We address the issue of identifying the mediators of effective interactions in cuprates superconductors. Specifically, we use inversion theory to analyze Raman spectra of optimally and over-doped La$_{2-x}$Sr$_x$CuO$_4$ samples. This allows us to extract the so-called glue function without making any a priori assumption based on any specific model. We use instead two different techniques, namely the singular value decomposition and a multi-rectangle decomposition. With both techniques we find consistent results showing that: i) two distinct excitations are responsible for the glue function, which have completely different doping dependence. One excitation becomes weak above optimal doping, where on the contrary the other keeps (or even slightly increases) its strength; ii) there is a marked temperature dependence on the weight and spectral distribution of these excitation, which therefore must have a somewhat critical character. It is quite natural to identify and characterize these two distinct excitations as damped antiferromagnetic spin waves and damped charge density waves, respectively. This sets the stage for a scenario in which superconductivity is concomitant and competing with a charge ordering instability.
Zero field and longitudinal field muon spin relaxation measurements have been performed in optimally doped and overdoped superconductors LaFeAsO$_{1-x}$F$_x$ in order to investigate the magnetic fluctuation over a wide range of temperature and longitudinal field. We have observed no sign of magnetic fluctuation against temperature in the muons' time window (10$^{-5}\sim$ 10$^{-9}$s). Considering the current results and other results, i.e., spin fluctuation observed by neutron scattering, pseudogap-like behaviors by NMR and photoemission spectroscopy, it is suggested that not only the spin fluc…
In conventional superconductors the magnitude of the pairing fluctuation is primarily determined by Tc and the superconducting (SC) coherence length, ξ. In systems with strong structural and electronic anisotropies, the interlayer separation, s, plays a significant role. In cuprates, the pseudogap (PG) correlation induces a downturn in the temperature dependent resistivity. As Tc is approached from above, this downturn in the resistivity is supposed to either i) add to or ii) join smoothly to that due to paraconductivity caused by short-lived Cooper pairs. It is important to differentiate betw…
Using angle-resolved photoemission spectroscopy, we studied the electronic structure of NaFe$_{1-x}$Co$_x$As from an optimally doped superconducting compound ($x=0.028$) to a heavily overdoped non-superconducting one ($x=0.109$). Similar to the case of "122" type iron pnictides, our data suggest that Co dopant in NaFe$_{1-x}$Co$_x$As supplies extra charge carriers and shifts the Fermi level accordingly. In the $x=0.109$ compound, the hole-like bands around the zone center $Γ$ move to deeper binding energies and an electron pocket appears instead. The overall band renormalization remains basica…
The dispersion of the Cu-O bond-stretching vibrations in overdoped La$_{1.7}$Sr$_{0.3}$CuO$_4$ (not superconducting) has been studied by high resolution inelastic neutron scattering. It was found that the doping-induced renormalization of the so-called breathing and the half-breathing modes is larger than in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$. On the other hand, the phonon linewidths are generally smaller in the overdoped sample. Features observed in optimally doped La$_{1.85}$Sr$_{0.15}$CuO$_4$ which suggest a tendency towards charge stripe formation are absent in overdoped La$_{1.…
Single crystals of the optimally doped, moderately and strongly overdoped high temperature superconductor Tl2Ba2CuO6+x (Tl-2201) with Tc=80, 56 and 30K, respectively, have been investigated by polarized Raman scattering. By taking the peak position of the B_1g component of electronic Raman scattering as 2Delta_0 we found that the reduced gap value (2Delta_0/k_BT_c) strongly decreases with increasing doping. The behavior of the low frequency scattering for the B_1g and B_2g scattering components is similar for optimally doped and overdoped crystals and can be described by a w^3 - and w -law, re…
Based on an unconventional Fermi liquid model, we present several results on the optimally doped and overdoped cuprate superconductors. For the normal state, we provide an analytic demonstration, backed by self-consistent Baym-Kadanoff (BK) numerical calculations, of the linear in $T$ resistivity and linear in 1/$ε$ optical conductivity, provided the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential $μ$. Moreover, we find that the interactions tend to pin these strong density of states peaks close to $μ$. We …
Low temperature specific heat has been measured in optimally doped and highly overdoped non-superconducting BaFe$_{2-x}$TM$_x$As$_{2}$ ($TM$ = Co and Ni) single crystals. By using the data of the overdoped samples, we successfully removed the phonon contribution of the optimally doped ones, and derived the electronic specific heat coefficient $γ_e$. Remarkably, we found a continuing temperature dependent $γ_e(T)$ which follows the quadratic relation $γ_e=γ_0+αT^2$ in the low temperature limit. Together with the very small residual term $γ_0$, linear magnetic field dependence of $γ_e$, it is co…
This paper treats a number of issues of the cuprates, ranging from the spin resonance peak and the linear one-particle scattering rate to the superconducting transition, in the frame of a Fermi liquid model. Recent ARPES expts. by Valla et al., Science vol. 285, 2110 (1999), and e-print cond-mat/0003407, directly support the linearity of the one-particle scattering rate everywhere in the Brillouin zone we obtained here. We show that the origin of this linearity is the strong linear in energy term of the imaginary part of the carrier susceptibility. This result yields directly a linear in tempe…
Recent Raman experiments [F. Venturini et al., Phys. Rev. Lett. {\bf 89}, 107003-1,(2002)] done in $Bi_2 Sr_2 Ca Cu_2 O_4$ have found that antinodal quasiparticles become insulating when the doping is varied from overdoped to optimally doped while nodal quasiparticles remain metallic. We propose a simple explanation based on the incoherence of the spectral function in the antinodal direction due to the strong scattering suffered by the quasiparticles in the proximity of the Van Hove singularity.
By means of magnetization, specific heat and muon-spin relaxation measurements, we investigate high-pressure oxidized \mohpo, in which overdoping is achieved up to $p \sim 0.45$ hole/Cu, well beyond the $T_c - p$ superconducting dome of cuprates, where Fermi liquid behavior is expected. Surprisingly, we find bulk superconductivity with $T_c$=84 K and superfluid density similar to those of optimally doped Y123. On the other hand, specific heat data display a large electronic contribution at low temperature, comparable to that of nonsuperconducting overdoped La214. These results point at an unus…
An inelastic neutron scattering study of overdoped Bi_2Sr_2CaCu_2O_{8+δ} $ (T_c = 83 K) has revealed a resonant spin excitation in the superconducting state. The mode energy is E_res=38 meV, significantly lower than in optimally doped Bi_2Sr_2CaCu_2O_{8+δ} (T_c = 91 K, E_ res =43 meV). This observation, which indicates a constant ratio E_res /k_B T_c \sim 5.4, helps resolve a long-standing controversy about the origin of the resonant spin excitation in high-temperature superconductors.
We use polarized inelastic neutron scattering to study low-energy spin excitations and their spatial anisotropy in electron-overdoped superconducting BaFe$_{1.85}$Ni$_{0.15}$As$_{2}$ ($T_c=14$ K). In the normal state, the imaginary part of the dynamic susceptibility, $χ^{\prime\prime}(Q,ω)$, at the antiferromagnetic (AF) wave vector $Q=(0.5,0.5,1)$ increases linearly with energy for $E\le 13$ meV. Upon entering the superconducting state, a spin gap opens below $E\approx 3$ meV and a broad neutron spin resonance appears at $E\approx 7$ meV. Our careful neutron polarization analysis reveals that…
Scanning tunneling spectroscopy (STS) studies reveal long-range (~100 nm) spatial homogeneity in optimally and underdoped superconducting YBa_2Cu_3O_{7-δ} (YBCO) single crystals and thin films, and macroscopic spatial modulations in overdoped (Y_{0.7}Ca_{0.3})Ba_2Cu_3O_{7-δ} (Ca-YBCO) epitaxial films. In contrast, STS on an optimally doped YBa_2(Cu_{0.9934}Zn_{0.0026}Mg_{0.004})_3O_{6.9} single crystal exhibits strong spatial modulations and suppression of superconductivity over a microscopic scale near the Zn or Mg impurity sites, and the global pairing potential is also reduced relative to t…
In our recent paper we presented empirical evidences suggesting that electrons in cuprate superconductors are strongly coupled to unscreened c-axis polar phonons. In the overdoped regime the c-axis metallizes and we present here simple theoretical arguments demonstrating that the observed effect of the metallic c-axis screening on the polar electron-phonon coupling is consistent with a strongly overdamped c-axis charge dynamics in the optimally doped system, becoming less dissipative in the overdoped regime.
We study the critical charge dynamics of the superconducting to the normal-state transition for LSCO thin films with a wide range of the Sr concentration, by measuring the frequency-dependent excess parts of the complex microwave conductivity, which is induced by the superconducting fluctuations. We present a dynamic scaling analysis of the complex fluctuation conductivity, which includes the information on the universality class and the dimensionality of the critical charge dynamics as a function of the Sr concentration, the film thickness and the magnetic field. In our previous study (H. Kit…
One of the central issues concerning the mechanism of high temperature superconductivity in cuprates is the nature of the ubiquitous charge order and its implications to superconductivity. Here we use scanning tunneling microscopy to investigate the evolution of charge order from the optimally doped to strongly overdoped Bi2Sr2CuO6+δ cuprates. We find that with increasing hole concentration, the long-range checkerboard order gradually evolves into short-range glassy patterns consisting of diluted charge puddles. Each charge puddle has a unidirectional nematic internal structure, and exhibits c…
We show that the zero field normal-state resistivity above Tc for various levels of electron doping - both for LaO1-xFxFeAs (La-1111) and SmO1-xFxFeAs (Sm-1111) members of the 1111-iron-pnictide superconductor family - can be scaled in a broad temperature range from 20 to 300 K onto single curves for underdoped La-1111 (x=0.05-0.075), for optimally and overdoped La-1111 (x=0.1-0.2) and for underdoped Sm-1111 (x=0.06-0.1) compounds. The scaling was performed using the energy scale Δ, the resistivity ρ_Δ and the residual resistivity ρ_0 as scaling parameters as well as by applying a recently pro…
The electronic structure of the high-T_c superconductor Tl2Ba2CuO6+d is studied by ARPES. For a very overdoped Tc=30K sample, the Fermi surface consists of a single large hole pocket centered at (pi,pi) and is approaching a topological transition. Although a superconducting gap with d_x^2-y^2 symmetry is tentatively identified, the quasiparticle evolution with momentum and binding energy exhibits a marked departure from the behavior observed in under and optimally doped cuprates. The relevance of these findings to scattering, many-body, and quantum-critical phenomena is discussed.
We present results from the study of a highly overdoped (OD) Bi2212 with a $T_{c}=51$K using high resolution angle-resolved photoemission spectroscopy. The temperature dependent spectra near the ($π,0$) point show the presence of the sharp peak well above $T_{c}$. From the nodal direction, we make comparison of the self-energy with the optimally doped and underdoped cuprates, and the Mo(110) surface state. We show that this OD cuprate appears to have properties that approach that of the Mo. Further analysis shows that the OD has a more $k$-independent lineshape at the Fermi surface than the lo…
Resonant inelastic x-ray scattering (RIXS) at the copper K absorption edge has been performed for heavily overdoped samples of La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x= 0.25$ and 0.30. We have observed the charge transfer and molecular-orbital excitations which exhibit resonances at incident energies of $E_i= 8.992$ and 8.998 keV, respectively. From a comparison with previous results on undoped and optimally-doped samples, we determine that the charge-transfer excitation energy increases monotonically as doping increases. In addition, the $E_i$-dependences of the RIXS spectral weight and absorption…
Resonating valence bond states in a doped Mott insulator was proposed to explain superconductivity in cuprates in January 1987 by Anderson. A challenging task then was proving existence of this unconventional mechanism and a wealth of possibilities, with a rigor acceptable in standard condensed matter physics, in a microscopic theory and develop suitable many body techniques. Shortly, a paper by Anderson, Zou and us (BZA) undertook this task and initiated a program. Three key papers that followed, shortly, essentially completed the program, as far as superconductivity is concerned: i) a gauge …
We studied Zn-substitution effect on the high-T_c superconductors, underdoped La_{2-x}Sr_xCu_{1-y}Zn_yO_4 (x=0.10; y=0, 0.01, 0.02), optimally doped (x=0.15; y=0, 0.02), and overdoped (x=0.20; y=0, 0.03, 0.06) in a temperature range of T=4.2-300 K, using Cu nuclear quadrupole resonance (NQR) spin-echo technique. We found full disappearance of the Cu NQR signals for the Zn-substituted, Sr-underdoped x=0.10 samples below about 40 K, partial disappearance for the Sr-optimally doped ones below about 50 K, but not for the overdoped x=0.20 ones. From the Zn-doping, the Sr-doping and the temperature …
We use scanning tunneling microscopy to investigate Bi2Sr2Ca2Cu3O10+δ trilayer cuprates from the optimally doped to overdoped regime. We find that the two distinct superconducting gaps from the inner and outer CuO2 planes both decrease rapidly with doping, in sharp contrast to the nearly constant Tc. Spectroscopic imaging reveals the absence of quasiparticle interference in the antinodal region of overdoped samples, showing an opposite trend to that in single- and double-layer compounds. We propose that the existence of two types of inequivalent CuO2 planes and the intricate interaction betwee…
We report a detailed spectroscopic study of the electron doped cuprate superconductor Pr(2-x)Ce(x)CuO(4-δ) using point contact junctions for x=0.125(underdoped), x=0.15(optimally doped) and x=0.17(overdoped). From our conductance measurements we are able to identify bosonic resonances for each doping. These excitations disappear above the critical temperature, and above the critical magnetic field. We find that the energy of the bosonic excitations decreases with doping, which excludes lattice vibrations as the paring glue. We conclude that the bosonic mediator for these cuprates is more likel…
We take advantage of the connection between the free carrier optical conductivity and the glue function in the normal state, to reconstruct from the infrared optical conductivity the glue-spectrum of ten different high-Tc cuprates revealing a robust peak in the 50-60 meV range and a broad con- tinuum at higher energies for all measured charge carrier concentrations and temperatures up to 290 K. We observe that the strong coupling formalism accounts fully for the known strong temperature dependence of the optical spectra of the high Tc cuprates, except for strongly underdoped samples. We observ…
Single-particle spectroscopic probes, such as scanning tunneling and angle-resolved photoemission spectroscopy (ARPES), have provided us with crucial insights into the complex electronic structure of the high-Tc cuprates, in particular for the under and optimally doped regimes where high-quality crystals suitable for surface-sensitive experiments are available. Conversely, the elementary excitations on the heavily overdoped side of the phase diagram remain largely unexplored. Important breakthroughs could come from the study of Tl2Ba2CuO6+d (Tl2201), a structurally simple system whose doping l…
The spin dynamics of high temperature superconductors measured by inelastic neutron scattering is reviewed. The spin susceptibility evolves a lot with increasing doping from the undoped insulating state to the overdoped metallic state. In the superconducting state, a strong magnetic resonance peak occurs in the spin excitation spectrum whose energy is proportional to the superconducting temperature. In underdoped and optimally doped regimes, normal state antiferromagnetic fluctuations are observed, proving the existence of strong electronic correlations in cuprates. They are characterized by a…
We report a systematic study of Zn-substitution effect on Cu NQR spectrum for high $T_c$ superconductors La$_{2-x}$Sr$_x$Cu$_{1-y}$Zn$_y$O$_4$ from carrier-underdoped to -overdoped regimes (polycrystalline samples, $x$ =0.10, 0.15, and 0.20). We observed no appreciable wipeout effect for the overdoped samples, a gradual and partial wipeout effect below about 80 K for the optimally doped ones, and very abrupt and full wipeout effect below about 40 K for the underdoped ones. The wipeout effect indicates a highly enhanced spectral weight of Cu spin fluctuations at a low frequency. We associate th…
We report a neutron scattering study of the spin excitation spectrum in the superconducting state of slightly overdoped Bi2Sr2CaCu2O8+d system (Tc=87 K). We focus on the dispersion of the resonance peak in the superconducting state that is due to a S=1 collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the YBa2Cu3O6+x system for a similar doping level i.e. x= 0.95-1), which consists of intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, deduced from angle resolved p…
The thermal conductivity of optimally doped NaFe$_{0.972}$Co$_{0.028}$As ($T_c \sim$ 20 K) and overdoped NaFe$_{0.925}$Co$_{0.075}$As ($T_c \sim$ 11 K) single crystals were measured down to 50 mK. No residual linear term $κ_0/T$ is found in zero magnetic field for both compounds, which is an evidence for nodeless superconducting gap. Applying field up to $H$ = 9 T ($\approx H_{c2}/4$) does not noticeably increase $κ_0/T$ in NaFe$_{1.972}$Co$_{0.028}$As, which is consistent with multiple isotropic gaps with similar magnitudes. The $κ_0/T$ of overdoped NaFe$_{1.925}$Co$_{0.075}$As shows a relati…
We present a coherent scenario for the physics of cuprate superconductors, which is based on a charge-driven inhomogeneity, i.e. the ``stripe phase''. We show that spin and charge critical fluctuations near the stripe instability of strongly correlated electron systems provide an effective interaction between the quasiparticles, which is strongly momentum, frequency, temperature and doping dependent. This accounts for the various phenomena occurring in the overdoped, optimally and underdoped regimes both for the normal and the superconductive phase.
We have calculated the tunneling conductance of a superconductor-insulator-superconductor junction based on the polaron-bipolaron theory of superconductivity. The predicted incoherent hump features are in quantitative agreement with tunneling spectra of optimally doped Bi2Sr2CaCu2O8+y and Bi2Sr2Ca2Cu3O10+y. We further show that angle-resolved photoemission spectra of underdoped cuprates are consistent with the Bose-Einstein condensation of inter-site bipolarons and that the superconducting gap symmetry is d-wave, which is determined by the anomalous kinetic process rather than by the pairing i…
New electronic Raman and I.R. spectroscopy results from optimally and overdoped high temperature superconducting (HTSC) cuprate systems are interpreted in terms of the negative-U, boson-fermion crossover model. Distinction is made between those features which follow the condensate gap, 2Delta(p), and those that are set by the local-pair binding energy, cursive U(p). The critical role of doping level psubc = 0.185 is highlighted in conjunction with the matter of developing quasiparticle incoherence, making connection here with recent transport and related results. E//c IR results in magnetic fi…
Electron-boson spectral density functions (EBSDFs) can be obtained from measured spectra using various spectroscopic techniques, including optical spectroscopy. EBSDFs, known as glue functions, have a magnetic origin. Here, we investigated EBSDFs obtained from the measured optical spectra of hole-doped cuprates with wide doping levels, from underdoped to overdoped cuprates. The average frequency of an EBSDF provides the timescale for the spin fluctuations to form Cooper pairs. This timescale is directly associated with retarded interactions between electrons. Using this timescale and Fermi vel…
Various properties of underdoped superconducting cuprates, including the momentum-dependent pseudogap opening, indicate a behavior which is neither BCS nor Bose-Einstein condensation (BEC) like. To explain this issue we introduce a two-gap model. This model assumes an anisotropic pairing interaction among two kinds of fermions with small and large Fermi velocities representing the quasiparticles near the M and the nodal points of the Fermi surface respectively. We find that a gap forms near the M points resulting into incoherent pairing due to strong fluctuations. Instead the pairing near the …
We report a combined study of the spin resonances and superconducting gaps for underdoped ($T_c=19$ K), optimally doped ($T_c=25$ K), and overdoped ($T_c=19$ K) Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals with inelastic neutron scattering and angle resolved photoemission spectroscopy. We find a quasi two dimensional spin resonance whose energy scales with the superconducting gap in all three compounds. In addition, anisotropic low energy spin excitation enhancements in the superconducting state have been deduced and characterized for the under and optimally doped compounds. Our data suggest…
We have investigated the optimally doped tri-layer cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ (Bi2223) by angle-resolved photoemission spectroscopy, and observed energy bands and Fermi surfaces originated from the outer and inner CuO$_2$ planes (OP and IP) separately. The OP band is overdoped (hole density $\sim$ 0.26/Cu) with a large d-wave gap of $Δ_0$ $\sim$ 43 meV while the IP is underdoped ($\sim$ 0.06/Cu) with an even large gap of $Δ_0$ $\sim$ 60 meV. We propose that the enhancement of the $Δ_0$ of IP is due to the minimal influence of out-of-plane disorder and that the OP gap is then en…
