G
Tutorial on High-Temperature Superconductivity

High-temperature superconductor materials and low-temperature superconductor materials differ markedly in charge response, as measured by transport and optical experiments; spin response, as indicated by static susceptibility, NMR, and inelastic neutron scattering experiments; and in single-particle spectral density, as evidenced by angle-resolved photoemission studies (ARPES).

The basic observations that appear to be crucial for understanding the mechanism of high-temperature superconductivity can be summarized as follows.

  • The action occurs primarily in the Cu-O planes, so that it suffices, in first approximation, to focus both experimental and theoretical attention on the behavior of their planar excitations and to focus as well on the two best-studied systems, the 1-2-3 system (YBa2Cu3O7-x) and the 2-1-4 system (La2-xSrxCuO4).

  • At zero doping and low temperature, both of the systems (YBa2Cu3O7-x and La2-xSrxCuO4) are antiferromagnetic (AF) insulators with an array of localized Cu2+ spins that alternate in sign throughout the lattice.

  • Holes may be injected into the Cu-O planes of the 1-2-3 system by adding oxygen; for the 2-1-4 system, strontium can be added. The resulting holes on the planar oxygen sites bond with the nearby Cu2+ spins, making it possible for the other Cu2+ spins to move and, in the process, destroying the long-range AF correlations found in the insulator.



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Opportunities in High Magnetic Field Science G Tutorial on High-Temperature Superconductivity High-temperature superconductor materials and low-temperature superconductor materials differ markedly in charge response, as measured by transport and optical experiments; spin response, as indicated by static susceptibility, NMR, and inelastic neutron scattering experiments; and in single-particle spectral density, as evidenced by angle-resolved photoemission studies (ARPES). The basic observations that appear to be crucial for understanding the mechanism of high-temperature superconductivity can be summarized as follows. The action occurs primarily in the Cu-O planes, so that it suffices, in first approximation, to focus both experimental and theoretical attention on the behavior of their planar excitations and to focus as well on the two best-studied systems, the 1-2-3 system (YBa2Cu3O7-x) and the 2-1-4 system (La2-xSrxCuO4). At zero doping and low temperature, both of the systems (YBa2Cu3O7-x and La2-xSrxCuO4) are antiferromagnetic (AF) insulators with an array of localized Cu2+ spins that alternate in sign throughout the lattice. Holes may be injected into the Cu-O planes of the 1-2-3 system by adding oxygen; for the 2-1-4 system, strontium can be added. The resulting holes on the planar oxygen sites bond with the nearby Cu2+ spins, making it possible for the other Cu2+ spins to move and, in the process, destroying the long-range AF correlations found in the insulator.

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Opportunities in High Magnetic Field Science If one adds sufficient holes, the system changes its ground state from an insulator to a superconductor. In the normal state of these superconducting materials, the itinerant, but nearly localized, Cu2+ spins form an unconventional Fermi liquid, with its quasi-particle spins displaying strong AF correlations even for systems at doping levels greater than those at which Tc is maximum—so-called “overdoped” materials. Measurements of HTS electronic properties in magnetic fields will be the key component of the experimental work that must be done before a full understanding of the HTS phenomenon will be attained. The main issues that can be addressed this way include these: Effects dependent on the quantization of electron states in high magnetic fields and so-called quantum oscillations (QO), of which two kinds can be distinguished: (1) oscillations of magnetic susceptibility (de Haas-van Alphen effect (dHvA)) and (2) oscillations of conductivity (Shubnikov-de Haas effect) and Cyclotron resonance (CR). For CR effects to be observed, ωcτ >> 1, where ωc is the cyclotron frequency and τ is the electron relaxation time. The maximum value of τ at Tc in optimally doped YBaCuO (Tc ≈ 92 K) is 10−13 s, and it drops by factor of 2-3 at room temperature. In order to observe CR or QO, the material must be in the normal state; for a typical ωc of ~1014 s−1, one needs T > 90 K and H > 500 T. Even higher fields may be necessary if the effective mass of the carriers in the material is greater than that of a free electron, and this explains why preliminary dHvA measurements made on optimally doped YBaCuO at H < 250 T did not give conclusive results. Superfluid density, ρs, in HTS materials is a key quantity that speaks to the nature of high-temperature superconductivity, and it can be studied using high magnetic fields. At zero temperature, ρs is a direct measure of the electronic states that participate in superconductivity, and at low temperatures, it probes low-lying, quasi-particle states, reflecting the symmetry of the order parameter. At intermediate temperatures, the superfluid density follows the temperature behavior of the order parameter and can reveal normal-state anomalies below Tc. Superfluid densities are obtained from measurements of the London penetration depth. Optical experiments combined with DC transport, AC penetration depth, and tunneling measurements will be instrumental in answering these long-standing questions about the nature of high-temperature superconductivity.

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Opportunities in High Magnetic Field Science An interesting feature of cuprate superconductors is that despite general condensate formation, not all carriers appear to participate in superconductivity. A considerable fraction of the carriers’ energy spectral weight does not condense.1 In optimally doped HTS materials, only a modest fraction (~1/5) of the spectral weight condenses, and even less condenses in under-doped cuprates. In this regard, HTS materials are very different from clean metallic superconductors, in which essentially every carrier pairs up and participates in superconductivity. In general, superfluid density arises from the condensation of the spectral weight from the broad interval of frequencies into a delta function at zero frequency. Thus, the study of superfluid densities in HTS materials may help reveal the nature of this puzzling behavior. The study of the effects of magnetic fields on superfluid density will thus be one of the central directions of HTS experimental studies in the years to come. Furthermore, the behavior of ρs as a function of temperature in high magnetic fields needs to be explored. Penetration depth measurements at frequencies between the kilohertz and terahertz regimes indicate a significant reduction in superfluid density in modest magnetic fields. Optical studies should be undertaken of underdoped as well as overdoped materials. Another important direction is the study of the superconductor-insulator transition at high magnetic fields by observing the shift of the spectral weight from low to high frequencies as a superconducting or normal state appears in the excitation spectrum. The behavior of ρs at zero temperature as a function of doping could also shed new light on the possible non-Fermi liquid nature of HTS materials. In the underdoped region, ρs increases with the doping parameter x (as in -O7-x) and is approximately proportional to increases in Tc. In the overdoped region, at first ρs increases with x beyond the optimal hole concentration despite the reduction in Tc, and then there is a final and abrupt decrease in ρs even if the hole concentration continues to increase. One can thus think of the following objectives for further research: To understand why both YBCO and BSCCO have superfluid densities ρs at zero temperature five times smaller than expected from general Bardeen-Cooper-Schrieffer (BCS) considerations, and yet why at the same time the ratio ρs(T)/ρs(0) agrees with BCS predictions. 1   In these materials, the carriers’ energies are distributed across an energy spectrum. Experiments have shown that carriers of certain energies do not condense and so do not participate in superconductivity.

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Opportunities in High Magnetic Field Science To provide conclusive evidence that over-doped cuprates are not classic Fermi liquids, and to resolve the question of whether there is a quantum critical point at zero temperature in the superconducting domain. To explore the differences between the electron- and hole-doped materials and whether the distinctions between them in d-wave pairing behavior hold in the superconducting state. The effect of magnetic fields perpendicular to Cu-O planes is also of great interest. Vortex arrays that form in a superconducting domain govern the magnetic and transport properties (see Appendix H). The quasi particles that appear near the nodes of the d-wave gap may make an essential contribution to the dynamic properties of these vortices. Measurements of optical conductivity in magnetic fields under different doping conditions will be critical to uncovering these quasi-particle effects. At the same time parallel (to the CuO planes) field studies could break new ground in cuprates. Indeed, one expects that in very thin films, the Zeeman energy will be sufficient to split low-lying “spin-up” and “spin-down” quasi particles. Thus, a portion of the Fermi surface near the nodes of the energy gap will become normal, even at 0 K, and this effect will be detectable because of the corresponding reduction in ρs(0). This state indeed would be a novel superconducting one.