Pseudogap and Charge Dynamics in CuO2 Planes in YBCO

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

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 response of correlated electron systems

Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b  =  4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b  =  1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T  =  0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].

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.

Pseudogap in cuprates in the loop-current ordered state

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors [Formula: see text], the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the [Formula: see text] directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the 'edge' of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the 'ordered' phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

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.

Electron correlation and charge transfer in superconducting superlattices

We use x-ray spectroscopy to examine the electronic structure of high-temperature superconducting superlattices [(Ba0.9Nd0.10)CuO(2 + delta)]2/[CaCuO2]2. The O 2p density of states reveals the insulating character of the individual component layers and the metallic character of the superlattices. We report the first direct observation of Zhang-Rice singlets in artificial high-temperature superconducting heteroepitaxial structures. The experimental findings in the superlattices and its component layers offer evidence of charge transport from the so-called charge reservoir layer to the superconducting infinite layer. This suggests a strong link between superconductivity and both electron correlation and charge transfer within the superlattices.

Anomalous enhancement of the coupling to the magnetic resonance mode in underdoped Pb-Bi2212

High-resolution angle-resolved photoemission with variable excitation energies is used to disentangle bilayer splitting effects and intrinsic (self-energy) effects in the electronic spectral function near the (pi,0) point of differently doped (Pb,Bi)(2)Sr(2)CaCu(2)O(8+delta). In contrast to overdoped samples, where intrinsic effects at the (pi,0) point are virtually absent, we find in underdoped samples intrinsic effects in the superconducting-state (pi,0) spectra of the antibonding band. This intrinsic effect is present only below the critical temperature and weakens considerably with doping. Our results give strong support for models which involve a strong coupling of electronic excitations with the resonance mode seen in inelastic neutron scattering experiments.

Neutron resonance in the cuprates and its effect on fermionic excitations

We argue that the exciton scenario for the magnetic resonance in the cuprate superconductors yields a small spectral weight of the resonance, in agreement with experiment. We show that the small weight is related to its concentration in a small region of momentum and energy. Despite this, we find that a large fermionic self-energy can indeed be generated by a resonance with such properties, i.e., the scattering from the resonance substantially affects the electronic properties of the cuprates below T(c).

Oxygen isotope effect in the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta)

We have measured the effect of oxygen isotope substitution on the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta). The frequency shift of the transverse optic phonons due to the substitution of 16O by 18O yields an isotope effect of the expected magnitude for copper-oxygen stretching modes with alpha=0.5+/-0.1. The reflectance shoulder at 400-500 cm(-1) shows a much smaller exponent of alpha=0.1+/-0.1 in the normal state and alpha=0.23+/-0.1 in the superconducting state. These observations suggest that the shoulder is of electronic origin and not due to a phonon mode as has been suggested recently.

Differential sum rule for the relaxation rate in the cuprates

Motivated by recent experiments by Basov et al., we study the differential sum rule for the effective scattering rate 1/tau(omega). We show that, in a dirty BCS superconductor, the area under 1/tau(omega) does not change between the normal and the superconducting states. For magnetically mediated pairing, a similar result holds between T<T(c) and T>or=T(c), while, in the pseudogap phase, 1/tau(omega) is just suppressed compared to 1/tau(omega) in the normal state. We argue that this violation of the differential sum rule in the pseudogap phase is due to the absence of the feedback effects from the pairing.

Electromagnetic response of static and fluctuating stripes in cuprate superconductors

Using infrared spectroscopy, we found that changes in the in-plane charge dynamics attributable to static stripe order in La(1.275)Nd(0.6)Sr(0.125)CuO(4) or superconductivity in La(1.875)Sr(0.125)CuO(4) are confined to energies smaller than 100 cm(-1). An absorption peak in the low- omega conductivity of the Nd-doped compound is suggestive of localization effects due to the reduced dimensionality of static charge stripes. Neither superconductivity nor static stripe ordering has a noticeable effect on the depression of the scattering rate at omega<1000 cm(-1) characteristic of the pseudogap state in other classes of moderately doped cuprates.

Absence of a loss of in-plane infrared spectral weight in the pseudogap regime of Bi(2)Sr(2)CaCu(2)O(8+delta)

The ab-plane reflectance of Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212) thin films was measured in the 30-25 000 cm(-1) range for one underdoped ( T(c) = 70 K), and one overdoped sample ( T(c) = 63 K) down to 10 K. We find similar behaviors in the temperature dependence of the normal-state infrared response of both samples. Above T(c), the effective spectral weight, obtained from the integrated conductivity, does not decrease when T decreases, so that no opening of an optical pseudogap is seen. We suggest that these are consequences of the pseudogap opening in the k = (0,pi) direction and of the in-plane infrared conductivity being mostly sensitive to the k = (pi,pi) direction.

Probing superconducting phase fluctuations from the current noise spectrum of pseudogapped metal-superconductor tunnel junctions

We study the current noise spectra of a tunnel junction of a metal with strong pairing phase fluctuation and a superconductor. It is shown that there is a characteristic peak in the noise spectrum at the intrinsic Josephson frequency omega(J) = 2eV when omega(J) is smaller than the pairing gap but larger than the pairing scattering rate. In the presence of an ac voltage, the tunneling current noise shows a series of characteristic peaks with increasing dc voltage. Experimental observation of these peaks will give direct evidence of the pair fluctuation in the normal state of high- T(c) superconductors and the pair decay rate can be estimated from the half width of the peaks.

Pseudogap phase in high- T(c) superconductors

We describe the approach of the superconducting state as a sequence of crossover phenomena. As the temperature is decreased, uncorrelated pairing of the electrons leads to the opening of a pseudogap at T(*)(F). Upon further lowering the temperature those electron pairs acquire well behaved itinerant features at T(*)(B), leading to partial Meissner screening and Drude-type behavior of the optical conductivity. Further decrease of the temperature leads to their condensation and superconductivity at T(c). The analysis is done on the basis of the boson-fermion model in the crossover regime between 2D and 3D.

Coupling strength of charge carriers to spin fluctuations in high-temperature superconductors

In conventional superconductors, the most direct evidence of the mechanism responsible for superconductivity comes from tunnelling experiments, which provide a clear picture of the underlying electron-phonon interactions. As the coherence length in conventional superconductors is large, the tunnelling process probes several atomic layers into the bulk of the material; the observed structure in the current-voltage characteristics at the phonon energies gives, through inversion of the Eliashberg equations, the electron-phonon spectral density alpha2F(omega). The situation is different for the high-temperature copper oxide superconductors, where the coherence length (particularly for c-axis tunnelling) can be very short. Because of this, methods such as optical spectroscopy and neutron scattering provide a better route for investigating the underlying mechanism, as they probe bulk properties. Accurate reflection measurements at infrared wavelengths and precise polarized neutron-scattering data are now available for a variety of the copper oxides, and here we show that the conducting carriers (probed by infrared spectroscopy) are strongly coupled to a resonance structure in the spectrum of spin fluctuations (measured by neutron scattering). The coupling strength inferred from those results is sufficient to account for the high transition temperatures of the copper oxides, highlighting a prominent role for spin fluctuations in driving superconductivity in these materials.