We performed Raman experiments on superconducting ${\rm Bi_2 Sr_2 (Ca_{1-x} Y_x) Cu_2 O_{8+δ}}$ (Bi-2212) and ${\rm YBa_{2} Cu_{3}O_{6+x}}$ (Y-123) single crystals. These results in combination with earlier ones enable us to analyze systematically the spectral features in the doping range $0.07 \le p \le 0.23$. In $B_{2g}$ ($xy$) symmetry we find universal spectra and the maximal gap energy $Δ_0$ to follow the superconducting transition temperature $T_c$. The $B_{1g}$ ($x^2-y^2$) spectra in Bi-2212 show an anomalous increase of the intensity towards overdoping, indicating that the corresponding energy scale is neither related to the pairing energy nor to the pseudogap, but possibly stems from a symmetry breaking transition at the onset point of superconductivity at $p_{\rm sc2} \simeq 0.27$.
A theory for electronic Raman scattering in the cuprate superconductors is presented with a specific emphasis on the polarization dependence of the spectra which can infer the symmetry of the energy gap. Signatures of the effects of disorder on the low frequency and low temperature behavior of the Raman spectra for different symmetry channels provide detailed information about the magnitude and the phase of the energy gap. Properties of the theory for finite T are discussed and compared to recent data concerning the doping dependence of the Raman spectra in cuprate superconductors, and remaini…
In a recent manuscript Phys. Rev. Lett. 127, 197001 (2021) Puviani et al. claim that the Higgs mode gives an enhancement of the Raman response in the symmetric $A_{1g}$ Raman channel of cuprates. Here we report a series of technical mistakes in their derivation that completely invalidate this conclusion. In particular, the Raman response function contains two renormalized vertices, with a clearly overcounting of diagrams and uncontrolled results for the Higgs-mode contribution.
While the low frequency electronic Raman response in the superconducting state of the cuprates can be largely understood in terms of a d-wave energy gap, a long standing problem has been an explanation for the spectra observed in A_{1g} polarization orientations. We present calculations which suggest that the peak position of the observed A_{1g} spectra is due to a collective spin fluctuation mode.
Although the low frequency electronic Raman response in the superconducting state of the cuprates can be largely understood in terms of a d-wave energy gap, a long standing problem has been an explanation for the spectra observed in the $A_{1g}$ polarization orientations. We present calculations which suggest that the peak position of the observed $A_{1g}$ spectra is due to a collective spin fluctuation mode.
The electronic Raman response in the electron-doped cuprate superconductors is studied based on the $t$-$t'$-$J$ model. It is shown that although the domelike shape of the doping dependent peak energy in the $B_{2g}$ symmetry is a common feature for both electron-doped and hole-doped cuprate superconductors, there are pronounced deviations from a cubic response in the $B_{1g}$ channel and a linear response in the $B_{2g}$ channel for the electron-doped case in the low energy limit. It is also shown that these pronounced deviations are mainly caused by a nonmonotonic d-wave gap in the electron-…
We discuss the possible existence a spin singlet excitation with charge $\pm2$ ($η$-mode) originating the $A_{1g}$ Raman resonance in cuprate superconductors. This $η$-mode relates the $d$-wave superconducting singlet pairing channel to a $d$-wave charge channel. We show that the $η$ boson forms a particle-particle bound state below the $2Δ$ threshold of the particle-hole continuum where $Δ$ is the maximum $d$-wave gap. Within a generalized random phase approximation and Bethe-Salpether approximation study, we find that this mode has energies similar to the resonance observed by Inelastic Neut…
We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprates. We show how a momentum independent pseudogap opens asymmetrically from the Fermi-surface but symmetric to the zeroes of the hybridized bonding dispersion, which results in false d-wave characteristics of the pseudogap at the Fermi level. By comparing against a d-wave form factor we illustrate the difficulty in identifying a momentum independent order in momentum averaged quantities such as the electronic Raman response. We identify a suppression in the single-particle density of states which pr…
We show by non resonant effect in HgBa$_2$CuO$_{4+δ}$ (Hg-1201)and by Zn substitutions in YBa$_2$Cu$_3$O$_{7-δ}$ (Y-123) compounds that the fully symmetric Raman spectrum has two distinct electronic contributions. The A$_{1g}$ response consists in the superconducting pair breaking peak at the 2$Δ$ energy and a collective mode close to the magnetic resonance energy. These experimental results reconcile the \textit{d-wave} model to the A$_{1g}$ Raman response function in so far as a collective mode that is distinct from the pair breaking peak is present in the A$_{1g}$ channel.
It has become clear that the anomalous properties of cuprate superconductors are intimately related to the formation of a pseudogap. Within the framework of the kinetic-energy-driven superconducting mechanism, the effect of the pseudogap on the electronic Raman response of cuprate superconductors in the superconducting-state is studied by taking into account the interplay between the superconducting gap and pseudogap. It is shown that the low-energy spectra almost rise as the cube of energy in the B_{1g} channel and linearly with energy in the B_{2g} channel. However, the pseudogap is strongly…
In superconductors the Anderson-Higgs mechanism allows for the existence of a collective amplitude (Higgs) mode which can couple to eV-light mainly in a non-linear Raman-like process. The experimental non-equilibrium results on isotropic superconductors have been explained going beyond the BCS theory including the Higgs mode. Furthermore, in anisotropic d-wave superconductors strong interaction effects with other modes are expected. Here we calculate the Raman contribution of the Higgs mode from a new perspective, including many-body Higgs oscillations effects and their consequences in convent…
Mechanism of unconventional superconductivity is still unknown even if more than 25 years have been passed since the discovery of high-Tc cuprate superconductors by J.G. Bednorz and K. A. Muller. Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole doped cuprates. Namely, how superconductivity and the critical temperature Tc are impacted by the pseudogap.
Raman scattering in the heavily overdoped (Y,Ca)Ba_2Cu_3O_{7-d} (T_c = 65 K) and Bi_2Sr_2CaCu_2O_{8+d} (T_c = 55 K) crystals has been investigated. For the both crystals, the electronic pair-breaking peaks in the A_{1g} and B_{1g} polarizations were largely shifted to the low energies close to a half of 2Delta_0, Delta_0 being the maximum gap. It strongly suggests s-wave mixing into the d-wave superconducting order parameter and the consequent manifestation of the Coulomb screening effect in the B_{1g}-channel. Gradual mixing of s-wave component with overdoping is not due to the change of crys…
We suggest, and demonstrate, a systematic approach to the study of cuprate superconductors, namely, progressive change of ion size in order to systematically alter the interaction strength and other key parameters. R(Ba,Sr)$_2$Cu$_3$O$_y$ (R={La, ... Lu,Y}) is such a system where potentially obscuring structural changes are minimal. We thereby systematically alter both dielectric and magnetic properties. Dielectric fluctuation is characterized by ionic polarizability while magnetic fluctuation is characterized by exchange interactions measurable by Raman scattering. The range of transition tem…
Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+δ}$ in the mid-infrared energy region. Combining photon-energy and momentum dependent RIXS measurements with…
We explored by electronic Raman scattering the superconducting state of Bi-2212 single crystal by performing a fine tuned doping study. We found three distinct energy scales in A1g, B1g and B2g symmetries which show three distinct doping dependencies. Above p=0.22 the three energies merge, below p=0.12, the A1g scale is no more detectable while the B1g and B2g scales become constant in energy. In between, the A1g and B1g scales increase monotonically with under-doping while the B2g one exhibits a maximum at p=0.16. The three superconducting energy scales appear to be an universal feature of ho…
We address the issue whether the data on optical conductivity and Raman scattering in electron-doped cuprates below $T_c$ support the idea that the $d-$wave gap in these materials is non-monotonic along the Fermi surface. We calculate the conductivity and Raman intensity for elastic scattering, and find that a non-monotonic gap gives rise to several specific features in optical and Raman response functions. We argue that all these features are present in the experimental data on Nd$_{2-x}$Ce$_{x}$CuO$_4$ and Pr$_{2-x}$Ce$_{x}$CuO$_4$ compounds.
Electronic Raman scattering with in and out of (ab) plane polarizations have been performed on HgBa2Ca2Cu3O8+d in a slightly underdoped single crystal with a critical temperature Tc=122 K. We find that the d-wave pairing gap at the antinodes is higher in energy (14 kBTc) than in other cuprates and that it varies very slowly up to Tc. This hints at a strong coupling nature of the pairing mechanism. Interestingly, we reveal that the pairing-gap feature in the Raman response displays a complex peak-dip-hump structure, in a fashion reminiscent of what observed by angle resolved photo-emission spec…
Certain significant fallacies are involved in discussions of the high-Tc mechanism unsolved for over 30 years in cuprate superconductors. These fallacies are explored with the aim of unravelling this mechanism. Moreover, using polarised electronic Raman scattering in inhomogeneous underdoped cuprate superconductors, the intrinsic nonlinear Raman spectrum is obtained by subtracting the pseudogap characteristic of a nonlinear from the linear Raman spectrum measured in the B2g mode of the node area below the critical temperature. The intrinsic nonlinear behaviour implies the existence of the noda…
We have calculated the Raman B$_{1g}$ and B$_{2g}$ spectra as a function of temperature, as well as doping, for the underdoped cuprates, using a model based on the resonating valence-bond spin-liquid. We discuss changes in intensity and peak position brought about by the presence of a pseudogap and the implied Fermi surface reconstruction, which are elements of this model. Signatures of Fermi surface reconstruction are evident as a sharp rise in the doping dependence of the antinodal to nodal peak ratio which occurs below the quantum critical point. The temperature dependence of the B$_{1g}$ p…
We report the Raman scattering measurements on the triple layer Bi2Sr2Ca2Cu3O10 (Bi2223) crystals of four different doping levels from slightly overdoped to strongly underdoped regimes. We observed a double pair-breaking peak in the antinodal B1g configuration that we attribute to the two antinodal gaps opening on the outer and inner CuO2-plane (OP and IP) band, respectively. The doping dependence of the pair-breaking peak energy was investigated. Considering the difference in doping level between the IP and OP, all the B1g pair-breaking peak energies for OP and IP were found to align on a sin…
We calculate the optical and Raman response within a phenomenological model of fermion quasiparticles coupled to nearly critical collective modes. We find that, whereas critical scaling properties might be masked in optical spectra due to charge conservation, distinct critical signatures of charge and spin fluctuations can be detected in Raman spectra exploiting specific symmetry properties. We compare our results with recent experiments on the cuprates.
One of the puzzling characteristics of the pseudogap phase of high-$T_c$ cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an associated pseudogap. Angle-resolved photoemission spectroscopy and electronic Raman scattering are two valuable tools which have shown universal features which are rather material-independent, and presumably intrinsic to the pseudogap phase. The doping and temperature dependence of the Fermi arcs and the pseudogap observed by photoemission near the antinode corr…
We calculate the Raman response contribution due to collective modes, finding a strong dependence on the photon polarizations and on the characteristic wavevectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, $La_{2-x}Sr_xCuO_4$ and $(Y_{1.97}Ca_{0.3})Ba_2CuO_{6.05}$, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks is only compatible with charge collective excitations at finite wavelength.
We consider the lightly doped cuprates Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ and La$_{2-x}$Sr$_x$CuO$_4$ (with $x=0.02$,0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe (or, more generically, charge-density wave) phase, which sets in at higher doping. We phenomenologically assume a quantum critical character for the longitudinal and transverse nematic, and for the charge-ordering fluctuations, and investigate the effects of these fluctuations in Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferre…
Calculations are presented for electronic Raman scattering and infrared conductivity in a $d_{x^{2}-y^{2}}$ superconductor including the effects of elastic scattering via anisotropic impurities and inelastic spin-fluctuation scattering. A consistent description of experiments on optimally doped Bi-2212 is made possible by considering the effects of correlations on both inelastic and elastic scattering.
The direct exchange integral and the transfer integral are calculated for the anti-bonding wave-function of the HTSC cuprates. The direct exchange integral yields a value three times larger than the indirect exchange of the t-J Hamiltonian. It also predicts positive exchange energy for neighboring parallel spins, contrary to the prediction of zero energy by the t-J Hamiltonian. A modified t-J Hamiltonian is proposed, and the implications of the results are discussed.
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, wh…
Recent experiments in underdoped hole-doped cuprates have shown the presence of two energy scales in the Raman spectrum in the superconducting state. This feature has a natural explanation in some models in which pseudogap and superconductivity compete. In electron-doped cuprates antiferromagnetic correlations are believed to survive in the superconducting state, and to produce a pseudogap above the critical temperature. Contrary to hole-doped systems, in electron-doped compounds only one energy scale appear since the pair breaking Raman intensity peaks in both B$_{1g}$ (antinodal) and B$_{2g}…
We present results for magnetic excitations in doped copper oxides using the random phase approximation and itinerant electrons. In the [1,0] direction the observed excitations resemble dispersive quasi-particles both in the normal and superconducting state similar as in recent resonant inelastic X-ray scattering (RIXS) experiments. In the [1,1] direction the excitations form, except for the critical region near the antiferromagnetic wave vector ${\bf Q}=(π,π)$, only very broad continua. Using the obtained spin propagators we calculate electron self-energies and their effects on electronic Ram…
We discuss how Raman spectra are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly-critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-Tc superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreeme…
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…
A recent microscopic model of the pseudogap state, based on the resonating valence bond (RVB) spin liquid, has provided a simple ansatz for the electronic self energy in which a gap forms on the antiferromagnetic Brillouin zone as the limit of a Mott insulator is approached in the underdoped regime. Here, the ansatz is employed to calculate the electronic specific heat when a superconducting gap is also included. We find qualitative agreement with all experimental observations in the underdoped regime of the cuprates. We explore the relationship of the theory to two other purely phenomenologic…
Within the stripe quantum critical point theory for high T_c superconductors, we point out that there is a direct contribution of charge collective fluctuations to the optical absorption and to the Raman spectra. In this latter case, we find that the critical charge collective modes can or can not be excited depending on the direction of their wavevector and on the polarization of the incoming and outgoing photons. This indicates a marked distinction between quasiparticles which are strongly and weakly coupled to critical collective modes and provides a direct confirmation that the order assoc…
The doping and temperature dependence of the electronic Raman response in cuprate superconductors is studied within the framework of the kinetic energy driven superconducting mechanism for the t-J model. It is shown that the temperature dependent depletion at low-energy shifts is faster in B_{1g} symmetry than in B_{2g} symmetry. In analogy to the domelike shape of the doping dependent superconducting transition temperature, the pair-breaking peak energy in B_{2g} channel increases with increasing doping in the underdoped regime, and reaches a maximum in the optimal doping, then decreases in t…
In the under- to optimal-doping regimes of electron-doped cuprates, it was theoretically suspected that there is a coexistence of superconducting (SC) and antiferromagnetic (AFM) orders. The quasi-particle excitations could be gapped by both orders, and the effective gap is non-monotonic d-wave-like in the momentum space. Alternatively the gap was also speculated as a pure pairing gap. Using an effective microscopic model, we consider the manifestation of the quasi-particle gap in the electronic Raman spectra in a range of doping levels, where the relative strength of the SC and AFM order para…
The microscopic details of flux line lattice state studied by muon spin rotation is reported in an electron-doped high-$T_{\rm c}$ cuprate superconductor, Sr$_{1-x}$La$_{x}$CuO$_{2}$ (SLCO, $x=0.10$--0.15). A clear sign of phase separation between magnetic and non-magnetic phases is observed, where the effective magnetic penetration depth [$λ\equivλ(T,H)$] is determined selectively for the latter phase. The extremely small value of $λ(0,0)$ %versus $T_{\rm c}$ and corresponding large superfluid density ($n_s \propto λ^{-2}$) is consistent with presence of a large Fermi surface with carrier den…
Quantum oscillations in a tilted magnetic field offer the possibility of distinguishing singlet versus triplet order parameters in the particle hole channel provided the measurements reflect a putative ``normal'' state of a density wave obtained by applying by high magnetic field at low temperatures. A theoretical analysis is given that compares spin density wave, a singlet $d$-density wave, and a triplet $d$-density wave. While the existence of a spin zero in the oscillation amplitude is a necessary consequence of a singlet order parameter, a triplet order parameter may or may not exhibit a s…
An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J_parallel and J_perp plus an additional four-spin interaction J_cyc. Within this model Sr123 and Sr14 can be described by x:=J_parallel/J_perp=1.5, x_cyc:=J_cyc/J_perp=0.2, J_perp^Sr123=1130 cm^-1 and J_perp^Sr14=1080 cm^-1. The couplings found…
Absolute resistivity measurements as a function of temperature from optimally doped YBa_2Cu_3O_(7), La_(2-x)Sr_xCuO_4, Bi_2Sr_2CaCu_2O_(8-x), and (Ca_0.1La_0.9)(Ba_1.65La_0.35)Cu_3O_y thin films are reported. Special attention is given to the measurement geometrical factors and the resistivity slope between Tc and T^{*}. The results are compared with a strong coupling theory for the resistivity derivative near T_c, which is based on hard core bosons (HCB), and with several weak coupling theories, which are BCS based. Surprisingly, our results agree with both paradigms. The implications of thes…
We present Raman experiments on underdoped and overdoped Bi2Sr2CaCu2O(8+d) (Bi-2212) single crystals. We reveal the pseudogap in the electronic Raman spectra in the B1g and B2g geometries. In these geometries we probe respectively, the antinodal (AN) and nodal (N) regions corresponding to the principal axes and the diagonal of the Brillouin zone. The pseudogap appears in underdoped regime and manifests itself in the B1g spectra by a strong depletion of the low energy electronic continuum as the temperature decreases. We define a temperature T* below which the depletion appears and the pseudoga…
We address what seemed to be a contradiction between the lanthanide series REBa$_2$Cu$_3$O$_y$ (RE123) and the charge-compensated series (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x} $)Cu$_{3}$O$_{y}$ (CLBLCO) regarding the superexchange ($J$) dependence of the maximum superconductivity (SC) critical temperature $T_c^{max}(J)$; RE and $x$ are implicit variables. This is done by measuring the Néel temperature and the temperature dependence of the magnetic order parameter for RE=Nd, Sm, Eu, Gd, Dy, Yb, Y, and for Y(BaSr)Cu$_3$O$_y$, at various very light dopings. The doping is determined by the…
In this paper we examine the effects of electron-hole asymmetry as a consequence of strong correlations on the electronic Raman scattering in the normal state of copper oxide high temperature superconductors. Using determinant quantum Monte Carlo simulations of the single-band Hubbard model, we construct the electronic Raman response from single particle Green's functions and explore the differences in the spectra for electron and hole doping away from half filling. The theoretical results are compared to new and existing Raman scattering experiments on hole-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ a…
Raman scattering in cuprate oxychlorides high-temperature superconductors single-crystals
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Institut NEEL CNRS/UGA UPR2940（NEEL研究所）；IMPMC-Sorbonne Universités, Université Pierre et Marie Curie, CNRS, IRD, MNHN（IMPMC-索邦大学，皮埃尔和玛丽·居里大学，CNRS，IRD，MNHN）；Synchrotron SOLEIL（SOLEIL同步辐射中心）；Department of Physics, University of Fribourg（弗里堡大学物理系）；Department of Materials Science, Graduate School of Engineering, Osaka Metropolitan University（大阪公立大学工学研究科材料科学系）
We describe results of electronic Raman-scattering experiments in differently doped single crystals of Y-123 and Bi-2212. The comparison of AF insulating and metallic samples suggests that at least the low-energy part of the spectra originates predominantly from excitations of free carriers. We therefore propose an analysis of the data in terms of a memory function approach. Dynamical scattering rates and mass-enhancement factors for the carriers are obtained. In B2g symmetry the Raman data compare well to the results obtained from ordinary and optical transport. For underdoped materials the d…
By comparing experiments that use Andreev Saint-James reflection, Raman scattering (B2g) and neutron scattering on the (cuprate) high temperature superconductors, evidence is found, that all of the techniques can measure the order parameter of these superconductors. The order parameter is the energy needed to take a superconducting boson out of the condensate. It has the same temperature and doping dependence as the superconducting transition temperature Tc. This condensation energy is different from the pairing energy (as measured by the pseudogap) except for the doping x = 0.27, where the tw…
Electron-phonon coupling (EPC) is one of the most common and fundamental interactions in solids. It not only dominates many basic dynamic processes like resistivity, thermal conductivity etc, but also provides the pairing glue in conventional superconductors. But in high-temperature superconductors (HTSC), it is still controversial whether or not EPC is in favor of paring. Despite the controversies, many experiments have provided clear evidence for EPC in HTSC. In this paper, we briefly review EPC in cuprate and iron-based superconducting systems revealed by Raman scattering. We introduce how …
We report electronic Raman scattering measurements on Bi$_2$Sr$_2$(Y$_{1-x}$Ca$_x$)Cu$_2$O$_{8+δ}$ single crystals at different doping levels. The dependence of the spectra on doping and on incoming photon energy is analyzed for different polarization geometries, in the superconducting and in the normal state. We find the scaling behavior of the superconductivity pair-breaking peak with the carrier concentration to be very different in B$_{1g}$ and B$_{2g}$ geometries. Also, we do not find evidence of any significant variation of the lineshape of the spectra in the overdoped region in both sym…
In a recent paper Kendziora et al concluded that the superconducting gap in overdoped Bi-2212 is isotropic. From data obtained from electronic Raman scattering measurements, their conclusion was based on the observation that pair breaking peaks occured at approximately the same frequency in different scattering geometries and that the normalized scattering intensity at low energies was strongly depleted. We discuss a different interpretation of the raw data and present new data which is consistent with a strongly anisotropic gap with nodes. The spectra can be successfully described by a model …
We present an investigation of charge-compensated antiferromagnetic (Ca$_{x}$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_{3}$O$_{y}$ single crystals using Raman scattering as well as muon spin rotation. In this system the parameter $x$ controls the Cu-O-Cu superexchange interaction via bond distances and buckling angles. The oxygen content $y$ controls the charge doping. In the absence of doping the two-magnon peak position is directly proportional to the superexchange strength $J$. We find that both $x$ and $y$ affect the peak position considerably. The Néel temperature determined from muon sp…
We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic energy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates.
We explore the strong variations of the electronic properties of copper-oxygen compounds across the doping phase diagram in a quantitative way. To this end we calculate the electronic Raman response on the basis of results from angle-resolved photoemission spectroscopy (ARPES). In the limits of our approximations we find agreement on the overdoped side and pronounced discrepancies at lower doping. In contrast to the successful approach for the transport properties at low energies, the Raman and the ARPES data cannot be reconciled by adding angle-dependent momentum scattering. We discuss possib…
The superconducting phase of the $\mathrm{HgBa}_2\mathrm{CuO}_{4+δ}$ (Hg-1201) and $\mathrm{HgBa}_2\mathrm{Ca}_2\mathrm{Cu}_3\mathrm{O}_{8+δ}$ (Hg-1223) cuprates has been investigated by Raman spectroscopy under hydrostatic pressure. Our analysis reveals that the increase of $T_c$ with pressure is slower in Hg-1223 cuprate compared to the Hg-1201 due to a charge carrier concentration imbalance (accentuated by pressure) between the $\mathrm{CuO}_2$ layers of Hg-1223. We find that the energy variation under pressure of the apical oxygen mode from which the charge carriers are transferred to the …
Recent experimental and theoretical studies have established that the spin-lattice relaxation rate, $1/T_1$, measured in nuclear magnetic resonance (NMR) experiments is a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. While some groups suggested that $1/T_1$ is solely determined by spin-flip scattering of BCS-like electrons, other groups stressed the importance of antiferromagnetic spin-fluctuations. We show that these two relaxation mechanisms give rise to a {\it qualitatively} different temperature and frequency dependence of $^{17}$O $1/T_1$.…
Raman and ARPES experiments have demonstrated that in superconducting underdoped cuprates nodal and antinodal regions are characterized by two energy scales instead of the one expected in BCS. The nodal scale decreases with underdoping while the antinodal one increases. Contrary to the behavior expected for an increasing energy scale, the antinodal Raman intensity decreases with decreasing doping. Using the Yang, Rice and Zhang (YRZ) model, we show that these features are a consequence of the non-conventional nature of the superconducting state in which superconductivity and pseudogap correlat…
Using an energy-momentum dispersion for Bi2Sr2CaCu2O8 obtained from angle-resolved photoelectron spectroscopy we show that the shrinking Fermi arc model of the pseudogap is inconsistent with Raman scattering below Tc and specific heat near T*. By simulating the quasiparticle energy dispersion curves we show that Fermi arcs are an artifact of a T-dependent scattering rate.
We have investigated the doping and temperature dependences of the pseudogap/superconducting gap in the single-layer cuprate La$_{2-x}$Sr$_x$CuO$_4$ by angle-resolved photoemission spectroscopy. The results clearly exhibit two distinct energy and temperature scales, namely, the gap around ($π$,0) of magnitude $Δ^*$ and the gap around the node characterized by the d-wave order parameter $Δ_0$, like the double-layer cuprate Bi2212. In comparison with Bi2212 having higher $T_c$'s, $Δ_0$ is smaller, while $Δ^*$ and $T^*$ are similar. This result suggests that $Δ^*$ and $T^*$ are approximately mate…
We present in-plane infrared reflectance measurement on two superconducting cuprates with relatively low T$_c$: a nearly optimally-doped Bi$_2$Sr$_{1.6}$La$_{0.4}$CuO$_{6+δ}$ with T$_c$=33 K and an underdoped La$_{1.89}$Sr$_{0.11}$CuO$_4$ with T$_c$=30 K. The measurement clearly reveals that the superconducting energy gap is distinct from the pseudogap. They have different energy scales and appear at different temperatures. The results suggest that the pseudogap is not a precursor to the superconducting state. The data also challenge the longstanding viewpoint that the superconductivity within…
