THESIS TITLE: Assessment of thermodynamic properties of pressurized hydride superconductors due to collective excitation of cooper pairs using the Bogoliubov-Valatin transformation.

STUDENT’S NAME: Churchill Oduor Wanyera

SUPERVISORS:

1. Michael Nakitare Waswa
2. Horace Kibe

ABSTRACT

Superconductivity is the state of a material characterized by close to zero dc electrical resistance, hence infinite conductivity by the material, when the temperature of the material is lowered below the critical temperature () in a zero magnetic field strength. There are two categories of superconductors; s-wave superconductors that are isotropic and d-wave superconductors that are anisotropic. The microscopic theory of superconductivity by Bardeen, Schrieffer and Cooper (BCS theory) explains s-wave pairing of charges under ambient pressure but it fails to explain charge pairing under high pressure. Studies have shown that superconductivity in hydrides is due to electron-phonon mediation. Studies propose that superconductivity in hydrides is due to collective behavior of particles rather than single particle behavior.  The immense pressure under which these hydrides super conduct has proved impractical for day to day use despite the high  they display. Models have been developed to explain the pressure effect on  but so far no unified model has been agreed upon to explain HTSC under pressure using the Bogoliubov-Valatin Transformation (BVT) formalism.  The developed theory was used in this work to give more understanding of the superconducting process under pressure and carry on a comparison with other researchers.  GeoGebra software was used to plot graphs and data generated using GetData graph Digitizer. The systems energy, specific heats, entropy and Sommerfield coefficient were determined.  Further, pressure effects on cell volume and energy were studied. The specific heat capacity for H₃S at 150GPa and =200K is found to be 0.011 meV/K while that of LaH₁₀ is 0.0315 meV/K at =237.9K and 210 GPa. At the same temperature, LaH₁₀ is found to have a higher specific heat capacity than H₃S. The systems have maximum =4.68 meV/K at T=6K for LaH₁₀. H₃S shows a Sommerfield coefficient of 0.00138 meV/K² while LaH₁₀ shows 0.00235 meV/K² at the same stated pressure values. The value of entropy for the two hydrides at their respective  is 0.15 meV/K² for H₃S and 0.13 meV/K² for LaH_10. The highest entropy for H₃S is 0.450 meV/K² and occurs at 900K while for LaH₁₀ highest entropy of 0.451 meV/K² occurs at 1000K. The two systems are found to have lowest entropy at . H₃S at a deformed volume of 158.4 a.u³ has energy of -220.76 meV. At v=100a.u³, E=0meV. Therefore the cell volume of H₃S is found to be 100a.u³. The bulk modulus for H₃S at 158.4a.u³ is B=129.8 GPa Similarly LaH₁₀ at a deformed volume of 81.5a.u³ has energy of -86.16 meV. At v=45 a.u³, E=0meV. Therefore the cell volume is found to be 45a.u³. From the study, the energy required to break the Cooper pairs in H₃S was found to be -220.76meV. The energy gap for the hydride at the stated pressure is 76mev. Twice this energy gives 152meV. A gap difference of 66.7meV is obtained and this is attributed to pressure increased that raises the energy required to break the Cooper pairs. However this does not apply for the results of LaH₁₀ with energy gap of 51meV and energy obtained of 86.16meV. These results will open up room for more discoveries towards the room temperature hydride superconductors under ambient pressure for practical applications.