Advances in Theoretical and Experimental Research of High Temperature Cuprate Superconductivity

The following sections are included:

• Contents
• Preface

High-temperature superconductors were discovered by J. G. Bendnorz and K. A. Müller in 1986. Before the discovery of high-temperature superconductivity in copper oxide perovskites, the transition temperature had increased from 4 K to 22–23 K when Kammerlingh Onnes first observed superconductivity in mercury in 1911. But since the Ba–La–Cu–O system at 40 K, discovered by Bednorz and Müller, the transition temperature has increased to 163 K in the Hg–Ba–Ca–Cu–O system under pressure in a very short time, which is several times higher than that considered before. Recently, an iron-based superconductor with T_C higher than 50 K has become the superconductor with the highest transition temperature, except for cuprates. The superconducting transition temperature and the discovery time are shown in Fig. 1.1…

A high-T_C superconducting phase diagram should always be at the center of studies on the superconducting mechanism. In this chapter, a complement of phase diagram will be created and a discussion about the abnormal knowledge which phase diagram tells us…

The following sections are included:

• Introduction
• An Introduction about Optical Properties of Solids
• Optical Properties of High-T_C Superconductors
• Whether the Superconducting Energy Gap Can be Observed in the In-Plane Infrared Measurement
• References

This chapter reviews results and insights on high-T_C superconductors from the nuclear magnetic resonance (NMR) technique, with emphasis on local hole density, d-wave superconducting gap and its consequences, and the nature of the pseudogap. In addition to the total hole density in the CuO₂ plane, the partition of the holes between Cu and O orbits is an important factor in determining T_C. The temperature dependence of the spin-lattice relaxation rate and the Knight shift indicate d-wave pairing, which brings about the extended quasi-particle states outside the vortex cores. The existence of nodes in the gap function also results in strong T_C reduction by non-magnetic impurity or crystal disorder. The zero-temperature normal state has been revealed by the application of strong magnetic fields up to 45 T to be a metallic state with finite density of states (DOS) at the Fermi level, which suggests that the pseudogap and the superconducting states are coexisting states of matter. The residual DOS remains quite large even in the vicinity of the Mott insulating phase.

The following sections are included:

• Introduction to Angle-Resolved Photoemission Spectroscopy
• Angle-Resolved Photoemission Spectroscopy Studies of Many-Body Effects in High-T_C Superconductors
  • The First Observation of Many-Body Effects in High-T_C Superconductors — Nodal Direction
  • The Origin of the 70 meV “Kink” Structure
  • Non-Traditional Electron–Phonon Coupling
  • Extracting the Boson Spectral Function from the ARPES Experimental Results
  • Many-Body Effects in Anti-Nodal Direction
  • The Possible and New Electronic Coupling Modes in High-T_C Superconductors
• References

The following sections are included:

• The Application of ARPES in the High-Temperature Superconductivity
• Superconducting Gap, Pseudogap and Two-Gap Problems
• Pseudogap
• Time-Reversal Symmetry Breaking
• References

In this chapter, we review the recent progress in the study of high-temperature superconductors using scanning tunneling microscopy (STM). We begin with a brief introduction to the principle of STM, and then describe various novel phenomena observed by STM in high-temperature superconductors and discuss the physics therein. These include the impurity resonance state, the electronic structure of vortex core, the energy gap inhomogeneity, the quasi-particle scattering interference, the density waves, the energy gap closing versus temperature and the coupling to bosonic modes. Open questions and challenges are also presented in the discussions.

Tunneling studies of Bi₂Sr₂CaCu₂O_8+δ (Bi2212) cuprate superconductors using submicron intrinsic Josephson junctions (IJJs) are reviewed. We begin with a brief overview of the early tunneling studies of BCS conventional superconductors and the recent experiments on the Bi2212 superconductors using the scanning tunneling microscope (STM), break junctions (BJs) and the IJJs techniques. This is followed by an introduction to the IJJs fabrication process and the elimination of IJJs self-heating through surface–layer contact improvement and IJJs size reduction to the submicron level. The resulting temperature- and magnetic-field-dependent tunneling spectra from the submicron IJJs are then described and discussed, in particular with respect to the possible superconducting pairing glue mechanism, the formation of Fermi arcs in the nodal region and the relationship between the cuprate pseudogap and the superconducting gap. Comparisons of these results with the STM, BJs, micron-sized IJJs, angle-resolved photoemission spectroscopy and optical experiments are also presented.

The following sections are included:

• Magnetic Structure and Phase Diagram
• Resistivity and Hall Coefficient
• Charge Confinement and c-Axis Transport
• Pseudogap and Resistivity
• Transport Properties under High Magnetic Field
• The Transport Properties of the Underdoped Samples
• References

The following sections are included:

• Introduction to Nernst Effect
• High-T_C Superconductor Phase Diagram and Pseudogap State
  • Electronic Phase Diagram
  • Pseudogap
• Nernst Effect of Hole-Doped High-T_C Superconductor
  • Vortex Nernst Signal Above T_C
  • Upper Critical Field H_C2
  • 2D Nature of Vortex Excitations Above T_C
  • Superconducting Phase Fluctuations Picture
    • Conventional fluctuations theory
    • Strong phase fluctuation theory (preformed pair theory)
    • Resonance valence bond (RVB) theory
• Nernst Effect in Electron-Doped High-T_C Superconductors
• Further Experimental Evidence of Superconducting Phase Fluctuation Picture: Magnetic Susceptibility Measured by Torque Technique
• Conclusions
• Acknowledgments
• References

It has been more than 20 years since the cuprate high-temperature superconductors (HTSC) were discovered. The various physical properties of the normal state and the superconducting state have been studied in great detail. The nature and transport behaviors of the low-energy quasi-particle (QP) in the superconducting state are undoubtedly important to explore the unconventional superconducting electronic states and the mechanism of superconductivity. In addition to the common techniques, such as the angle-resolved photoemission spectroscopy (ARPES), the penetration depth, the AC electrical conductivity and so on, the very low-temperature thermal conductivity κ also plays a very important role. Many experimental developments on heat transport have been made in the past ten years, but meanwhile more and more problems emerged in this field. In this chapter, we mainly introduce the developments and controversies of the very low-temperature thermal conductivity in HTSC.

High-temperature superconductivity is one of the most fascinating and challenging areas of condensed matter physics. In the past two decades, a huge number of theoretical and experimental studies have been contributed to the field and many crucial progresses have been made. Raman scattering has been extensively applied to high-T_C superconductors owing to its unique abilities to probe multiple primary excitations and symmetry selection rules. In this chapter, we present a brief review on Raman scattering experimental achievements in cuprate superconductors, with emphasis on pairing mechanism-related aspects such as electron–phonon coupling, pair-breaking peak and two-magnon, etc. We will also address some open questions.

Among various experimental tools employed in the research of high-T_C superconductivity, low-temperature specific heat has the merit of probing the low-energy quasi-particle excitations and reflecting the bulk property of the sample. In this chapter, we first provide a brief description of the related background of specific heat studies in high-T_C cuprates and then summarize the recent experimental results in La_2−xSr_xCuO₄ and Bi₂Sr_2−yLa_yCuO_6+δ single crystals. Calorimetric evidences for d-wave symmetry of the order parameter throughout the phase diagram, an anomalous doping dependence of the superconducting gap, an intimate relationship between the pseudogap and superconductivity, and a “Fermi arc” ground state in the underdoped regime are discussed. A picture of the superconducting condensation is also proposed and applied to account for the doping evolution of some basic superconducting properties shown in the phase diagram.

In this chapter, we mainly address a number of numerical and analytical advances on 2D Hubbard and t−J models as well as the relevant physical findings related to high-temperature superconductivity in the past 20 years. The gossamer superconductor model and its progress are also mentioned. The possible connections with the recently discovered iron-based superconductors are discussed as well. Finally, my personal understanding and reflection on the high-temperature superconducting theory are briefly described.

The following sections are included:

• Introduction
• The Method
• Overview
• Conclusion
• Postscript
• References

The parent compound of high-T_C superconductors is an anti-ferromagnetic insulator. Upon doping, the long-range anti-ferromagnetic order is suppressed and the compound becomes superconducting. The phase diagrams for the electron-doped and hole-doped are different. Based on a detailed analysis of electronic structures and experimental data, we propose that the electron-doped high-T_C superconductors are described by a two-band model. This model provides a natural account for the experimental data and suggests that the superconducting pairing of electron-doped high-T_C superconductors has the d_x²−y²-wave symmetry.

High-T_C superconductivity is realized by doping the antiferromagnetic Mott insulators, so that its superconducting phase is in proximity to the antiferromagnetic phase. Therefore, the understanding of the spin dynamics in high-T_C cuprates is considered to be essential to uncover the superconducting mechanism in these materials. Here, we will first give a brief review of the experimental results and then the theoretical understandings.

We present a review of the slave-boson mean-field theory and the related effective gauge-field theory of the RVB state and its application in the mechanism of high-temperature superconductivity. We also introduce the recent progress in RVB theory made possible by the combination of the effective-field theory approach and the variational approach based on Gutzwiller projected wave functions.

The strong correlation of electrons such as the magnetic ordering in transition metal oxides and the Kondo resonance in dilute magnetic compounds rising from the local exchange interactions were well-understood many-body effects in the past decades. The superconducting cuprate discovered in 1986 inspired a fascinating idea: the magnetic origin of superfluid. We speculate that the fluctuating spins on the oxygen sites in the CuO₂ layer created by the holes may pair into a resonating valence bond state with the quantum number S = 1, S_z = 0 via local exchange interactions, the same force responsible for magnetic ordering in the low-doped cuprate. Impurity doping drives the cuprate from an anti-ferromagnetic insulator to a superconductor, then a Fermi liquid, resulting in a rich phase diagram…

We review current progress in the neutron scattering studies of magnetic excitations in high-transition temperature (high-T_C) copper oxide superconductors. Since its discovery 20 years ago, understanding the microscopic origin of superconductivity in these copper oxides has been the “holy-grail” in condensed matter physics. In contrast to conventional superconductors, where the interaction that pairs the electrons to form the superconducting state is mediated by lattice vibrations (phonons), it is generally believed that magnetic excitations might play a fundamental role in the superconducting mechanism of copper oxides because superconductivity occurs when mobile “electrons” or “holes” are doped into the anti-ferromagnetic parent compounds. In this chapter, we summarize the key results on the magnetic excitations obtained by inelastic neutron scattering over the past 20 years. We discuss the status of the field and point out possible future directions.

The following sections are included:

• A Letter to the High-Temperature Superconducting Colleagues
• Conference Summary