d x 2 - y 2 superconductivity and the Hubbard model

The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhanced single-particle spectral weight near the ( ~ ,0) and (0, ~ ) points of the Brillouin zone, create optimum conditions for d x 2 - y 2 -wave pairing. These are two effects which act to enhance the d x 2 - y 2 -wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.     

Novel anisotropy in the superconducting gap structure of Bi2Sr2CaCu2O(8+delta) probed by quasiparticle heat transport

Since the nature of pairing interactions is manifested in the superconducting gap symmetry, the exact gap structure, particularly any deviation from the simple d(x(2)-y(2)) symmetry, would help in elucidating the pairing mechanism in high- T(c) cuprates. Anisotropic heat transport measurement in Bi(2)Sr(2)CaCu(2)O(8+delta) reveals that the quasiparticle populations are different for the two nodal directions and thus the gap structure must be uniquely anisotropic, suggesting that pairing is governed by interactions with a rather complicated anisotropy. Intriguingly, it is found that the "plateau" in the magnetic-field dependence of the thermal conductivity is observed only in the b-axis transport.     

Superconducting pairs with extreme uniaxial anisotropy in URu2Si2

We report magnetic field orientation-dependent measurements of the superconducting upper critical field in high quality single crystals of URu(2)Si(2) and find the effective g factor estimated from the Pauli limit to agree remarkably well with that found in quantum oscillation experiments, both quantitatively and in the extreme anisotropy (≈10(3)) of the spin susceptibility. Rather than a strictly itinerant or purely local f-electron picture being applicable, the latter suggests the quasiparticles subject to pairing in URu(2)Si(2) to be "composite heavy fermions" formed from bound states between conduction electrons and local moments with a protected Ising behavior. Non-Kramers doublet local magnetic degrees of freedom suggested by the extreme anisotropy favor a local pairing mechanism.     

Pairing symmetry in layered BiS2 compounds driven by electron-electron correlation

We investigate the pairing symmetry of layered BiS2 compomlds by assuming that electron-electron correlation is still important so that the pairing is rather short range. We lind that the extended .s-wave pairing symmetry always wins over d-wave when the pairing is confined between two short range sites up to next nearest neighbors. The pairing strength is peaked around the doping level ：r = 0.5. which is consistent with experimental observation. The extended s-wave pairing symmetry is very robust against spin orbital coupling because it is mainly determined by the structure of Fermi surfaces, Moreover. the extended s-wave pafiring can be distinguished from conventional swave pairing by measuring and comparing superconducting gaps of different Fermi surfaces.     

Robust dx2-y2 pairing symmetry in hole-doped cuprate superconductors

Although initially quite controversial, it is now widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wave function symmetry, and the controversy has now shifted to whether the pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y(0.7)Ca(0.3)Ba(2)Cu(3)O(7-delta) (Ca-doped Y-123), La2-xSrxCuO4 (La-214), and Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212), with doping levels covering the underdoped, optimal, and overdoped regions. Our work implies that predominantly d x2-y2 pairing symmetry is robust over a large variation in doping.     

铜氧化物超导体Bi2Sr2CaCu2O8+δ 多体相互作用的超高能量分辨和时间分辨 角分辨光电子能谱研究

自发现30 多年来,铜氧化物的高温超导机理仍未得到解释。传统超导电性起源于电 子–声子相互作用形成的电子配对,研究传统超导体中的多体相互作用为BCS 理论提供了有 力的证据。目前已证实铜氧化物高温超导体中存在着电子配对,但是引起配对的机制仍不清 楚。因此,对铜氧化物高温超导体中的多体相互作用研究是揭示高温超导机理的关键。角分辨 光电子能谱是研究固体电子结构最直接的技术手段,随着其分辨率的不断提升,在研究高温超 导体的多体相互作用中日益发挥重要的作用。近年来兴起的时间分辨角分辨光电子能谱在常规 角分辨光电子能谱的基础上增加了独特的时间维度,从而成为研究多体相互作用动力学的有力 手段。本文详细地介绍了我们利用超高能量分辨和时间分辨角分辨光电子能谱在铜氧化物超导 体Bi2Sr2CaCu2O8+δ 中多体相互作用的研究,包括在节点区域、反节点区域扭折的研究,多体 相互作用的动量依赖关系,配对电子自能的提取以及库珀对在激光泵浦下的受激辐射现象。     

Off-site repulsion-induced triplet superconductivity: a possibility for chiral p(x+y)-wave pairing in Sr2RuO4

In order to probe the effect of charge fluctuations on triplet pairing, we study the pairing symmetry in the one-band Hubbard model having the off-site Coulomb repulsion (V) on top of the on-site repulsion as a model for the gamma band of Sr2RuO4, a strong candidate for a triplet pairing superconductor. The result, obtained with the dynamical cluster approximation combined with the quantum Monte Carlo method, and confirmed from the fluctuation exchange approximation, shows that while d(x(2)-y(2)) pairing dominates over p in the absence of V, introduction of V makes p(x+y) and d(xy) dominant. The gap function for the chiral p(x+y)+ip(x-y) has nodes that are consistent with the recent measurement of specific heat in rotated magnetic fields in the ruthenate. This suggests that the off-site repulsion may play an essential role in triplet superconductivity in this material.     

Upper critical field of a superconductor with arbitrary spin-orbit scattering: CeCu2Si2 and UBe13

The upper critical field is determined for an even-parity singlet pairing state in the presence of arbitrary spin-orbit scattering. Comparison with critical field experiments suggests that superconductivity in CeCu₂Si₂ is a singlet pairing state, and in UBe₁₃ is either a triplet pairing state or is a singlet state with restrictive conditions that the pair orbital be nearly isotropic and that strong spin-orbit scattering increase strongly as the field increases.     

Nodal d + id pairing and topological phases on the triangular lattice of Na(x)CoO(2).yH(2)O: evidence for an unconventional superconducting state

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density x(c) where the normal state Fermi surface crosses the isolated zeros. For spin-singlet pairing, we show that the second-nearest-neighbor (d+id)-wave pairing can be the dominant pairing channel. The gapless critical state at x (c) approximately 0.25 has six Dirac points and is topologically nontrivial with a T3 spin relaxation rate below T(c). This picture provides a possible explanation for the unconventional superconducting state of Na(x)Co O(2). yH(2)O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.     

Broad peak in the dx2-y2 superconducting correlation length as a function of hole concentration in the two-dimensional t-J model

We have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D t-J model with s, dx2-y2, and dxy symmetry pairs. Our calculations differ from previous work by removing disconnected pieces from the original four-point correlator and by treating the resulting pairing correlator as a matrix. We find the correlation length for dx2-y2 pairing grows significantly with decreasing temperature and develops a broad peak as a function of doping around delta=0.25 for T/J=0.25 at J/t=0.4. The correlation lengths for s and dxy symmetry remain small and do not display peaks. Antiferromagnetic spin correlations at low doping act to suppress the dx2-y2 and dxy superconducting correlation lengths.     

Persistence of strong electron coupling to a narrow boson spectrum in overdoped Bi2Sr2CaCu2O(8+delta) tunneling data

A d-wave, Eliashberg analysis of break-junction and STM tunneling spectra on Bi2Sr2CaCu2O(8+delta) (Bi2212) reveals that the spectral dip feature is directly linked to strong electronic coupling to a narrow boson spectrum, evidenced by a large peak in alpha2F(omega). The tunneling dip feature remains robust in the overdoped regime of Bi2212 with bulk T(c) values of 56 K-62 K. This is contrary to recent optical conductivity measurements of the self-energy that suggest the narrow boson spectrum disappears in overdoped Bi2212 and therefore cannot be essential for the pairing mechanism. The discrepancy is resolved by considering the way each technique probes the electron self-energy, in particular, the unique sensitivity of tunneling to the off-diagonal or pairing part of the self-energy.     

Correlating off-stoichiometric doping and nanoscale electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+delta

A microscopic theory is presented for the observed electronic disorder in superconducting Bi2Sr2CaCu2O8+delta. The essential phenomenology is shown to be consistent with the existence of two types of interstitial oxygen dopants: those serving primarily as charge reservoirs and those close to the apical plane contributing both carriers and electrostatic potential to the CuO2 plane. The nonlinear screening of the latter produces nanoscale variations in the doped hole concentration, leading to electronic inhomogeneity. Based on an unrestricted Gutzwiller approximation of the extended t-J model, we provide a consistent explanation of the correlation between the observed dopant location and the pairing gap and its spatial evolutions. We show that the oxygen dopants are the primary cause of both the pairing gap disorder and the quasiparticle interference pattern.     

Local electronic structure of a single nonmagnetic impurity as a test of the pairing symmetry of electrons in (K,Tl)FexSe2 superconductors

We study the effect of a single nonmagnetic impurity on the recently discovered (K,Tl)Fe(x)Se(2) superconductors, within both a toy two-band model and a more realistic five-band model. We find that, out of five types of pairing symmetry under consideration, only the d(x(2)-y(2))-wave pairing gives rise to impurity resonance states. The intragap states have energies far away from the Fermi energy. The existence of these intragap states is robust against the presence or absence of interband scattering. However, the interband scattering does tune the relative distribution of local density of states at the resonance states. All these features can readily be accessed by STM experiments, and are proposed as a means to test the pairing symmetry of the new superconductors.     

Possible spin-tripletf-wave pairing due to disconnected fermi surfaces in NaxCoO2.yH2O

We propose that the spin-triplet pairing mechanism due to disconnected Fermi surfaces proposed in our previous study [Phys. Rev. B 63, 174507 (2001)]] may be at work in a recently discovered superconductor NaxCoO2.yH2O. We introduce a single band effective model that takes into account the pocketlike Fermi surfaces along with the van Hove singularity near the K point found in the band calculation results. Applying the fluctuation exchange method and solving the linearized Eliashberg equation, the most dominant pairing is found to have spin-triplet f-wave symmetry, where the nodes of the gap function do not intersect the pocket Fermi surfaces. The presence of finite Tc is suggested in sharp contrast to cases when the gap nodes intersect the Fermi surface.     

Magnetic field effect on the pairing state competition in quasi-one-dimensional organic superconductors (TMTSF)2X

We study the effect of the magnetic field on the pairing state competition in organic conductors (TMTSF)₂X by applying random phase approximation to a quasi-one-dimensional extended Hubbard model. We show that the singlet pairing, triplet pairing and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting states may compete when charge fluctuations coexist with spin fluctuations. This rises a possibility of a consecutive transition from singlet pairing to FFLO state and further to S_z = 1 triplet pairing upon increasing the magnetic field. We also show that the singlet and S_z = 0 triplet components of the gap function in the FFLO state have “d-wave” and “f-wave” forms, respectively, which are strongly mixed.     

Paired composite fermion phase of quantum Hall bilayers at nu=1/2+1/2

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling nu=1/2+1/2 for intermediate spacing between the layers. We identify the phase as p_(x)+ip_(y) pairing, and construct high accuracy trial wave functions to describe the ground state on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes.     

Phase-sensitive tests of the pairing state symmetry in Sr(2)RuO(4)

Exotic superconducting properties of have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet pairing is also compatible with the observed phase shifts in Josephson junctions and propose further experiments which would distinguish it from its spin-triplet counterpart.     

Evidence for a transition in the pairing symmetry of the electron-doped cuprates La(2-x)Ce(x)CuO(4-y) and Pr(2-x)Ce(x)CuO(4-y)

We present measurements of the magnetic penetration depth, lambda(-2)(T), in Pr(2-x)Ce(x)CuO(4-y) and La(2-x)Ce(x)CuO(4-y) films at three Ce doping levels, x, near optimal. Optimal and overdoped films are qualitatively and quantitatively different from underdoped films. For example, lambda(-2)(0) decreases rapidly with underdoping but is roughly constant above optimal doping. Also, lambda(-2)(T) at low T is exponential at optimal and overdoping but is quadratic at underdoping. In light of other studies that suggest both d- and s-wave pairing symmetry in nominal optimally doped samples, our results are evidence for a transition from d- to s-wave pairing near optimal doping.