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 conventional, spontaneous Raman spectroscopy. Our results suggest a significant contribution to the intensity of the A1g symmetry Raman spectrum in d-wave superconductors. In order to test our theory, we predict the presence of measurable characteristic oscillations in THz quench-optical probe time-dependent reflectivity experiments.
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…
Within the framework of the kinetic energy driven superconducting mechanism, the doping dependence of the electromagnetic response in the electron-doped cuprate superconductors is studied. It is shown that although there is an electron-hole asymmetry in the phase diagram, the electromagnetic response in the electron-doped cuprate superconductors is similar to that observed in the hole-doped cuprate superconductors. The superfluid density depends linearly on temperature, except for the strong deviation from the linear characteristics at the extremely low temperatures.
The order parameter in superconductivity of cuprates is investigated in the framework of the Bogoliubov theory. By using a simplifying assumption about the electronic states, it is predicted an effective critical temperature Tc* > Tc associated to the coherent gap D0. A connection between D0 and the antinodal pseudogap DPG is proposed allowing for a comprehensive picture of the main experimental features of cuprate superconductors.
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.
The vortex transport entropy in the mixed state of the cuprate superconductors YBa$_2$Cu$_3$O$_{7-δ}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ at the maximum Nernst or Ettingshausen signal below $T_c$ is discussed. The vortex transport entropy per CuO$_2$ double layer in the cuprate epitaxial films is found to be close to the Boltzmann constant.
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…
We study the lowest energy state in the CuO$_2$ plane of cuprate superconductors, related to the vibration that does not involve distortions of constituent units of the plane, the Rigid Unit Mode (RUM). We discuss the correlated motion in the plane due to RUM on temperature decrease, and possible relevance of this phonon for superconductivity.
In order to explore the reason why the single-layered cuprates, La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ ($T_c\simeq$ 40K) and HgBa$_2$CuO$_{4+δ}$ ($T_c\simeq$ 90K), have such a significant difference in $T_c$, we study a two-orbital model that incorporates the $d_{z^2}$ orbital on top of the $d_{x^2-y^2}$ orbital. It is found, with the fluctuation exchange approximation, that the $d_{z^2}$ orbital contribution to the Fermi surface, which is stronger in the La system, works against d-wave superconductivity, thereby dominating over the effect of the Fermi surface shape. The result resolves the long-standin…
Short review of the topical comprehension of Cuprate High-Temperature Superconductors, featuring structural and metallurgical aspects that optimize their superconducting properties with respect to technical applications.
The formula frequently used to describe the c-axis infrared response of the coupled electron-phonon system of bilayer cuprate superconductors and providing important insights into the physics of these materials has been originally obtained at the level of the phenomenological multilayer model. Here we derive it using diagrammatic perturbation theory.
We propose a microscopic explanation of the pseudogap features discovered in the normal state specific heat and magnetic susceptibility of cuprates. In the framework of the bipolaron theory of high-Tc superconductors we explain the magnitude of the carrier specific heat and susceptibility as well as their universal scaling with temperature over a wide range of doping.
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…
Anisotropy, thermal and quantum fluctuations and their dependence on dopant concentration appear to be present in all cuprate superconductors, interwoven with the microscopic mechanisms responsible for superconductivity. Here we review anisotropy, in-plane and c-axis penetration depths, isotope effect and conductivity measurements to reassess the universal behavior of cuprates as revealed by the doping dependence of these phenomena and of the transition temperature.
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 critically review recent and earlier results on isotope effects in cuprate superconductors and emphasize that the sample preparation and the isotope exchange and back exchange are crucial in understanding and interpreting the data. Only extremely careful preparation techniques yield reliable results and permit differentiation between real isotope effects and marginal ones. The former are substantial and highlight the lattice vibrational importance in cuprate superconductors.
When combining the BCS expression of Tc with a shear modulus constant model, we can demonstrate that Tc oscillates depending on the number of the cuprate planes and that it reaches its first maximum for three planes. This is in good agreement with experimental data and suggests that the electron- phonon coupling is essential to the superconductivity of the cuprates.
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…
Phase-sensitive tests of pairing symmetry have provided strong evidence for predominantly d-wave pairing symmetry in both hole- and electron-doped high-Tc cuprate superconductors. Temperature dependent measurements in YBCO indicate that the d-wave pairing dominates, with little if any imaginary component, at all temperatures from 0.5K through Tc. In this article we review some of this evidence and discuss the implications of the universal d-wave pairing symmetry in the cuprates.
Using the scaling theory of quantum critical phenomena we present a detailed analysis of various superconducting properties of La$_{2-x}$Sr$_{x}$CuO$_{4}$, Y$_{0.8}$Ca$_{0.2}$-123, Tl-1212 and Tl-2201. Our results include: the experimental data are fully consistent with a 2D insulator to superconductor (ISQ) transition in the underdoped limit. The quantum critical properties appear to be equivalent to those of a dirty 2D bosonic system with long range Coulomb interaction. Together with previous evidence, this transition appears to be a generic feature of cuprate superconductors. The 3D superco…
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…
The orbital component of the order parameter in the cuprate high-Tc cuprate superconductors is now well established, in large part because of phase sensitive tests. Although it would be desirable to use such tests on other unconventional superconductors, there are a number of favorable factors associated with the properties of the cuprates, and a number of technical advances, that were required for these tests to be successful. In this review I will describe the development of phase sensitive pairing symmetry tests using SQUID microscopy, underlining the factors favoring these experiments in t…
It is conjectured that the anomalous spin dynamics observed in the normal state of cuprate superconductors might find its origin in a nearly ordered spin system which is kept in motion by thermally meandering charged domain walls. `Temperature sets the scale' finds a natural explanation, while a crossover to a low temperature quantum domain wall fluid is implied.
We study the effects of quantum vortex fluctuations in two-dimensional superconductors using a dual theory of vortices, and investigate the relevance to underdoped cuprates where the superconductor-insulator transition (SIT) is possibly driven by quantum vortex proliferation. We find that a broad enough phase fluctuation regime may exist for experimental observation of the quantum vortex fluctuations near SIT in underdoped cuprates. We propose that this scenario can be tested via pair-tunneling experiments which measure the characteristic resonances in the zero-temperature pair-field susceptib…
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 present macroscopic experimental evidence for field-induced microscopic quantum fluctuations in different hole- and electron-type cuprate superconductors with varying doping levels and numbers of CuO$_2$ layers per unit cell. The significant suppression of the zero-temperature in-plane magnetic irreversibility field relative to the paramagnetic field in all cuprate superconductors suggests strong quantum fluctuations due to the proximity of the cuprates to quantum criticality.
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 show by means of the theory of the order parameter phase fluctuations that the temperature of "closing" (or "opening") of the gap (and pseudogap) in the electron spectra of superconductors with anisotropic order parameter takes place within a finite temperature range. Every Fourier-component of the order parameter has its own critical temperature.
Since their experimental discovery in 1989, the electron-doped cuprate superconductors have presented both a major challenge and a major opportunity. The major challenge has been to determine whether these materials are fundamentally different from or essentially similar to their hole-doped counterparts; a major opportunity because answering this question would strongly constrain the possible explanations for what is the essential physics that leads to high temperature superconductivity in the cuprates, which is still not agreed upon. Here we argue that experimental results over the past 30 ye…
We outline the universal and finite temperature critical properties of the 3D-XY model, extended to anisotropic extreme type-II superconductors, as well as the universal quantum critical properties in 2D. On this basis we review: (i) the mounting evidence for 3D-XY behavior in optimally doped cuprate superconductors and the 3D to 2D crossover in the underdoped regime; (ii) the finite size limitations imposed by inhomogeneities; (iii) the experimental evidence for a 2D-XY quantum critical point in the underdoped limit, where the superconductor to insulator transition occurs; (iv) the emerging i…
We propose two possible new compounds, Ba$_2$CuO$_2$Fe$_2$As$_2$ and K$_2$CuO$_2$Fe$_2$Se$_2$, which hybridize the building blocks of two high temperature superconductors, cuprates and iron-based superconductors. These compounds consist of square CuO$_2$ layers and antifluorite-type Fe$_2$X$_2$ (X=As,Se) layers separated by Ba/K. The calculations of binding energies and phonon spectrums indicate that they are dynamically stable, which ensures that they may be experimentally synthesized. The Fermi surfaces and electronic structures of the two compounds inherit the characteristics of both cuprat…
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 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…
Impurity doping like Zn atoms in cuprates were systematically studied to provide important information on the pseudogap phase because this process substantially reduces $T_c$ without effect $T^*$. Despite many important results and advances, the normal phase of these superconductors is still subject of a great debate. We show that the observed Zn-doped data can be reproduced by constructing a nanoscale granular superconductor whose resistivity transition is achieved by Josephson coupling, what provides also a simple interpretation to the pseudogap phase.
Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current, $I_c$, measured via JSTS, images the spatial form of the superconducting order parameter in $d_{x^2-y^2}$-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that $I_c$ probes the existence of phase-incoherent superconducting correlations in the pseudo-gap region of the cuprate superconductors, thus providing unprecedented insight into it…
We investigate the issues of competing orders and quantum criticality in cuprate superconductors via experimental studies of the high-field thermodynamic phase diagrams and the quasiparticle tunneling spectroscopy. Our results suggest substantial field-induced quantum fluctuations in all cuprates investigated, and their correlation with quasiparticle spectra implies that both electron- (n-type) and hole-doped (p-type) cuprate superconductors are in close proximity to a quantum critical point that separates a pure superconducting (SC) phase from a phase consisting of coexisting SC and a competi…
We review the field of high temperature cuprate superconductors, with an emphasis on the nature of their electronic properties. After a general overview of experiment and theory, we concentrate on recent results obtained by angle resolved photoemission, inelastic neutron scattering, and optical conductivity, along with various proposed explanations for these results. We conclude by reviewing efforts which attempt to identify the energy savings involved in the formation of the superconducting ground state.
Enhancing the temperature at which superconductivity is observed is a long-standing objective for materials scientists. Recent tantalizing experiments suggest a possible route for achieving this.
The correlation between the charge-order wave vector Q_{CD} and second-neighbor hopping t' in cuprate superconductors is studied based on the t-t'-J model. It is shown that the magnitude of the charge-order wave vector Q_{CD} increases with the increase of t', and then the experimentally observed differences of the magnitudes of the charge-order wave vector Q_{CD} among the different families of cuprate superconductors at the same doping concentration can be attributed to the different values of t'.
The transport of heat and charge in the overdoped cuprate superconductor Tl_2Ba_2CuO_(6+delta) was measured down to low temperature. In the normal state, obtained by applying a magnetic field greater than the upper critical field, the Wiedemann-Franz law is verified to hold perfectly. In the superconducting state, a large residual linear term is observed in the thermal conductivity, in quantitative agreement with BCS theory for a d-wave superconductor. This is compelling evidence that the electrons in overdoped cuprates form a Fermi liquid, with no indication of spin-charge separation.
Within the spin-fermion model for cuprate superconductors, the influence of the intersite Coulomb interactions $V_2$ and $V_2'$ between holes located at the next-nearest-neighbor oxygen ions of CuO$_2$ plane on the implementation of the d_{x^2-y^2}-wave pairing is studied. It is shown that d-wave pairing can be suppressed only for unphysically large values of $V_2$ and $V_2'$.
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…
Recent development in the physics of high-temperature superconductivity is reviewed, with special emphasis on the studies of the low-energy excitations of cuprate and iron-based superconductors. For cuprate superconductors, a phenomenology based on coexisting competing orders with superconductivity in the ground state of these doped Mott insulators is shown to provide a consistent account for a wide range of experimental findings. In the case of iron-based superconductors, studies of the low-energy excitations reveal interesting similarities and differences when compared with cuprate supercond…
We study a simple BCS-like model which describes unconventional superconductivity on the basis of an electron-electron attraction corresponding to the delta-shell potential: $U(r) = -g δ(r-r_0)$. It predicts a $T_c$ vs. doping behavior similar to that characteristic of the High-$T_c$ cuprates.
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 correspondin…
Quasiparticle tunneling spectra of both hole-doped (p-type) and electron-doped (n-type) cuprates are studied using a low-temperature scanning tunneling microscope. The results reveal that neither the pairing symmetry nor the pseudogap phenomenon is universal among all cuprates, and that the response of n-type cuprates to quantum impurities is drastically different from that of the p-type cuprates. The only ubiquitous features among all cuprates appear to be the strong electronic correlation and the nearest-neighbor antiferromagnetic Cu^{2+}-Cu^{2+} coupling in the CuO_2 planes.
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.
