International Journal of Physics and Mathematical Sciences ISSN: 2277-2111 (Online) An Open Access, Online International Journal Available at http://www.cibtech.org/jpms.htm 2017 Vol. 7 (3) July-September, pp. 1-6/Kibe et al. Research Article Centre for Info Bio Technology (CIBTech) 1 SPECIFIC HEAT OF THE INTEGRATED S-WAVE AND P-WAVE PAIRING IN URANIUM AND CERIUM BASED HEAVY- FERMION SUPERCONDUCTORS Kibe H.E. 1 , *Sakwa T.W. 1 and Khanna K.M. 2 1 Department of Physics, Masinde Muliro University of Science and Technology, P. o. Box 190 Kakamega, Kenya 2 Department of Physics, University of Eldoret, P.O. Box 1125, Eldoret, Kenya *Author for Correspondence ABSTRACT The s-wave and p-wave Cooper pairing in Uranium and Cerium based HF systems has been studied by analyzing the periodic Anderson model by means of the Bogoliubov-Valatin approach (BVT) while focusing on the interorbital Cooper pairing between a conduction electron (c electron) and an f electron, called the “c-f pairing.” It is shown that the s-wave and p-wave superconductivity appears to coexist with long-range antiferromagnetic order. Moreover, the study with different reference systems used in the BVT shows that the interorbital c-f pairing is essential for the appearance of the s-wave and p-wave superconductivity. The ground state energy (E o ) specific heat (C v ) and electronic specific heat coefficient (γ) of HF superconductors have been determined in the framework of the integrated s-wave and p-wave pairing model. The critical temperature for Uranium and Cerium based compounds is T C =1.8K and T C =1.2K respectively which are in agreement with known experimental values. The results show that uranium based compounds can be modelled for high temperature superconductivity. Keywords: Heavy Fermion, Specific Heat, Superconducting Transition INTRODUCTION A remarkable variety of collective electronic phenomena have been discovered in compounds with partially filled f-orbitals where electronic correlations are dramatically enhanced. In these compounds the entanglement of the rather localized f-electrons with the surrounding itinerant electrons starts at relatively high temperature leading to the development of low-energy composite quasiparticles with a heavy effective mass. Tuning the hybridization between f-orbitals and itinerant electrons can destabilize the heavy Fermi liquid state at low temperatures towards an antiferromagnetically ordered ground state. The multiorbital nature of which is one of the characteristic features of HF systems, which are composed of itinerant electrons in the conduction orbitals (c electrons) and localized electrons in the f orbitals (f electrons) (Keisuke & Daisuke, 2015). The correlation between c and f electrons leads to various intriguing phenomena, such as the Kondo effect (Pfeiderer et al., 2009) quantum critical behavior (Shishido et al., 2010) and magnetic orderings due to the Ruderman-Kittel-Kasuya-Yosida interaction (Hewson, 1997). Recently, the importance of such orbital degrees of freedom has also been recognized in the studies of superconductivity in the other strongly correlated electron systems (Keisuke & Daisuke, 2015). The multiorbital nature is considered to be the key for understanding the high-Tc superconducting properties in iron pnictides (Stewart, 2011). Previous studies Keisuke & Yamamoto (2013) suggested that the multiorbital nature can be a source of s-wave superconductivity in HF systems. Hanzawa and Yosida and Spalek (Spalek, 1988) discussed the interorbital Cooper pairing between c and f electrons, which we call the “c-f pairing,” as a possible mechanism for s-wave superconductivity. HF materials contain elements whose f-shell electrons are strongly correlated, thus, giving rise to a large effective mass in the quasiparticles excitations. Due to the large Coulomb repulsion between the electrons and their strongly correlated behavior, it is expected that the pairs formed in the HF superconducting state will not be s-wave. Instead, they are expected to pair up in the asymmetric p-wave or the anisotropic d- wave schemes in order to avoid the large spatial overlap associated with the symmetric s-wave state.