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The complexity of competing interactions in high-temperature superconductors provides a fertile ground for collective modes of different origins. Their coupling to the superconducting order parameter may give important insight into the microscopic pairing mechanism. One prominent example in cuprates is the magnetic resonant mode, whose experimental observation spawned theoretical investigations of pairing scenarios mediated by antiferromagnetic fluctuations. Now, phase-resolved nonlinear terahertz spectroscopy of the superconducting Higgs mode offers a new way to reveal the coupling between the collective modes and the superconducting order parameter. Using this technique, we discover a new collective mode distinct from the heavily damped Higgs mode in different families of cuprates. We discuss the origin of this mode and characterize its interplay with the Higgs mode. Our results demonstrate Higgs spectroscopy as a new approach to uncover interactions directly relevant to superconductivity. This technique opens up entirely new avenues for understanding unconventional superconductivity and calls for supporting theoretical work to unlock its full power.

The perfectly linear temperature dependence of the electrical resistivity observed as $T \rightarrow$ 0 in a variety of metals close to a quantum critical point is a major puzzle of condensed matter physics . Here we show that $T$-linear resistivity as $T \rightarrow$ 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bi-layer cuprate Bi2212 and found that it exhibits a $T$-linear dependence with the same slope as in the single-layer cuprates Bi2201, Nd-LSCO and LSCO, despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the $T$-linear coefficient (per CuO$_2$ plane), $A_1$, is given by the universal relation $A_1 T_F = h / 2e^2$, where $e$ is the electron charge, $h$ is the Planck constant and $T_F$ is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1 / $\tau$ of charge carriers reaches the Planckian limit whereby $\hbar / \tau = k_B T$, works not only for hole-doped cuprates but also for electron-doped cuprates despite the different nature of their quantum critical point and strength of their electron correlations., Comment: main + SI

We have used the electric--field effect to modulate the resistivity of the surface of underdoped Sr$_{0.88}$La$_{0.12}$CuO$_{2+x}$ thin films, allowing opposite modifications of the electron and hole density in the CuO$_2$ planes, an original situation with respect to conventional chemical doping in electron-doped materials. When the Hall effect indicates a large contribution of a hole band, the electric--field effect on the normal state resistivity is however dominated by the electrons, and the superconducting transition temperature increases when carriers are transfered from holes to electrons.

Signatures of antiferromagnetism (AF) in the underdoped Ln2-xCexCuO4 (Ln = Nd, Pr,...) family are observed even for doping levels for which superconductivity exists. We have looked for a similar property in a different electron-doped cuprate family, Sr1-xLaxCuO2, which consists of CuO2 planes separated by Sr/La atoms, and is exempt of the possible influence of magnetic rare earth ions. We report in-plane magnetoresistance measurements in the normal state of underdoped, superconducting, c-axis oriented, epitaxial Sr1-xLaxCuO2 thin films. This probe is sensitive to spin arrangement and we find that the in-plane magnetoresistance, which is negative and does not saturate for T, exhibits an angular dependence when measured upon rotating a magnetic field within the CuO2 planes. The analysis reveals a superposition of fourfold and twofold angular oscillations. Both of these increase in amplitude with increasing field and decreasing and appear below a temperature, which gets higher with decreasing doping levels. Our results demonstrate that these magnetoresistance oscillations, also observed for the Ln2-xCexCuO4 (Ln = Nd, Pr,...) family and attributed to an AF signature, are, without ambiguity, a property of CuO2 planes. Besides, these oscillations vary with doping in an unusual way compared to previous results: fourfold oscillations are essentially present in the more underdoped samples while only twofold oscillations are visible in the less underdoped ones. This intriguing observation appears to be a consequence of spin dilution with increasing doping level., 25 pages, 6 figures

The in-plane penetration depth of Sr$_{0.88}$La$_{0.12}$CuO$_{2+x}$ thin films at various doping obtained from oxygen reduction has been measured, using AC susceptibility measurements. For the higher doping samples, the superfluid density deviates strongly from the s-wave behavior, suggesting, in analogy with other electron-doped cuprates, a contribution from a nodal hole pocket, or a small gap on the Fermi surface such as an anisotropic s-wave order parameter. The low value of the superfluid densities, likely due to a strong doping-induced disorder, places the superconducting transition of our samples in the phase-fluctuation regime.

We use angle resolved photoemission spectroscopy to probe the electronic excitations of the non-superconducting state that exists between the antiferromagnetic Mott insulator at zero doping and the superconducting state at larger dopings in Bi_2Sr_2CaCu_2O_{8+��}. We find that this state is a nodal liquid whose excitation gap becomes zero only at points in momentum space. Despite exhibiting a resistivity characteristic of an insulator and the absence of coherent quasiparticle peaks, this material has the same gap structure as the d-wave superconductor. We observe a smooth evolution of the spectrum across the insulator-to-superconductor transition, which suggests that high temperature superconductivity emerges when quantum phase coherence is established in a non-superconducting nodal liquid., 16 pages, 5 figures

The time-averaged and low--frequency noise transport properties were investigated in the vicinity of the superconductor--insulator transition for a Bi$_2$Sr$_{2-x}$La$_{x}$CuO$_{6+��}$ ($x=0.3$) thin film. The results are consistent with a superconductor (metal) embedded in a strong insulator, the latter showing two-dimensional variable range hopping properties. The weak insulator behavior -- if any -- is attributed to the metallic inclusions only.

The resistance noise in a Bi_2Sr_2CaCu_2O$_{8+\delta}$ thin film is found to increase strongly in the underdoped regime. While the increase of the raw resistance noise with decreasing temperature appears to roughly track the previously reported pseudogap temperature for this material, standard noise analysis rather suggests that the additional noise contribution is driven by the proximity of the superconductor-insulator transition.

We find that peaks in the autocorrelation of angle resolved photoemission spectroscopy data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in the superconducting state show dispersive behavior for binding energies smaller than the maximum superconducting energy gap. For higher energies, though, a striking anomalous dispersion is observed that is a consequence of the interaction of the electrons with collective excitations. In contrast, in the pseudogap phase, we only observe dispersionless behavior for the autocorrelation peaks. The implications of our findings in regards to Fourier transformed scanning tunneling spectroscopy data are discussed., Comment: 5 pages, 4 figures

Angle resolved photoemission on underdoped Bi2Sr2CaCu2O8 reveals that the magnitude and d-wave anisotropy of the superconducting state energy gap are independent of temperature all the way up to Tc. This lack of T variation of the entire k-dependent gap is in marked contrast to mean field theory. At Tc the point nodes of the d-wave gap abruptly expand into finite length ``Fermi arcs''. This change occurs within the width of the resistive transition, and thus the Fermi arcs are not simply thermally broadened nodes but rather a unique signature of the pseudogap phase., Comment: Accepted by Phys. Rev. Lett

The resistance noise in a Bi_2Sr_2CaCu_2O$_{8+��}$ thin film is found to increase strongly in the underdoped regime. While the increase of the raw resistance noise with decreasing temperature appears to roughly track the previously reported pseudogap temperature for this material, standard noise analysis rather suggests that the additional noise contribution is driven by the proximity of the superconductor-insulator transition.

We find that peaks in the autocorrelation of angle resolved photoemission spectroscopy data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+��}$ in the superconducting state show dispersive behavior for binding energies smaller than the maximum superconducting energy gap. For higher energies, though, a striking anomalous dispersion is observed that is a consequence of the interaction of the electrons with collective excitations. In contrast, in the pseudogap phase, we only observe dispersionless behavior for the autocorrelation peaks. The implications of our findings in regards to Fourier transformed scanning tunneling spectroscopy data are discussed., 5 pages, 4 figures

The in-plane resistivity and Hall coefficient have been measured for the single-layer compound Bi$_2$Sr$_2$CuO$_{6+\delta}$ for the whole range of doping states. The deviation of the Hall coefficient, $R_H$, from a high-temperature linear behavior and the temperature dependence of the Hall angle are both only weakly dependent upon doping, contrasting with Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ and Bi$_2$Sr$_2$CaCuO$_{8+\delta}$. This is in contradiction with former proposals that the transverse transport detects the formation of incoherent Cooper pairs in the pseudogap state. Conversely, the analysis of the data using a phenomenological angular dependent scattering rate clearly allows to distinguish between underdoped and overdoped states, and we propose that the maximum in $R_H(T)$ simply arises due to the combination of a large isotropic scattering rate and an anisotropic temperature dependent one.

The in-plane resistivity and Hall coefficient have been measured for the single-layer compound Bi$_2$Sr$_2$CuO$_{6+��}$ for the whole range of doping states. The deviation of the Hall coefficient, $R_H$, from a high-temperature linear behavior and the temperature dependence of the Hall angle are both only weakly dependent upon doping, contrasting with Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+��}$ and Bi$_2$Sr$_2$CaCuO$_{8+��}$. This is in contradiction with former proposals that the transverse transport detects the formation of incoherent Cooper pairs in the pseudogap state. Conversely, the analysis of the data using a phenomenological angular dependent scattering rate clearly allows to distinguish between underdoped and overdoped states, and we propose that the maximum in $R_H(T)$ simply arises due to the combination of a large isotropic scattering rate and an anisotropic temperature dependent one.

The pseudogap phase in the cuprates is a most unusual state of matter: it is a metal, but its Fermi surface is broken up into disconnected segments known as Fermi arcs. Using angle resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in momentum space and the resulting arcs depend only on the ratio T/T*(x), where T*(x) is the temperature below which the pseudogap first develops at a given hole doping x. In particular, the arcs collapse linearly with T/T* and extrapolate to zero extent as T goes to 0. This suggests that the T = 0 pseudogap state is a nodal liquid, a strange metallic state whose gapless excitations are located only at points in momentum space, just as in a d-wave superconductor., Comment: to appear, Nature Physics (July 2006)

The in-plane magnetoresistance of an epitaxial Bi$_2$Sr$_2$CuO$_{6+\delta}$ thin film was systematically investigated as a function of doping, above $T_c$. The orbital magnetoconductance is used to extract the crossover field line $H_{c2}^*(T)$ in the fluctuation regime. This field is found in good agreement with the upper critical field obtained from resistivity data below $T_c$, and exhibits a similar upward curvature, thus pointing toward the existence of a critical correlation length. The consequences regarding the nature of the resistive transition are discussed.

We report the observation of a change in Fermi surface topology of Bi2Sr2CaCu2O8 with doping. By collecting high statistics ARPES data from moderately and highly overdoped samples and dividing the data by the Fermi function, we answer a long standing question about the Fermi surface shape of Bi2Sr2CaCu2O8 close to the (pi,0) point. For moderately overdoped samples (Tc=80K) we find that both the bonding and antibonding sheets of the Fermi surface are hole-like. However for a doping level corresponding to Tc=55K we find that the antibonding sheet becomes electron-like. This change does not directly affect the critical temperature and therefore the superconductivity. However, since similar observations of the change of the topology of the Fermi surface were observed in LSCO and Bi2Sr2Cu2O6, it appears to be a generic feature of hole-doped superconductors. Because of bilayer splitting, though, this doping value is considerably lower than that for the single layer materials, which again argues that it is unrelated to Tc.

The in-plane magnetoresistance of an epitaxial Bi$_2$Sr$_2$CuO$_{6+��}$ thin film was systematically investigated as a function of doping, above $T_c$. The orbital magnetoconductance is used to extract the crossover field line $H_{c2}^*(T)$ in the fluctuation regime. This field is found in good agreement with the upper critical field obtained from resistivity data below $T_c$, and exhibits a similar upward curvature, thus pointing toward the existence of a critical correlation length. The consequences regarding the nature of the resistive transition are discussed.

The current dependence of the excess conductivity is measured up to $\simeq 3 T_c$ for a Bi$_2$Sr$_2$CuO$_{6+��}$ thin film, as a function of doping. It is found to be anomalously sensitive to the transport current and to behave as a universal function of $T/T_c$ in the whole doping range. We discuss these results in the perspective of a granular superconductor with a gapless-like behavior.

The autocorrelation of angle resolved photoemission data from the high temperature superconductor Bi2Sr2CaCu2O8+d shows distinct peaks in momentum space which disperse with binding energy in the superconducting state, but not in the pseudogap phase. Although it is tempting to attribute a non-dispersive behavior in momentum space to some ordering phenomenon, a de-construction of the autocorrelation reveals that the non-dispersive peaks arise not from ordering, but rather from the tips of the Fermi arcs, which themselves do not change with binding energy., Comment: 4 pages, 3 figures

We examine the momentum and energy dependence of the scattering rate of the high temperature cuprate superconductors using angle resolved photoemission spectroscopy. The scattering rate is of the form a + b*w. The inelastic coefficient b is found to be isotropic. The elastic term, a, however, is found to be highly anisotropic in the pseudogap phase of optimal doped samples, with an anisotropy which correlates with that of the pseudogap. This can be contrasted with heavily overdoped samples, which show an isotropic scattering rate in the normal state.

Although initially quite controversial, it has been widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wavefunction symmetry. The controversy has now shifted to whether the high-Tc pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y0.7Ca0.3Ba2Cu3O7-x (Ca-doped Y-123), La2-xSrxCuO4 (La-214) and Bi2Sr2CaCu2O8+x (Bi-2212),with doping levels covering the underdoped, optimal and overdoped regions. Our work implies that time-reversal invariant, predominantly dx2-y2 pairing symmetry is robust over a large variation in doping, and underscores the important role of on-site Coulomb repulsion in the making of high-temperature superconductivity., 4 pages, 4 figures

The in-plane infrared and visible (3 meV-3 eV) reflectivity of Bi2Sr2CaCu2O8+d (Bi-2212) thin films is measured between 300 K and 10 K for different doping levels with unprecedented accuracy. The optical conductivity is derived through an accurate fitting procedure. We study the transfer of spectral weight from finite energy into the superfluid as the system becomes superconducting. In the over-doped regime, the superfluid develops at the expense of states lying below 60 meV, a conventional energy of the order of a few times the superconducting gap. In the underdoped regime, spectral weight is removed from up to 2 eV, far beyond any conventional scale. The intraband spectral weight change between the normal and superconducting state, if analyzed in terms of a change of kinetic energy is ~1 meV. Compared to the condensation energy, this figure addresses the issue of a kinetic energy driven mechanism., Comment: 13 pages with 9 figures included

One of the interesting features of the photoemission spectra of the high temperature cuprate superconductors is the presence of a large signal (referred to as the "background'') in the unoccupied region of the Brillouin zone. Here we present data indicating that the origin of this signal is extrinsic and is most likely due to strong scattering of the photoelectrons. We also present an analytical method that can be used to subtract the background signal.

We have studied the evolution of the thermoelectric power S(T) with oxygen doping of single-layered Bi2Sr2CuO6+d thin films and ceramics in the overall superconducting (Tc, S290K) phase diagram. While the universal relation between the room-temperature thermopower S290K and the critical temperature is found to hold in the strongly overdoped region (d>0.14), a strong violation is observed in the underdoped part of the phase diagram. The observed behaviour is compared with other cuprates and the different scenarios are discussed., 7 pages, 5 figures

Temperature and doping dependent tunneling spectroscopy on $Bi_2Sr_2CaCu_2O_{8+\delta}$ single crystals has been investigated by using break-junction technique. The results provide direct evidence that the pseudogap persists into heavily overdoped regime, possibly in whole doping range of the superconducting phase. The gap value determined from the peak-to-peak of the conductance, $\Delta_{p-p}$, exhibits a jump-like increase as $T$ is raised across the critical temperature. The magnitude of the jump, the pseudogap opening temperature and superconducting gap decrease with raising doping. The $\Delta_{p-p}$ below $T_c$ can be naturally treated as the vector sum of two competing orders: a BCS-like superconducting gap and a residual pseudogap., Comment: 4 pages, 5 figures, 1 table

Temperature and doping dependent tunneling spectroscopy on $Bi_2Sr_2CaCu_2O_{8+��}$ single crystals has been investigated by using break-junction technique. The results provide direct evidence that the pseudogap persists into heavily overdoped regime, possibly in whole doping range of the superconducting phase. The gap value determined from the peak-to-peak of the conductance, $��_{p-p}$, exhibits a jump-like increase as $T$ is raised across the critical temperature. The magnitude of the jump, the pseudogap opening temperature and superconducting gap decrease with raising doping. The $��_{p-p}$ below $T_c$ can be naturally treated as the vector sum of two competing orders: a BCS-like superconducting gap and a residual pseudogap., 4 pages, 5 figures, 1 table

We have measured the dynamics of individual magnetic fluxoids entering and leaving thin film, photolithographically patterned rings of underdoped high-temperature superconductor BSCCO using a variable sample temperature scanning SQUID microscope. These measurements can be understood within a phenomenological model in which the fluxoid number changes by thermal activation of a Pearl vortex in the ring wall. We place upper limits on the "vison" binding energy in these samples from these measurements., Comment: 4 pages, 4 figures

Photoemission spectra of Bi2Sr2CaCu2O8 reveal that the high energy feature near (pi,0), the "hump", scales with the superconducting gap and persists above Tc in the pseudogap phase. As the doping decreases, the dispersion of the hump increasingly reflects the wavevector (pi,pi) characteristic of the undoped insulator, despite the presence of a large Fermi surface. This can be understood from the interaction of the electrons with a collective mode, supported by our observation that the doping dependence of the resonance observed by neutron scattering is the same as that inferred from our data., Comment: 4 pages (revtex), 5 figures (eps)