Eliashberg analysis of tunneling experiments: support for the pairing glue hypothesis in cuprate superconductors

Evidence for the validity of the pairing glue interpretation of high temperature superconductivity is presented using a modified Eliashberg analysis of experimental superconductor-insulator-superconductor (SIS) tunneling data in B2Sr2CaCu2O8 (Bi2212) over a wide range of doping. This is accomplished by extracting detailed information on the diagonal and anomalous contributions to the quasiparticle self-energy. In particular, a comparison of the imaginary part of the anomalous self-energy ImΦ(ω) and the pairing glue spectral function α2F(ω) used in the model is consistent with Hubbard model simulations in the literature. In addition, the real part of the diagonal self-energy for optimal doped Bi2212 bears a strong resemblance to that obtained from photoemission experiments.     

Correlation of tunneling spectra in Bi(2)Sr(2)CaCu(2)O(8+delta) with the resonance spin excitation

New break-junction tunneling data are reported in Bi(2)Sr(2)CaCu(2)O(8+delta) over a wide range of hole concentration from underdoped (T(c) = 74 K) to optimal doped (T(c) = 95 K) to overdoped (T(c) = 48 K). The conductances exhibit sharp dips at a voltage, Omega/e, measured with respect to the superconducting gap. Clear trends are found such that the dip strength is maximum at optimal doping and that Omega scales as 4.9kT(c) over the entire doping range. These features link the dip to the resonance spin excitation and suggest quasiparticle interactions with this mode are important for superconductivity.     

Doping dependence of the coupling of electrons to bosonic modes in the single-layer high-temperature Bi2Sr2CuO6 superconductor

A recent highlight in the study of high-T(c) superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (Bi2Sr2CuO6). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to c-axis phonons due to the rapid change of the c-axis screening in this doping range.     

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.     

Evidence for a pseudogap in underdoped Bi{2}Sr_{2}CaCu{2}O{8+delta} and YBa2Cu3O6.50 from in-plane optical conductivity measurements

The real part of the in-plane optical self-energy data in underdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} (Bi-2212) and ortho II YBa2Cu3O6.5 contains new and important information on the pseudogap. Using a theoretical model approach, a major new finding is that states lost below the pseudogap Delta_{pg} are accompanied by a pileup of states just above this energy. The pileup along with a sharp mode in the bosonic spectral function leads to an unusually rapid increase in the optical scattering rate as a function of frequency and a characteristically sloped peak in the real part of the optical self-energy. These features are not found in optimally doped and overdoped samples and represent the clearest signature so far in the in-plane optical conductivity of the opening of a pseudogap.     

Quasiparticle liquid in the highly overdoped Bi(2)Sr(2)CaCu(2)O(8+delta)

Results from the study of a highly overdoped (OD) Bi(2)Sr(2)CaCu(2)O(8+delta) with a T(c) = 51 K using angle-resolved photoemission spectroscopy are presented. We observe a sharp peak in the spectra near ( pi,0) that persists well above T(c), a nodal self-energy which approaches that seen for the Mo(110) surface state, and a more k-independent line shape at the Fermi surface than the lower-doped cuprates. This allows for a realistic comparison of the lifetime values to the experimental resistivity measurements. These observations point to the validity of the quasiparticle picture for the OD even in the normal state.     

Anomalous momentum dependence of the quasiparticle scattering rate in overdoped Bi2Sr2CaCu2O8

The question of the anisotropy of the electron scattering in high temperature superconductors is investigated using high resolution angle-resolved photoemission data from Pb-doped Bi2Sr2CaCu2O8 (Bi2212) with suppressed superstructure. The scattering rate of low energy electrons along two bilayer-split pieces of the Fermi surface is measured (via the quasiparticle peak width), and no increase of scattering towards the antinode (pi,0) region is observed, contradicting the expectation from Q=(pi,pi) scattering. The results put a limit on the effects of Q=(pi,pi) scattering on the electronic structure of this overdoped superconductor with still very high T(c).     

Nuclear magnetic resonance study of the electron-doped high-temperature superconducting cuprates

Nuclear magnetic resonance (NMR) measurements have been made on two of the electron-doped high-temperature superconducting cuprates (HTSCs), Pr_2−xCe_xCuO₄ and Sr_0.9La_0.1CuO₂ that represent the two known electron-doped structures. The results are compared with the more-studied hole-doped HTSCs. We show that the electron and hole-doped HTSCs probe a similar antiferromagnetic spin fluctuation spectrum in the normal state, which provides support for theories of superconductivity where the pairing is mediated by antiferromagnetic spin fluctuations and the superconducting order parameter has a d_x²−y² symmetry. Contrary to results from underdoped and hole-doped HTSCs, there is no evidence for a normal-state pseudogap in the NMR data from measurements on the electron-doped HTSCs. Therefore, the electron-doped HTSCs can be better compared with overdoped and hole-doped HTSCs where the normal-state pseudogap is absent. The antiferromagnetic spin fluctuation spectrum as probed by the Cu spin–lattice relaxation rate, is independent of the doped electrons per Cu. A similar effect is observed in the overdoped and hole-doped HTSC, Y_1−xCa_xBa₂Cu₃O_7−δ for a hole concentration range of 0.063. The anomalous Cu NMR linewidth anisotropy observed in the electron-doped HTSCs suggests a small and static spin variation for temperatures up to room temperature.     

Fourfold structure of vortex-core states in Bi2Sr2CaCu2O8+delta

We present a detailed study of vortex-core spectroscopy in slightly overdoped Bi2Sr2CaCu2O8+delta using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of (4.3 +/- 0.3)a0. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at +/-6 meV. Since the core-state energy is proportional to the superconducting gap magnitude , our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.     

Bilayer splitting in the electronic structure of heavily overdoped Bi(2)Sr(2)CaCu(2)O(8+delta).

The electronic structure of heavily overdoped Bi(2)Sr(2)CaCu(2)O(8+delta) is investigated by angle-resolved photoemission spectroscopy. The long-sought bilayer band splitting in this two-plane system is observed in both normal and superconducting states, which qualitatively agrees with the bilayer Hubbard model calculations. The maximum bilayer energy splitting is about 88 meV for the normal state feature, while it is only about 20 meV for the superconducting peak.     

Tunneling into the normal state of Pr2-xCexCuO4

The temperature dependence of the tunneling conductance was measured for various doping levels of Pr(2-x)CexCuO4 using planar junctions. A normal state gap is seen at all doping levels studied, x=0.11 to x=0.19. We find it to vanish above a certain temperature T*. T* is greater than T(c) for the underdoped region and it follows T(c) on the overdoped side. This behavior suggests finite pairing amplitude above T(c) on the underdoped side.     

Scanning tunneling spectroscopy of Bi(2)Sr(2)CuO(6+delta): new evidence for the common origin of the pseudogap and superconductivity

Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi(2)Sr(2)CuO(6+delta) between 275 mK and 82 K. Below T(c) = 10 K, the spectra show a gap with well-defined coherence peaks at +/-Delta(p) approximately 12 meV, which disappear at T(c). Above T(c), the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T(*) approximately 68 K. The comparison with Bi(2)Sr(2)CaCu(2)O(8+delta) demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin.     

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。     

Crossover from coherent to incoherent electronic excitations in the normal state of Bi(2)Sr(2)CaCu(2)O(8+delta)

Angle resolved photoemission spectroscopy (ARPES) and resistivity measurements are used to explore the overdoped region of the high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). We find evidence for a new crossover line in the phase diagram between a coherent metal phase, for lower temperatures and higher doping, and an incoherent metal phase, for higher temperatures and lower doping. The former is characterized by two well-defined spectral peaks in ARPES due to coherent bilayer splitting and superlinear behavior in the resistivity, whereas the latter is characterized by a single broad spectral feature in ARPES and a linear temperature dependence of the resistivity.     

High-energy scale revival and giant kink in the dispersion of a cuprate superconductor

In the present photoemission study of a cuprate superconductor Bi1.74Pb0.38Sr1.88CuO6+delta, we discovered a large scale dispersion of the lowest band, which unexpectedly follows the band structure calculation very well. Similar behavior observed in blue bronze and the Mott insulator Ca2CuO2Cl2 suggests that the origin of hopping-dominated dispersion in an overdoped cuprate might be quite complicated. A giant kink in the dispersion is observed, and the complete self-energy containing all interaction information is extracted for a doped cuprate. These results recovered significant missing pieces in our current understanding of the electronic structure of cuprates.     

Anomalous enhancement of the coupling to the magnetic resonance mode in underdoped Pb-Bi2212

High-resolution angle-resolved photoemission with variable excitation energies is used to disentangle bilayer splitting effects and intrinsic (self-energy) effects in the electronic spectral function near the (pi,0) point of differently doped (Pb,Bi)(2)Sr(2)CaCu(2)O(8+delta). In contrast to overdoped samples, where intrinsic effects at the (pi,0) point are virtually absent, we find in underdoped samples intrinsic effects in the superconducting-state (pi,0) spectra of the antibonding band. This intrinsic effect is present only below the critical temperature and weakens considerably with doping. Our results give strong support for models which involve a strong coupling of electronic excitations with the resonance mode seen in inelastic neutron scattering experiments.     

Bosonic spectral density of epitaxial thin-film La1.83Sr0.17CuO4 superconductors from infrared conductivity measurements

We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La(1.83)Sr(0.17)CuO(4). Using Eliashberg's formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La(2-Sr(x)CuO(4) with another high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). The bosonic spectral functions of the two materials account for the low T(c) of LSCO as compared to Bi-2212.     

Absence of a loss of in-plane infrared spectral weight in the pseudogap regime of Bi(2)Sr(2)CaCu(2)O(8+delta)

The ab-plane reflectance of Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212) thin films was measured in the 30-25 000 cm(-1) range for one underdoped ( T(c) = 70 K), and one overdoped sample ( T(c) = 63 K) down to 10 K. We find similar behaviors in the temperature dependence of the normal-state infrared response of both samples. Above T(c), the effective spectral weight, obtained from the integrated conductivity, does not decrease when T decreases, so that no opening of an optical pseudogap is seen. We suggest that these are consequences of the pseudogap opening in the k = (0,pi) direction and of the in-plane infrared conductivity being mostly sensitive to the k = (pi,pi) direction.     

Absence of static phase separation in the high T(c) cuprate YBa(2)Cu(3)O(6+y)

We use 89Y NMR in YBa(2)Cu(3)O(6+y) in order to evaluate with high sensitivity the distribution of hole content p in the CuO2 planes. For y=1 and y=0.6, this hole doping distribution is found narrow with a full width at half maximum smaller than Deltap=0.025. This rules out any large static phase separation between underdoped and optimally doped regions in contrast with the one observed by STM in Bi2212 and by NQR in LaSrCuO. This establishes that static electronic phase separation is not a generic feature of the cuprates.     

Hidden charge 2e Boson in doped Mott insulators

We construct the low-energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, a charge 2e bosonic field emerges at low energy. The charge 2e boson mediates dynamical spectral weight transfer across the Mott gap and creates a new charge e excitation by binding a hole. The result is a bifurcation of the electron dispersion below the chemical potential as observed recently in angle-resolved photoemission on Pb-doped Bi2Sr2CaCu2O8+delta (Pb2212).