Muon Spin Relaxation Studies of Zn-Substitution Effects in High-Tc Cuprate Superconductors

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

From Ising Resonant Fluctuations to Static Uniaxial Order in Antiferromagnetic and Weakly Superconducting CeCo(In_{1-x}Hg_{x})_{5}(x=0.01)

CeCo(In_{0.990}Hg_{0.010})_{5} is a charge doped variant of the d-wave CoCoIn_{5} superconductor with coexistent antiferromagnetic and superconducting transitions occurring at T_{N}=3.4 and T_{c}=1.4  K, respectively. We use neutron diffraction and spectroscopy to show that the magnetic resonant fluctuations present in the parent superconducting phase are replaced by collinear c-axis magnetic order with three-dimensional Ising critical fluctuations. No low-energy transverse spin fluctuations are observable in this doping-induced antiferromagnetic phase and the dynamic resonant spectral weight predominately shifts to the elastic channel. Static (τ>0.2  ns) collinear Ising order is proximate to superconductivity in CeCoIn_{5} and is stabilized through hole doping with Hg.

Raising the Critical Temperature by Disorder in Unconventional Superconductors Mediated by Spin Fluctuations

We propose a mechanism whereby disorder can enhance the transition temperature T_{c} of an unconventional superconductor with pairing driven by exchange of spin fluctuations. The theory is based on a self-consistent real space treatment of pairing in the disordered one-band Hubbard model. It has been demonstrated before that impurities can enhance pairing by softening the spin fluctuations locally; here, we consider the competing effect of pair breaking by the screened Coulomb potential also present. We show that, depending on the impurity potential strength and proximity to magnetic order, this mechanism results in a weakening of the disorder-dependent T_{c}-suppression rate expected from Abrikosov-Gor'kov theory, or even in disorder-generated T_{c} enhancements.

Complementary Response of Static Spin-Stripe Order and Superconductivity to Nonmagnetic Impurities in Cuprates

We report muon-spin rotation and neutron-scattering experiments on nonmagnetic Zn impurity effects on the static spin-stripe order and superconductivity of the La214 cuprates. Remarkably, it was found that, for samples with hole doping x≈1/8, the spin-stripe ordering temperature T_{so} decreases linearly with Zn doping y and disappears at y≈4%, demonstrating a high sensitivity of static spin-stripe order to impurities within a CuO_{2} plane. Moreover, T_{so} is suppressed by Zn in the same manner as the superconducting transition temperature T_{c} for samples near optimal hole doping. This surprisingly similar sensitivity suggests that the spin-stripe order is dependent on intertwining with superconducting correlations.

Suppression of Superfluid Density and the Pseudogap State in the Cuprates by Impurities

We use scanning tunneling microscopy (STM) to study magnetic Fe impurities intentionally doped into the high-temperature superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Our spectroscopic measurements reveal that Fe impurities introduce low-lying resonances in the density of states at Ω_{1}≈4  meV and Ω_{2}≈15  meV, allowing us to determine that, despite having a large magnetic moment, potential scattering of quasiparticles by Fe impurities dominates magnetic scattering. In addition, using high-resolution spatial characterizations of the local density of states near and away from Fe impurities, we detail the spatial extent of impurity-affected regions as well as provide a local view of impurity-induced effects on the superconducting and pseudogap states. Our studies of Fe impurities, when combined with a reinterpretation of earlier STM work in the context of a two-gap scenario, allow us to present a unified view of the atomic-scale effects of elemental impurities on the pseudogap and superconducting states in hole-doped cuprates; this may help resolve a previously assumed dichotomy between the effects of magnetic and nonmagnetic impurities in these materials.

Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x

The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold (6)Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.

Local destruction of superconductivity by non-magnetic impurities in mesoscopic iron-based superconductors

The determination of the pairing symmetry is one of the most crucial issues for the iron-based superconductors, for which various scenarios are discussed controversially. Non-magnetic impurity substitution is one of the most promising approaches to address the issue, because the pair-breaking mechanism from the non-magnetic impurities should be different for various models. Previous substitution experiments demonstrated that the non-magnetic zinc can suppress the superconductivity of various iron-based superconductors. Here we demonstrate the local destruction of superconductivity by non-magnetic zinc impurities in Ba0.5K0.5Fe2As2 by exploring phase-slip phenomena in a mesoscopic structure with 119 × 102 nm(2) cross-section. The impurities suppress superconductivity in a three-dimensional 'Swiss cheese'-like pattern with in-plane and out-of-plane characteristic lengths slightly below ∼1.34 nm. This causes the superconducting order parameter to vary along abundant narrow channels with effective cross-section of a few square nanometres. The local destruction of superconductivity can be related to Cooper pair breaking by non-magnetic impurities.

Momentum-dependent charge correlations in YBa2Cu3O6+δ superconductors probed by resonant X-ray scattering: evidence for three competing phases

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

Concerning the superconducting gap symmetry in YBa₂Cu₃O₇- δ, YBa₂Cu₄O, and La₂ - xSrxCuO₄ determined from muon spin rotation in mixed states of crystals and powders

Muon spin rotation (μ(+)SR) measurements of square-root second moments of local magnetic fields σ in superconducting mixed states, as published for oriented crystals and powder samples of YBa(2)Cu(3)O(7 - δ) (δ≈0.05), YBa(2)Cu(4)O(8) and La(2 - x)Sr(x)CuO(4) (x ∼ 0.15-0.17), are subjected to comparative analysis for superconducting gap symmetry. For oriented crystals it is shown that anomalous dependences of σ on temperature T and applied field H, as-measured and extracted a- and b-axial components, are attributable to fluxon depinning and disorder that obscure the intrinsic character of the superconducting penetration depth. Random averages derived from oriented crystal data differ markedly from corresponding non-oriented powders, owing to the weaker influence of pinning in high-quality crystals. Related indicators for pinning perturbations, such as non-monotonic H dependence of σ, irreproducible data and strong H dependence of apparent transition temperatures, are also evident. Strong intrinsic pinning suppresses thermal anomalies in c-axis components of σ, which reflect nodeless gap symmetries in YBa(2)Cu(3)O(7 - δ) and YBa(2)Cu(4)O(8). For YBa(2)Cu(3)O(7 - δ), the crystal (a-b components, corrected for depinning) and powder data all reflect a nodeless gap (however, a-b symmetries remain unresolved for crystalline YBa(2)Cu(4)O(8) and La(1.83)Sr(0.17)CuO(4)). Inconsistencies contained in multiple and noded gap interpretations of crystal data, and observed differences between bulk μ(+)SR and surface-sensitive measurements are discussed.

Electronic inhomogeneity in a Kondo lattice

Inhomogeneous electronic states resulting from entangled spin, charge, and lattice degrees of freedom are hallmarks of strongly correlated electron materials; such behavior has been observed in many classes of d -electron materials, including the high-T c copper-oxide superconductors, manganites, and most recently the iron–pnictide superconductors. The complexity generated by competing phases in these materials constitutes a considerable theoretical challenge—one that still defies a complete description. Here, we report a manifestation of electronic inhomogeneity in a strongly correlated f -electron system, using CeCoIn5 as an example. A thermodynamic analysis of its superconductivity, combined with nuclear quadrupole resonance measurements, shows that nonmagnetic impurities (Y, La, Yb, Th, Hg, and Sn) locally suppress unconventional superconductivity, generating an inhomogeneous electronic “Swiss cheese” due to disrupted periodicity of the Kondo lattice. Our analysis may be generalized to include related systems, suggesting that electronic inhomogeneity should be considered broadly in Kondo lattice materials.

Insensitivity of the superconducting gap to variations in the critical temperature of Zn-substituted Bi2Sr2CaCu2O(8+δ) superconductors

The phase diagram of the superconducting high-T(c) cuprates is governed by two energy scales: T*, the temperature below which a gap is opened in the excitation spectrum, and T(c), the superconducting transition temperature. The way these two energy scales are reflected in the low-temperature energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing we prepared a set of samples having the same T* but different T(c)'s, and measured their gap using angle-resolved photoemission spectroscopy (ARPES). We show that T(c) is not related to the gap shape or size, but it controls the size of the coherence peak at the gap edge.

Incommensurate magnetic order and dynamics induced by spinless impurities in YBa(2)Cu(3)O(6.6)

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa(2)Cu(3)O(6.6), an underdoped high-temperature superconductor that exhibits a prominent spin pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La(2-x)Sr(x)CuO(4) suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.

Total suppression of superconductivity by high magnetic fields in YBa(2)Cu(3)O(6.6)

We have studied the variation of transverse magnetoresistance of underdoped YBCO(6.6) crystals, either pure or with reduced T(c) down to 3.5 K by electron irradiation, in fields up to 60 T. We find evidence that the superconducting fluctuation contribution to the conductivity is suppressed only above a threshold field H(c)'(T), which is found to vanish at T(c)' > T(c). In the pure YBCO(6.6) sample, H(c)' is already 50 T at T(c). We find that increasing disorder weakly depresses H(c)'(0), T(c)', and T(nu), the onset of the Nernst signal. Thus, these energy scales appear more characteristic of the 2D local pairing than the pseudogap temperature which is not modified by disorder.

Structural matters in HTSC: the origin and form of stripe organization and checkerboarding

The paper deals with the controversial charge and spin self-organization phenomena in the HTSC cuprates, of which neutron, x-ray, STM and ARPES experiments give complementary, sometimes apparently contradictory glimpses. The examination has been set in the context of the boson-fermion, negative-U understanding of HTSC advocated over many years by the author. Stripe models are developed which are 2-q in nature and diagonal in form. For such a geometry to be compatible with the data rests upon both the spin and charge arrays being face-centred. Various special doping concentrations are closely looked at, in particular p = 0.1836 or 9/49, which is associated with the maximization of the superconducting condensation energy and the termination of the pseudogap regime. The stripe models are dictated by real space organization of the holes, whereas the dispersionless checkerboarding is interpreted in terms of correlation driven collapse of normal Fermi surface behaviour and response functions. The incommensurate spin diffraction below the 'resonance energy' is seen as in no way expressing spin-wave physics or Fermi surface nesting, but is driven by charge and strain (Jahn-Teller) considerations, and it stands virtually without dispersion. The apparent dispersion comes from the downward dispersion of the resonance peak, and the growth of a further incoherent commensurate peak pursuant upon the falling level of charge stripe organization under excitation.

Muon spin relaxation studies of magnetic-field-induced effects in high-Tc superconductors

Muon spin relaxation measurements in high transverse magnetic fields [FORMULA: SEE TEXT] revealed strong field-induced quasistatic magnetism in the underdoped and Eu-doped (La,Sr)2CuO4 and La1.875Ba0.125CuO4, existing well above Tc and TN. The susceptibility counterpart of Cu spin polarization, derived from the muon spin relaxation rate, exhibits a divergent behavior towards T approximately 25 K. No field-induced magnetism was detected in overdoped La1.81Sr0.19CuO4, optimally doped Bi2212, and Zn-doped YBa2Cu3O7.

Correlation between superfluid density and T(C) of underdoped YBa2Cu3O6+x near the superconductor-insulator transition

We report measurements of the ab-plane superfluid density n(s) (magnetic penetration depth lambda) of heavily underdoped films of YBa2Cu3O6+x, with T(C)'s from 6 to 50 K. We find the characteristic length for vortex unbinding transition equal to the film thickness, suggesting strongly coupled CuO2 layers. At the lowest dopings, T(C) is as much as 5 times larger than the upper limit set by the 2D Kosterlitz-Thouless-Berezinskii transition temperature calculated for individual CuO2 bilayers. Our main finding is that T(C) is not proportional to n(s)(0); instead, we find T(C) proportional to ns(1/2.3+/-0.4). This conflicts with a popular point of view that quasi-2D thermal phase fluctuations determine the transition temperature.

Theory of doped Mott insulators: duality between pairing and magnetism

By bosonizing the electronic t-J model exactly on any two-dimensional (2D) lattices, and integrating out the gauge fluctuations combined to slave particles beyond mean fields, we obtain a theory in terms of physical Cooper pair and spin condensates. In the sense of mutual Berry phase they turn out to be dual to each other. The mutual duality is the missing key in the resonant-valance-bond idea [Science 235, 1196 (1987)]] to work as a paradigm of doped 2D Mott insulators. We argue that the essential aspects of high-T(c) phenomenology can be explained in the present framework.

Novel in-gap spin state in Zn-doped La1.85Sr0.15CuO4

Low-energy spin excitations of La(1.85)Sr(0.15)Cu(1-y)Zn(y)O4 were studied by neutron scattering. In y=0.004, the incommensurate magnetic peaks show a well-defined "spin gap" below T(c). The magnetic signals at omega=3 meV decrease below T(c)=27 K for y=0.008, also suggesting the gap opening. At lower temperatures, however, the signal increases again, implying a novel in-gap spin state. In y=0.017, the spin gap vanishes and elastic magnetic peaks appear. These results clarify that doped Zn impurities induce the novel in-gap state, which becomes larger and more static with increasing Zn.

Influence of pair breaking and phase fluctuations on disordered high Tc cuprate superconductors

Electron irradiation has been used to introduce point defects in a controlled way in underdoped and optimally doped YBa(2)Cu(3)O(7-delta) crystals. This technique allows us to perform very accurate measurements of T(c) and of the ab plane resistivity in a wide range of defect contents x(d) down to T(c)=0. The variation of T(c) and of the transition width with x(d) do not follow current predictions of pair-breaking theories. The data are rather compatible, at least for the highly damaged regime, with the expected influence of phase fluctuations. These results open new questions about the evolution of the defect induced T(c) depression over the phase diagram of the cuprates.

Common energy scale for magnetism and superconductivity in underdoped cuprates: a muon spin resonance investigation of (Ca(x)La(1-x)) (Ba(1.75-x)La(0.25+x))Cu3O(y)

We characterize the spontaneous magnetic field, and determine the associated temperature T(g), in the superconducting state of (Ca(x)La(1-x)) (Ba(1.75-x)La(0.25+x)) Cu(3)O(y) using zero and longitudinal field muon spin resonance measurements for various values of x and y. Our major findings are (i) T(g) and T(c) are controlled by the same energy scale, (ii) the phase separation between hole poor and hole rich regions is a microscopic one, and (iii) spontaneous magnetic fields appear gradually with no moment size evolution.

T(c) suppression in co-doped striped cuprates

We propose a model that explains the reduction of T(c) due to the pinning of stripes by planar impurity co-doping in cuprates. A geometrical argument about the planar fraction of carriers affected by stripe pinning leads to a linear T(c) suppression as a function of impurity concentration z. The critical value z(c) for the vanishing of superconductivity is shown to scale like T(2)(c) in the incompressible stripe regime and becomes universal in the compressible regime. Our theory agrees very well with the experimental data in single- and bilayer cuprates co-doped with Zn, Li, Co, etc.

Local magnetic order vs superconductivity in a layered cuprate

We report on the phase diagram for charge-stripe order in La1.6-xNd0. 4SrxCuO4, determined by neutron and x-ray scattering studies and resistivity measurements. From an analysis of the in-plane resistivity motivated by recent nuclear-quadrupole-resonance studies, we conclude that the transition temperature for local charge ordering decreases monotonically with x, and hence that local antiferromagnetic order is uniquely correlated with the anomalous depression of superconductivity at x approximately 1 / 8. This result is consistent with theories in which superconductivity depends on the existence of charge-stripe correlations.

63Cu NMR evidence for enhanced antiferromagnetic correlations around Zn impurities in YBa2Cu3O6.7

Doping the high- T(c) superconductor YBa2Cu3O6.7 with 1.5% of nonmagnetic Zn impurities in CuO2 planes is shown to produce a considerable broadening of 63Cu NMR spectra, as well as an increase of low-energy magnetic fluctuations detected in 63Cu spin-lattice relaxation measurements. A model-independent analysis demonstrates that these effects are due to the development of staggered magnetic moments on many Cu sites around each Zn and that the Zn-induced moment in the bulk susceptibility might be explained by this staggered magnetization. Several implications of these enhanced antiferromagnetic correlations are discussed.

Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+delta

Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+delta. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within approximately 15 A of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.