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Strong-Coupling Theory of High-Temperature Superconductivity

Book Description

High-temperature superconductivity has transformed the landscape of solid state science, leading to the discovery of new classes of materials, states of matter, and concepts. However, despite being over a quarter of a century since its discovery, there is still no single accepted theory to explain its origin. This book presents one approach, the strong-coupling or bipolaron theory, which proposes that high-temperature superconductivity originates from competing Coulomb and electron-phonon interactions. The author provides a thorough overview of the theory, describing numerous experimental observations, and giving detailed mathematical derivations of key theoretical findings at an accessible level. Applications of the theory to existing high-temperature superconductors are discussed, as well as possibilities of liquid superconductors and higher critical temperatures. Alternative theories are also examined to provide a balanced and informative perspective. This monograph will appeal to advanced researchers and academics in the fields of condensed matter physics and quantum-field theories.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Table of Contents
  6. Preface
  7. 1 Coulomb and Fröhlich interactions
    1. 1.1 Bare Hamiltonian
    2. 1.2 Harmonic approximation
    3. 1.3 Generic Hamiltonian in the Wannier representation
    4. 1.4 Fröhlich EPI in doped polar insulators
  8. 2 Small polarons
    1. 2.1 Canonical transformations
    2. 2.2 Lang–Firsov canonical transformation
    3. 2.3 Ideal gas of small polarons
    4. 2.4 Mobile small-Fröhlich polaron
    5. 2.5 Polaron spectral function
  9. 3 Inverse-coupling expansion technique
    1. 3.1 Polaron self-energy
    2. 3.2 Phonon self-energy
    3. 3.3 Attraction between polarons
  10. 4 High-temperature superconductivity
    1. 4.1 Weak-coupling regime
    2. 4.2 Strong-coupling regime: Polaronic t-Jp model
    3. 4.3 Superlight small bipolarons in the t-Jp model
    4. 4.4 Interplane tunnelling of bipolarons and giant mass anisotropy
    5. 4.5 High Tc
    6. 4.6 Residual polaron–polaron repulsion and BEC to BCS crossover
  11. 5 Converting boson–fermion mixtures
    1. 5.1 Charged bosons mixed with fermions
    2. 5.2 Pseudogap and superconducting gap
    3. 5.3 Mobile fermions hybridized with immobile negative U centres
      1. 5.3.1 Absence of the BCS–BEC crossover in the BFM
      2. 5.3.2 3D BFM: Pairing of bosons
  12. 6 Superconductivity from repulsion: Theoretical constraints
    1. 6.1 Motivation
    2. 6.2 Kohn–Luttinger effect from the screened Coulomb repulsion
    3. 6.3 Pairing of 2D-repulsive fermions on a lattice
    4. 6.4 Superconductivity from strong Hubbard repulsion
  13. 7 Theory and experiment: Confirmed predictions
    1. 7.1 Unconventional-upper critical field
    2. 7.2 Unconventional isotope effects, pseudogap and high Tc
      1. 7.2.1 Different isotope effects on the critical temperature and the London penetration depth
      2. 7.2.2 Quantitative explanation of isotope effects, Tc and the magnetic field penetration depth
    3. 7.3 Unconventional Lorenz number: Double-charged carriers
  14. 8 Experiments explained: Normal state
    1. 8.1 Normal state in-plane kinetics and magnetic spin susceptibility
    2. 8.2 C-axis resistivity
    3. 8.3 Normal-state orbital magnetoresistance
    4. 8.4 Nuclear-magnetic relaxation rate
    5. 8.5 Orbital diamagnetism and Nernst effect
    6. 8.6 Mid-infrared absorption
    7. 8.7 Angle-resolved photoemission and quantum oscillations
  15. 9 Experiments explained: Superconducting state
    1. 9.1 Specific heat anomaly
    2. 9.2 Unconventional symmetry of the order parameter
      1. 9.2.1 Unconventional Cooper pairs glued by conventional phonons
      2. 9.2.2 Strong coupling: d-wave Bose condensate
    3. 9.3 Doping dependence of Tc and the penetration depth
      1. 9.3.1 Screening of EPI and BEC–BCS crossover at overdoping
      2. 9.3.2 Boomerang effect and boson–fermion mixture at overdoping
    4. 9.4 BEC signatures in the optical sum rule
    5. 9.5 Giant and nil proximity effects in cuprate superconductors
    6. 9.6 NS and SS tunnelling: Pseudogap and superconducting gap
      1. 9.6.1 Cuprate band structures
      2. 9.6.2 NS tunnelling
      3. 9.6.3 SS tunnelling
  16. 10 Further predictions
    1. 10.1 Magnetic pair breaking and colossal magnetoresistance
    2. 10.2 Feasibility of a liquid superconductor
    3. 10.3 Route to room-temperature superconductivity
  17. References
  18. Index