parameter symmetries. The most notable contribution of the work presented in this thesis is the application of the Klemm-Clem transformations to analytically calculate the full angular and temperature dependencies of the upper critical field for orthorhombic materials, which may prove to be useful to experimentalists in identifying these exotic states of matter experimentally. Second, this work formulates a double spin-split ellipsoidal Fermi surface (FS) model for ferromagnetic superconductors in the normal state, which introduces a field dependence to the effective mass in one crystallographic direction on the dominant Fermi surface and to the chemical potential, and is subsequently applied to the normal state of URhGe to explain theoretically the anomalous specific heat data of Aoki and Flouquet. Extension of this work to understanding the still elusive reentrant high-field superconducting phase of URhGe and the S-shaped upper critical field curve for external magnetic field parallel to the b-axis direction inUCoGe is discussed. Third, this work also presents theoretical fits to the upper critical field data of Kittika et al. for Sr2RuO4 using the helical p-wave states and including Pauli limiting effects of the three components of the triplet pair-spin fixed to the highly conducting layers by strong spin-orbit coupling.

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