Spin-fluctuation Induced Pairing Symmetry In Novel Unconventional Superconductors

Superconductivity is one of the major fields in condensed matter physics.The framework of the microscopic theory of superconductivity states that two electrons near the Fermi surface can have an effective attractive interaction by exchanging bosonic quasi-particles,such as phonons and spin fluctuations,and this effective attractive interaction brings about a phase coherent pair condensate.The pairing symmetry of Cooper pair is an important feature for uncovering the effective pairing interaction in a superconductor.Recently,the discoveries of the novel cuprate superconductor Ba2CuO4-y and the new kagome superconductor AV3Sb5(A=K,Rb,Cs)have stirred great interest in its essential electronic states and superconducting properties.However,the mechanisms of superconductivity in Ba2CuO4-y and AV3Sb5 are still unclear.This motivates the investigations of this thesis.In the first chapter,we present an introduction to pairing symmetry,which includes the macroscopic and microscopic description of superconductivity,the pointgroup symmetry classification of gap functions,and the experiments detecting the gap functions.In the second chapter,we first introduce the slave-boson mean-field method and then present the weak-coupling theory of spin-fluctuation induced superconductivity.In the third chapter,considering the close relationship between the magnetism and superconductivity in conventional cuprate superconductors and it is not clear which role the correlation plays in the new superconductor Ba2CuO4-δ,we start with an effective two-orbital Hubbard model for Ba2CuO4-y to investigate the evolutions of the electronic states with the increasing filling number n and correlation U by employing rotationally invariant slave-boson mean field method.We demonstrate that with increasing filling number n,the paramagnetic system evolves from two-band character to single-band ones,with the band nature of the d3z2-r2 and dx2-y2 orbitals to the dx2-y2 orbital.Considering the magnetic correlations,the system displays one Slater antiferromagnetic(AFM)metallic phase in 2<n<2.14 and a PM phase in n>2.14 at U=2 eV,or two distinct AFM metallic phases in 2<n<2.52 and 2.74<n<3,and a PM phase in 2.52<n<2.74 respectively,at U=4 eV.From the experimental spin coupling value of about 150 meV,compared with the total-energy difference between the Néel AFM and paramagnetic phases,we estimate that 2<U<4 eV or so in Ba2CuO3.2,implying that Ba2CuO3.2 is at least an intermediated correlated system.Our results show that near realistic superconducting state around n=2.6 the intermediate correlated Ba2CuO3.2 should display single-band character.In the fourth chapter,we start with an effective two-orbital Hubbard model for Ba2CuO4-y to study the evolution of pairing strength in Ba2CuO3.2 with the increasing correlation U and the evolution of pairing strength in Ba2CuO4-y with increasing filling number n by using the weak-coupling theory of spin-fluctuation induced superconductivity.We find that for Ba2CuO3.2,s-wave dominates in the region of 1<U<2.15 eV,and dx2-y2-wave dominates in the region of 2.15<U<2.4 eV.There are three domes in the pairing strength of Ba2CuO4-y with increasing filling number n.dx2-y2-wave dominates in the first dome 2.35<n<2.38,s-wave domanites in the second dome 2.38<n<2.615,and dx2-y2-wave dominates in the third dome 2.615<n<2.65.Considering s-wave dominate in the large correlation region of 1<U<2.15 eV and in the large second dome 2.38<n<2.615,we predict the pairing symmetry in Ba2CuO3.2 is s-wave.In the fifth chapter,based on the band structures for CsV3Sb5 in the pristine phase,we first construct an effective six-band model for the low-energy processes.we start with an effective six-band model for CsV3Sb5 to study the evolution of pairing strength in CsV3Sb5 with the increasing correlation U.The results show that the E1u(p+ip-wave)pairing dominates in the region of 0<U<0.32 eV,the A2g(I wave)in the region of 0.32<U<0.75 eV and the E2g(d+id-wave)in the region of 0.75<U<1 eV.Considering that the correlation in AV3Sb5 is weak or intermediate,these results suggest that pairing symmetry is A2g(I-wave)in the CsV3Sb5,which can explain some recent experiments about pairing symmetry.In the sixth chapter,based on the orbital selective pairing scenario,we start with a two-orbital Hubbard model to study the effects of the asymmetry of band and crystal field splitting,which are the key ingredients for orbital-selective Mott phase,on the pairing strength for two-dimensional(2D)square lattice and triangular lattice by using the weak-coupling theory of spin-fluctuation induced superconductivity.The results show that both the spin-singlet pairing strengths as a function of crystal field splitting,for 2D square lattice at filling number n=2.15 and 2D triangular lattice at filling number n=2.85,display a sharp peak.Asymmetry of band enhance both the spinsinglet and spin-triplet pairing in the 2D square lattice at filling number n=2.15 and spin-triplet pairing in the 2D triangular lattice at filling number n=2.85.However,the asymmetry of band suppresses the spin-singlet pairing in the 2D triangular lattice at filling number n=2.85.In the seventh chapter,a summary and outlook for all investigations in this thesis are given.