Study Of Several Unconventional Superconductors Using Density Functional Theory And Singular-mode Functional Renormalization Group Method

Study of superconductivity is an active field in condensed matter physics. The discovery of high-Tc superconductors and other unconventional superconductors al-ways inspires researchers’ interest and effort. Search for new superconductors as well as elucidation of the pairing mechanism are two main themes in this field. In this dis-sertation, we introduce and use two theoretical approaches:one is density functional theory, the other is singular-mode functional renormalization group (SMFRG) method, which we use to study several unconventional superconductors.In Chapter Ⅰ, a brief introduction of superconductivity is given. We also give the basic outline of two methods to study superconductors:density functional theory and singular-mode functional renormaliztiong group (SMFRG). The technical process of both two methods is shown.Recently, superconductivity is discovered in Ni-based chalcogenides. Experi-ments find they exhibit features similar to that of heavy-fermion systems and d-wave pairing. In Chapter Ⅱ, We study these two superconductors using Quantum ESPRSSO packages. We find the electronic structure are similar with KNi2Se2/S2. We also give phonon dispersion and electron-phonon coupling of TlNi2Se2by means of PHonon software. The results show that TlNi2Se2may be a electron-phonon superconductors with electron-phonon coupling constant λ～0.93. The pairing mechanism in this system is still under discussion.Recently, SrPtAs is found to be a superconductor with a hexagonal lattice rather than the square lattice in most unconventional superconductors. The μSR measure-ment for SrPtAs suggests time-reversal symmetry breaking (TRSB) and a nodeless pairing gap. The TRSB implies the pairing in SrPtAs is unconventional. The situa-tion motivates us to study the pairing mechanism and pairing symmetry of SrPtAs on a microscopic level. In Chapter III, We first construct tight-binding models for the new superconductor SrPtAs according to DFT calculation combined with maximally localized Wannier functions(MLWF). We then investigate the effect of electron corre-lation and spin-orbital coupling (SOC) in Cooper pairing by singular mode functional renormalization group (SMFRG) method. We find that out of the five d-orbitals of Pt, the (dxz,dyz)-orbitals are the active ones responsible for superconductivity, and fer-romagnetic spin fluctuations enhanced by the proximity to the van Hove singularity triggers f-wave triplet pairing. The superconducting transition temperature increases as the Fermi level approaches the van Hove singularity until ferromagnetism sets in. Because of SOC, the spin fluctuations have easy-plane anisotropy, and the d-vector of the triplet pairing component is pinned along the out-of-plane direction. Finally, experimental perspectives are discussed.Sr2Ru04is the first prime candidate for spin-triplet superconductor. However, there are several key unresolved issues in understanding the experiments. Previous theories mostly treat either the γ band or a and0bands. In Chapter IV, we study superconductivity in a three-orbital model of Sr2RuO4. The results of SMFRG show the system favors ap+ip’Cooper pairing, which is induced by a small wave vector (Q-(1/5.1/5)π) spin fluctuation at low energy scales. The pairing perdominantly on the7-band derived from the dxy orbital. After projecting the pairing gap function onto Fermi surface, we find that there is a deep minima in amplitude on the γ-Fermi surface near (π,0) and (0,π). We propose that the minima makes the chiral edge modes fragile already against a moderate amount of impurities. We also perform multi-patch FRG method calculation and obtain qualitative agreement.BiSs-based superconductors is a family of superconductors which is newly dis-covered. A lot of experimental and theoretical works have been devoted into this field. However, previous theoretical studies do not consider the strong spin-orbital coupling in this system. In Chapter V, we study the newly discovered BiS2-based supercon-ductors using spin symmetry-broken SU(2) SMFRG method. Based on two orbital model including the spin-orbital coupling (SOC) part, we find the BiS2-based super-conductors may have a dominant triplet pairing component in addition to a subdom-inant singlet component arising from the spin-orbital coupling. The pairing respects time reversal symmetry and d*x2_y2pairing symmetry. The dominant triplet gap causes gap sign changes between the spin-split Fermi pockets. We obtain similar results for a large doping region when the Fermi surface evolves around the Lifshitz points. We mainly discuss three main cases across the Lifshitz points. Above the Lifshitz points, the gap is nodeless, and the superconducting state is weak topological. Above the Lif-shitz filling level, the gap becomes nodal. Looking into the particle-hole channel, we find the triplet pairing is induced by ferromagnetic spin fluctuations, and a coexisting subdominant antiferromagnetic spin fluctuations are associated to the d*x2-y2-wave gap structure. Finally, the relevance to experiments is discussed.Sr2IrO4is a novel Jeff=1/2Mott insulator and invokes great interest. Both pre-vious experiments and theories propose that high Tc superconductivity in Sr2IrO4can be achieved by doping. However, there lacks an unbias theoretical study on the micro-scopic level. In Chapter VI, we investigate possible superconductivity in doped Sr2IrO4using spin symmetry-broken SU(2) SMFRG. For both electron doped and hole doped cases, the system develops superconducting instabilities but the superconducting prop-erties are obviously different. In the electron doped case, a d*x2-y2-wave superconduct-ing phase is found in a narrow doping region. The pairing is driven by spin fluctuations within the single conduction band. In hole doped case, an s±*-wave pairing is favored, due to the spin fluctuations within and across the two conduction bands. In all cases there are comparable singlet and triplet components in the pairing function. We also find the Hund’s coupling reduces (enhances) superconductivity for electron (hole) dop-ing. Our results imply that the Jef f=1/2Mott insulator Sr2IrO4will develop high Tc superconductivity by carrier doping. Finally, we discuss experimental perspectives.In Chapter VII, we present a summary of this dissertation, and give some outlooks for the investigation.