The spectral energy gap is an important signature that defines states of quantum matter: insulators, density waves and superconductors have very different gap structures. The momentum-resolved nature of angle-resolved photoemission spectroscopy (ARPES) makes it a powerful tool to characterize spectral gaps. ARPES has been instrumental in establishing the anisotropic d-wave structure of the superconducting gap in high-transition-temperature (Tc) cuprates, which is different from the conventional isotropic s-wave superconducting gap. Shortly afterwards, ARPES demonstrated that an anomalous gap above Tc, often termed the pseudogap, follows a similar anisotropy. The nature of this poorly understood pseudogap and its relationship with superconductivity has since become the focal point of research in the field. To address this issue, the momentum, temperature, doping and materials dependence of spectral gaps have been extensively examined with significantly improved instrumentation and carefully matched experiments in recent years. This article overviews the current understanding and unresolved issues of the basic phenomenology of gap hierarchy. We show how ARPES has been sensitive to phase transitions, has distinguished between orders having distinct broken electronic symmetries, and has uncovered rich momentum- and temperature-dependent fingerprints reflecting an intertwined and competing relationship between the ordered states and superconductivity that results in multiple phenomenologically distinct ground states inside the superconducting dome. These results provide us with microscopic insights into the cuprate phase diagram. The superconducting energy gap is perhaps the best-known of the spectral gaps in a superconductor, but there are many other types, including density waves and the mysterious pseudogap. This Review Article surveys what angle-resolved photoemission spectroscopy has revealed about the various gaps.

/pdf/energy-gaps-in-high-transition-temperature-cuprate-19y1y1z3i5.pdf

Energy gaps in high-transition-temperature cuprate superconductors

Upon introducing charge carriers into the copper–oxygen sheets of the enigmatic lamellar cuprates, the ground state evolves from an insulator to a superconductor and eventually to a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (ρ ∝ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here, we first demonstrate for the quintessential compound HgBa2CuO4+δ a dramatic switch from linear to purely quadratic (Fermi liquid-like, ρ ∝ T2) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives insight into the p-T phase diagram and reveals the fundamental resistance per copper–oxygen sheet in both linear (ρ☐ = A1☐T) and quadratic (ρ☐ = A2☐T2) regimes, with A1☐ ∝ A2☐ ∝ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insight into the nonuniversal features exhibited by certain compounds.

/pdf/universal-sheet-resistance-and-revised-phase-diagram-of-the-3154i5442p.pdf

Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors

When Bednorz and Müller discovered the superconductivity in a compound La-Ba-Cu-O in 1986, it was considered as a breakthrough in the research of the superconductivity. This leads to the discovery of the other cuprate superconductors, and immediately the transition temperature of the synthesizedmaterials reached to the liquid nitrogen temperature. Today the maximum transition temperature of the cuprate superconductors changes from 35K for La2−xSrxCuO4 to 138K for Hg1−xTlxBa2Ca2Cu3Oy (the highest record under normal pressure, which extends to ∼160K at high pressure) [1]. 2.1 General Properties of Cuprates 2.1.1 Crystal Structure As a common property, all cuprate superconductors have a layered perovskite structure that consists of alternating conducting CuO2 layers and insulating blocking layers that provide charge carriers to the CuO2 layers. Even though this is the general scheme, the numbers of the CuO2 layers are different in different cuprate families. In Fig. 2.1, as an example to 1-, 2-, and 3layer cuprate families had been shown. In this thesis, we worked with double layer YBa2Cu3Oy system, because the additional structures, namely the CuO-chains in this system give some advantage in our measurements by increasing the conductivity along the c-axis. YBa2Cu3Oy is a system, where the charge doping can be adjusted with oxygen annealing. And this material belongs to the hole doped case, where we will show the electronic phase diagram in the next section. In cuprates, it is also possible to create hole doping in the system with substituting positive ions by ions of smaller valence, such as Sr2+ to La3+ sites in La2−xSrxCuO4. Zn-substitution that been used in this study, on the other hand does not alter the doping level. © Springer Japan 2015 E. Uykur, Pseudogap and Precursor Superconductivity Study of Zn doped YBCO, Springer Theses, DOI 10.1007/978-4-431-55510-0_2 5 6 2 High Temperature Cuprate Superconductors Fig. 2.1 Crystal structure of 1 (La2−xSrxCuO4 [2]), 2 (YBa2Cu3Oy [3]), and 3 (Hg1−xTlxBa2Ca2Cu3Oy [1]) layer cuprates

/pdf/high-temperature-cuprate-superconductors-29rc5t9ntb.pdf

High-Temperature Cuprate Superconductors

Charge density modulations have been observed in all families of high–critical temperature (Tc) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa2Cu3O7–δ and Nd1+xBa2–xCu3O7–δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli–electron volts, and pervade a large area of the phase diagram.

Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor.

We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of hole-doped cuprate superconductors. New data for the Nernst coefficient ν(T) of YBa2Cu3Oy (YBCO), La1.8−xEu0.2SrxCuO4 (Eu-LSCO), and La1.6−xNd0.4SrxCuO4 (Nd-LSCO) are presented and compared with previously published data on YBCO, Eu-LSCO, Nd-LSCO, and La2−xSrxCuO4 (LSCO). The temperature Tν at which ν/T deviates from its high-temperature linear behavior is found to coincide with the temperature at which the resistivity ρ(T) deviates from its linear-T dependence, which we take as the definition of the pseudogap temperature T★—in agreement with the temperature at which the antinodal spectral gap detected in angle-resolved photoemission spectroscopy (ARPES) opens. We track T★ as a function of doping and find that it decreases linearly vs p in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low p,T★ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of T★(p) to p=0 yields T★(p→0)≃TN(0), the Neel temperature for the onset of antiferromagnetic order at p=0, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing p,T★(p) extrapolates linearly to zero at p≃pc2, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favor pseudogap formation also favor pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above the critical temperature Tc, as a function of doping, and find that a narrow fluctuation regime tracks Tc, and not T★. This confirms that the pseudogap phase is not a form of precursor superconductivity, and fluctuations in the phase of the superconducting order parameter are not what causes Tc to fall on the underdoped side of the Tc dome.

/pdf/pseudogap-temperature-t-of-cuprate-superconductors-from-the-45x3bmc3sb.pdf

Pseudogap temperature T* of cuprate superconductors from the Nernst effect

Microwave absorption measurements in magnetic fields from 0 up to 16 T were used to determine the temperature range of superconducting fluctuations above the superconducting critical temperature ${T}_{c}$ in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\mathrm{\ensuremath{\delta}}}$. Measurements were performed on deeply underdoped, slightly underdoped, and overdoped single crystals. The temperature range of the superconducting fluctuations above ${T}_{c}$ is determined by an experimental method which is free from arbitrary assumptions about subtracting the nonsuperconducting contributions to the total measured signal and/or theoretical models to extract the unknown parameters. The superconducting fluctuations are detected in the $\mathit{ab}$ plane, and $c$-axis conductivity, by identifying the onset temperature ${T}^{\ensuremath{'}}$. Within the sensitivity of the method, this fluctuation regime is found only within a fairly narrow region above ${T}_{c}$. Its width increases from 7 K in the overdoped sample (${T}_{c}=89 \mathrm{K}$) to, at most, 23 K in the deeply underdoped sample (${T}_{c}=57 \mathrm{K}$), so that ${T}^{\ensuremath{'}}$ falls well below the pseudogap temperature ${T}^{*}$. Implications of these findings are discussed in the context of other experimental probes of superconducting fluctuations in the cuprates.

Temperature range of superconducting fluctuations above T c in YBa 2 Cu 3 O 7-δ single crystals

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Temperature range of superconducting fluctuations above T c in YBa 2 Cu 3 O 7-δ single crystals