Optical conductivity of c axis oriented YBa2Cu3O6.70: Evidence for a pseudogap

Analogies of phonon anomalies and electronic gap features in the infrared response of Sr14-xCaxCu24O41and underdoped YBa2Cu3O6+x

We present an experimental and theoretical study which compares the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr14-xCa_xCu₂₄O₄₁(SCCO) with those of the underdoped high-T_csuperconductor YBa₂Cu₃O6+x(YBCO) and thereby reveals some surprising analogies. Specifically, we present a phenomenological model that describes the anomalous doping- and temperature-dependence of some of the phonon features in thea-axis response (field along the rungs of the ladders) of SCCO. It assumes that the phonons are coupled to charge oscillations within the ladders. Their changes with decreasing temperature reveal the formation of a crystal (density wave) of hole pairs that are oriented along the rungs. We also discuss the analogy to a similar model that was previously used to explain the phonon anomalies and an electronic plasma mode in thec-axis response (field perpendicular to the CuO₂planes) of YBCO. We further confirm that an insulator-like pseudogap develops in thea-axis conductivity of SCCO which closely resembles that in thec-axis conductivity of YBCO. Most surprisingly, we find that thec-axis conductivity (field along the legs of the ladders) of SCCO is strikingly similar to the in-plane one (field parallel to the CuO₂planes) of YBCO. Notably, in both cases a dip feature develops in the normal state spectra that is connected with a spectral weight shift toward low frequencies and can thus be associated with precursor superconducting pairing correlations that are lacking macroscopic phase coherence. This SCCO-YBCO analogy indicates that collective degrees of freedom contribute to the low-energy response of underdoped highT_ccuprates and it even suggests that the charges in the CuO₂planes tend to segregate forming quasi-one-dimensional structures similar to the two-leg ladders, as predicted for the stripe-scenario or certain intertwinned states.

Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap [Formula: see text] in real-space, and a characteristic quasiparticle scattering interference (QPI) signature [Formula: see text] in wavevector space. By studying strongly underdoped Bi2Sr2CaDyCu2O8 at hole-density ~0.08 in the superconductive phase, we detect the 8a0-periodic [Formula: see text] modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature [Formula: see text] that is predicted specifically for the temperature dependence of an 8a0-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi2Sr2CaDyCu2O8 pseudogap phase.

Non-linear Terahertz driving of plasma waves in layered cuprates

The hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered cuprates. So far, THz light pulses have been used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency lies in the THz range. However, the high-energy in-plane plasma mode has been considered insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to markedly different thermal effects for the out-of-plane and in-plane response, linking in both cases the emergence of non-linear photonics across T_c to the superfluid stiffness. Our results show that THz light pulses represent a preferential knob to selectively drive phase excitations in unconventional superconductors.

Josephson coupling determines the superconducting phase stiffness and sets the energy scale of plasma waves. Here, the authors show that THz light can induce two-plasmon excitations of both out-of-plane and in-plane phase modes, leading however to markedly different resonant and thermal effects due to the strong anisotropy of the Josephson couplings.

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

Infrared probe of pseudogap in electron-doped Sr2IrO4

We report on infrared spectroscopy experiments on the electronic response in (Sr_1-x La _x )₂IrO₄ (x = 0, 0.021, and 0.067). Our data show that electron doping induced by La substitution leads to an insulator-to-metal transition. The evolution of the electronic structure across the transition reveals the robustness of the strong electronic correlations against the electron doping. The conductivity data of the metallic compound show the signature of the pseudogap that bears close similarity to the analogous studies of the pseudogap in the underdoped cuprates. While the low energy conductivity of the metallic compound is barely frequency dependent, the formation of the pseudogap is revealed by the gradual suppression of the featureless conductivity below a threshold frequency of about 17 meV. The threshold structure develops below about 100 K which is in the vicinity of the onset of the short-range antiferromagnetic order. Our results demonstrate that the electronic correlations play a crucial role in the anomalous charge dynamics in the (Sr_1-x La _x )₂IrO₄ system.

Optical studies of high-temperature superconducting cuprates

The optical studies of high-temperature superconducting cuprates (HTSC) are reviewed. From the doping dependence of room temperature spectra, a dramatic change of the electronic state from a Mott (charge transfer) insulator to a Fermi liquid has been revealed. Additionally, the unusual 2D nature of the electronic state has been found. The temperature dependence of the optical spectra provided a rich source of information on the pseudogap, superconducting gap, Josephson plasmon, transverse Josephson plasma mode and precursory superconductivity. Among these issues, Josephson plasmons and transverse Josephson plasma mode were experimentally discovered by optical measurements, and thus are unique to HTSC. The effect of the spin/charge stripe order is also unique to HTSC, reflecting the conducting nature of the stripe order in this system. The pair-breaking due to the stripe order seems stronger in the out-of-plane direction than in the in-plane one.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

Formation of gapless Fermi arcs and fingerprints of order in the pseudogap state of cuprate superconductors

We use angle-resolved photoemission spectroscopy and a new quantitative approach based on the partial density of states to study properties of seemingly disconnected portions of the Fermi surface (FS) that are present in the pseudogap state of cuprates called Fermi arcs. We find that the normal state FS collapses very abruptly into Fermi arcs at the pseudogap temperature (T*). Surprisingly, the length of the Fermi arcs remains constant over an extended temperature range between T* and T(pair), consistent with the presence of an ordered state below T*. These arcs collapse again at the temperature below which pair formation occurs (T(pair)) either to a point or a very short arc, whose length is limited by our experimental resolution. The tips of the arcs span between points defining a set of wave vectors in momentum space, which are the fingerprints of the ordered state that causes the pseudogap.

Implications of charge ordering in high Tc cuprate superconductors in far-infrared spectroscopy

We addressed the issue of the absence of far-infrared signatures pertaining to charge ordering in the published far-infrared reflectivity data of La2-xSrxCuO4 single crystals while other experimental probes reveal that charge ordering is a hallmark of superconducting cuprates. Through direct comparison of the far-infrared data reported by various groups side by side and also with the Raman scattering data, we found that the inconsistencies stem from the failure in capturing delicate spectral features embedded in the close-to-perfect ab-plane far-infrared reflectivity of La2-xSrxCuO4 single crystals by misidentifying the reflectivity as the Drude-like metallic reflectivity. The analysis of the close-to-true reflectivity data reveals that only a small fraction (<3%) of the total doping-induced charge carriers (electrons) are itinerant on the electron lattice made up with the rest of the electrons (>97%) at all doping levels up to 16%. We conclude that the far-infrared reflectivity study is far from being ready to construct a coherent picture of the ubiquitous charge ordering phenomenon and its relationship with the high Tc superconductivity.

Interlayer penetration depth in the pseudogap phase of cuprate superconductors

The opening of a pseudogap in the electronic structure of the underdoped high Tc cuprates has a profound effect on superconducting properties. Here we consider the c-axis penetration depth. A phenomenological model of the pseudogap due to Yang, Rice, and Zhang (YRZ) is used. It is based on the idea of a resonating valence bond spin liquid. A simplifying limit, the arc model, is also considered as it provides useful analytic formulas. The zero temperature value of the superfluid density n(s)(T = 0) is greatly reduced with increasing values of the pseudogap (Δpg). This value reflects the reconstruction of the Fermi surface from the large contour of Fermi liquid theory to ever smaller Luttinger pockets as Δpg becomes larger. Also, as temperature is increased the ratio n(s)(T)/n(s)(0) as a function of the reduced temperature t = T/T(c) decreases more rapidly than in the corresponding Fermi liquid (Δpg = 0) as states which have both superconducting and pseudogap become more significantly sampled.

Interlayer coherence and superconducting condensate in the c-axis response of optimally doped Ba(Fe(1-x)Co(x))2As2 high-T(c) superconductor using infrared spectroscopy

We report on the infrared studies of the interlayer charge dynamics of a prototypical pnictide superconductor Ba(Fe(0.926)Co(0.074))(2)As(2). We succeeded in probing the intrinsic interlayer response by performing infrared experiments on the crystals with a cleaved ac surface. Our experiments identify the coexistence of the suppression of the electronic spectral weight and the development of a coherent Drude-like response in the normal state. The formation of the interlayer condensate is clearly observed in the superconducting state and appears to be linked to coherent contribution to the normal-state conductivity.

Origin of the magnetic field induced changes of the transverse plasma mode in the c-axis infrared response of underdoped YBa2Cu3O(7-δ)

We report on results of our theoretical study of magnetic field induced changes of the c-axis infrared response of bilayer cuprate superconductors using the phenomenological multilayer model involving the conductivity of the spacing layers and that of the bilayer units. For H perpendicular to the planes, the local conductivities have been expressed in terms of a two-fluid approximation--as weighted averages of the superconducting state ones and the normal state ones representing contributions of the vortex cores, the weight of the latter increasing linearly with the field. This allows us to reproduce and interpret the fast decrease with increasing H of the well known 400 cm(-1) peak (transverse plasma mode) in the c-axis conductivity, observed by LaForge and co-workers. For the local conductivities of underdoped YBa(2)Cu(3)O(7-δ) with T(c)=58 K reported by Dubroka and co-workers and the fraction of the normal state (T ≈ T(c)) component given by (μ(0)H/25 T), the computed field induced changes of the reflectivity are in quantitative agreement with the data. This suggests that the response at H=0 and T ≈ T(c) is close to that at H=25 T < H(c2) and T ≪ T(c), in accord with theories attributing the above T(c) state to that of a superconductor lacking long-range phase coherence. Also discussed are changes of the response induced by H parallel to the CuO(2) planes.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.

Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O(7-δ) (R=Y, Gd, Eu) superconducting crystals from infrared spectroscopy

We show that a multilayer analysis of the infrared c-axis response of RBa2Cu3O(7-δ) (R=Y, Gd, Eu) provides important new information about the anomalous normal-state properties of underdoped cuprate high temperature superconductors. In addition to competing correlations which give rise to a pseudogap that depletes the low-energy electronic states below T*≫T(c), it enables us to identify the onset of a precursor superconducting state below T(ons)>T(c). We map out the doping phase diagram of T(ons) which reaches a maximum of 180 K at strong underdoping and present magnetic field dependent data which confirm our conclusions.

Superconducting energy gap and c-axis plasma frequency of (Nd,Sm)FeAsO0.82F0.18 superconductors from infrared ellipsometry

We present far-infrared ellipsometric measurements of polycrystalline samples of the pnictide superconductor RFeAsO0.82F0.18 (R=Nd and Sm). We find evidence that the electronic properties are strongly anisotropic such that the optical spectra are dominated by the weakly conducting c-axis response similar to the cuprate high-temperature superconductors. We deduce an upper limit of the c-axis superconducting plasma frequency of omega pl,c(SC)< or =260 cm(-1) corresponding to a lower limit of the c-axis magnetic penetration depth of lambda c > or =6 microm and lambda c/lambda ab > or =30 as compared to lambda ab=185 nm from muon spin rotation [A. Drew, arXiv:0805.1042 [Phys. Rev. Lett. (to be published)]]. We also observe a gaplike suppression of the conductivity in the superconducting state with a shoulderlike feature at omegaSC* approximately 300 cm(-1) and spectral shape which is consistent with an unconventional order parameter with 2Delta approximately omegaSC* approximately 37 meV.

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

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

Evidence for two separate energy gaps in underdoped high-temperature cuprate superconductors from broadband infrared ellipsometry

We present broadband infrared ellipsometry measurements of the c-axis conductivity of underdoped RBa_{2}Cu_{3}O_{7-delta} (R=Y, Nd, and La) single crystals. Our data show that separate energy scales are underlying the redistributions of spectral weight due to the normal state pseudogap and the superconducting gap. Furthermore, they provide evidence that these gaps do not share the same electronic states and do not merge on the overdoped side. Accordingly, our data are suggestive of a two gap scenario with a pseudogap that is likely extrinsic with respect to superconductivity.

Phonon analysis of the S = 1 quantum spin systems Ni(5)Te(4)O(12)X(2) (X = Cl and Br)

We report our investigations of the electrodynamic response of the S = 1 quantum spin systems Ni(5)Te(4)O(12)X(2) (X = Cl and Br), which develop a magnetic ordered state below 30 K. We measure the optical reflectivity over a broad spectral range extending from the far infrared up to the ultraviolet. Besides identifying the electronic interband transitions, we primarily focus our attention on the lattice dynamics, emphasizing the phonon modes spectrum and its temperature dependence. Our findings do not reveal any direct link between possible structural anomalies and the transition into the magnetically ordered state at low temperatures.

Nickel impurity-induced enhancement of the pseudogap of cuprate high-T(c) superconductors

The influence of magnetic Ni and nonmagnetic Zn impurities on the normal-state pseudogap (PG) in the c-axis optical conductivity of (Sm,Nd)Ba(2){Cu(1-y)(Ni,Zn)(y)}(3)O(7-delta) crystals was studied by spectral ellipsometry. We find that these impurities, which strongly suppress superconductivity, have a profoundly different impact on the PG. Zn gives rise to a gradual and inhomogeneous PG suppression while Ni strongly enhances the PG. Our results challenge theories that relate the PG either to precursor superconductivity or to other phases with exotic order parameters, such as flux phase or d-density wave states, that should be suppressed by potential scattering. The apparent difference between magnetic and nonmagnetic impurities instead points towards an important role of magnetic correlations in the PG state.

New Josephson plasma modes in underdoped YBa2Cu3O6.6 induced by a parallel magnetic field

The c-axis reflectivity spectrum of underdoped YBa2Cu3O6.6 (YBCO) is measured below T(c)=59 K in parallel magnetic fields H parallel CuO2 up to 7 T. Upon application of a parallel field, a new peak appears at finite frequency in the optical conductivity at the expense of suppression of c-axis condensate weight. We conclude that the dramatic change originates from different Josephson coupling strengths between bilayers with and without Josephson vortices. We find that the 400 cm(-1) broad conductivity peak in YBCO gains the spectral weight under parallel magnetic field; this indicates that the condensate weight at omega=0 is distributed to this peak as well as to the new optical Josephson mode.

Systematic (63)Cu NQR and (89)Y NMR study of spin dynamics in Y(1-z)Ca(z)Ba(2)Cu(3)O(y) across the superconductor-insulator boundary

We demonstrate that the spin dynamics in underdoped Y(1-z)Ca(z)Ba(2)Cu(3)O(y) for y approximately equal to 6.0 exhibit qualitatively the same behavior to underdoped La(2-x)Sr(x)CuO(4) for an equal amount of hole concentration p = z/2 = x< or =0.11. However, a spin gap appears as more holes are doped into the CuO(2) plane by increasing the oxygen concentration to y approximately equal to 6.5 for a fixed value of Ca concentration z. Our results also suggest that Ca doping causes disorder effects that enhance the low frequency spin fluctuations.

Nesting induced precursor effects: a renormalization group approach

We develop a controlled weak coupling renormalization group (RG) approach to itinerant electrons. Within this formalism we rederive the phase diagram for two-dimensional non-nested systems. We then study how nesting modifies this phase diagram. We show that competition between particle-particle and particle-hole channels leads to the manifestation of an unstable precursor fixed point in the RG flow. This effect should be experimentally measurable, and may be relevant for an explanation of pseudogaps in the high temperature superconductors, as a crossover phenomenon.

Phase transitions in the incoherent lattice fluctuations in YBa2Cu3O(7-delta)

The growing body of experimental evidence for the existence of complex textures of charges and spins in the high-temperature superconductors has drawn attention to the so-called 'stripe-phase' models as a possible basis for the mechanism of superconductivity in these materials. Such observations have until now been restricted to systems where the texture dynamics are slow or suppressed altogether, and do not include the important case of YBa2Cu3O(7-delta). It seems likely that the dynamic behaviour of stripes, which has been suggested to undergo several phase transitions as a function of temperature, should also be reflected in the lattice properties of the host materials, and this forms the motivation for our present experiments. Specifically, we use MeV helium ion channelling, an ultrafast real-space probe of atomic displacements (with sub-picometre resolution), to probe incoherent lattice fluctuations in YBa2Cu3O(7-delta) as a function of temperature and oxygen doping. We detect lattice fluctuations that are larger than the expected thermal vibration component, and which show anomalies characteristic of the phase transitions anticipated for a dynamic stripe phase. Comparison of our lattice results with single-particle-tunnelling and photoemission data highlights the importance of spin-charge separation phenomena in the copper oxide superconductors.

Sum rules and interlayer conductivity of high-Tc cuprates

Analysis of the interlayer infrared conductivity of cuprate high-transition temperature superconductors reveals an anomalously large energy scale extending up to midinfrared frequencies that can be attributed to formation of the superconducting condensate. This unusual effect is observed in a va- riety of materials, including Tl2Ba2CuO6+x, La2-xSrxCuO4, and YBa2Cu3O6.6, which show an incoherent interlayer response in the normal state. Midinfrared range condensation was examined in the context of sum rules that can be formulated for the complex conductivity. One possible interpretation of these experiments is in terms of a kinetic energy change associated with the superconducting transition.