Phenomenological Calculations On Heavy Fermion Superconductivity

Heavy fermion superconductor is one kind of the typical unconventional su-perconductors.Recent developments in experiments have driven the emergence of various novel quantum phenomena in heavy fermion superconductivity,such as strange superconducting behaviors,Q-phase,quadrupolar orders,unconventional quantum criticalities,etc.Despite its low superconducting transition temperature,the peculiarities in heavy fermion superconductivity have been tightly connected with the frontier of condensed matter physics.Understanding the mechanism in heavy fermion superconductivity will ultimately improve our knowledge of uncon-ventional superconductivity and help us to explore novel superconductors,like bulk topological superconductors.In this thesis,we are trying to construct a phenomenological theoretical framework to study the heavy fermion supercon-ductivity.which has been implemented on CeCoIn₅and CeCu₂Si₂.The phenomenological approach contain the following three considerations:?1?The electronic structures of the specific heavy fermion compounds are obtained from either first-principle calculations combined with appropriate treatments on correlations or the tight-binding model extracted from the fitting to experiments.?2?Under the scenario where the pairing is driven by the quantum critical fluc-tuations,we consider a phenomenological susceptibility,which could yield a rea-sonable effective pair interaction.?3?By analyzing the orbital characters on the Fermi surfaces,we study the properties of superconductivity by taking advantages of the Eliashberg theory.First,motivated by the phenomenological BCS-like T_cformula from the two-fluid model in heavy fermions,we explored the related microscopic correspondence to CeCoIn₅.Choosing the tihgt-binding dispersions extracted from the scanning tunneling spectroscopy and taking a phenomenological susceptibility,we studied the superconducting behavior of CeCoIn₅.The Eliashberg calculations have shown a d_x2_-y2-wave symmetry,which is consistent with the previous studies.More importantly,a T_cscaling relation which is similar to the phenomenological BCS-like T_cformula has been found.This provides a microscopic support to the two-fluid model.The typical heavy fermion superconductor CeCu₂Si₂,which was believed to possess a line-nodal superconductivity in the past thirty years,are now indicated by many more precise experiments to be nodeless.Theories trying to explore the pairing symmetry all failed with to explain the nodeless structure,whereas proposals by experiments are lack of microscopic theoretic support.To find the exact pairing symmetry of CeCu₂Si₂,we first perform the first-principle calcula-tions.The obtained electronic structures are consistent with the previous studies.Then,we formulate a two-band Eliashberg theory with phenomenological pairing interactions.As a result,we obtain a phase diagram in which all possible super-conducting pairing symmetries are listed.A nodeless s^±-wave pairing is obtained when the inter-band pair scattering is dominated.Besides,this nodeless solution has the gap ratio consistent with the experiments,where the sign structures could also explain the superconducting signals from the neutron scattering and nuclear magnetic resonance experiments.With discussions on the orbital characters on the Fermi surfaces and the evolution of the Fermi surface topologies,we predict the superconductivity in CeCu₂Si₂primarily coming from the hole Fermi surface.And there would be a nodeless s^±-to nodal s-wave crossover when increasing the pressure,since the dominant pairing interaction changes from the interband to intraband one.