Theoretical Studies On Magnetic Order And Superconductivity In Heavy-Fermion Compounds

In the past decades, the study of heavy-fermion compounds (HFC), in which thelocal magnetic moments are strongly coupled to the conducting electrons, have beenone of the most important topics in the condensed matter physics, and the Kondo latticemodel (KLM) is believed to capture the basic physics of HFC. In the strong Kondo-coupling limit, a disordered Kondo singlet state arises due to Kondo screening efectbetween local magnetic moments and conducting electrons; while in the limit of weakKondo-coupling, the system forms a long-range magnetic order (LRMO) due to the in-termoment Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. However, when theKondo coupling strength is intermediate, these two competing mechanisms cannot sup-press each other, resulting in many important novel phenomena, for example, the coex-istence of LRMO and Kondo singlet, heavy fermion superconductivity and non-Fermi-liquid behavior, which have attracted great attention in this field. The thesis is devotedto investigating the first two important issues.Experimental investigations indicate that LRMO can coexist with the Kondoscreening efect in HFC. For example, in the last year, researchers found that magneticorder appears simultaneously with heavy-fermion characteristics in YbNi4P2. We startwith the previous research work on the competition and coexistence between LRMOand the Kondo screening efect in the KLM at zero temperature. By taking into accountthe thermal fluctuations, the competition and coexistence between the Kondo screeningefect and the long-range ferromagnetic order(LRFO) is studied at finite temperature andfar away from half-filling, then the phase diagram is obtained. In the coexistence phase,we derived the analytic formulas to determine the Curie temperature TCand the Kondotemperature TK, at which LRFO and the Kondo screening disappears, respectively. Wefind that the suppression of LRFO and the Kondo screening in the coexistence phase iscaused by the competition between them rather than the thermal fluctuation. In addi-tion, We point out that the spin-polarized coexistence phase is characterized by a finiteminimal-excited energy gap for the spin-up quasi-particles, in contrast, the non-spin-polarized coexistence phase without this excited energy gap could only exist in a verynarrow parameter region. We are able to calculate these two critical temperatures quan-titatively for the first time, and establish a more physically meaningful phase diagram at finite temperature.On the other hand, by reviewing the properties of40kinds of HFS materials, weconclude that the pairing mechanism of HFS is not induced by the electron-phononcoupling as in conventional-superconductor, but likely by the inter-moment magneticcorrelation. By Using Kondo-Heisenberg lattice model on two-dimensional square lat-tice near half-filling, we propose a possible d-wave pairing mechanism of HFS, in-duced by local inter-moment anti-ferromagnetic(AFM) correlations. Taking the para-magnetic heavy-fermi liquid state in the limit of strong Kondo coupling (large-J_K) asthe start point, we find that when the short-range AFM correlation strength JHis rel-atively small, d-wave spinon singlet pairing between the local magnetic moments canreduce the ground state energy substantially, and also give rise to the superconductingpairing between the conducting electrons in the presence of the Kondo screening efect.The spinion pairings appear around (π, π) point in the Brillouin zone, while the pair-ings between the conducting electrons arise near (0, π) and (π,0) points. As the ratioof J_H/J_Kincreases, the resulting d-wave superconducting state changes from a gaplessnodal state to a nodeless state, indicating a continuous phase transition. Such a mecha-nism provides a theoretical support to the study of the competition between LRMO andsuperconductivity.