Title Page

Title Page

Indice

Indice

Foreword

Foreword

Gruppo fotografico dei partecipanti al Corso

Gruppo fotografico dei partecipanti al Corso

Sir Nevill Mott-70 years in physics

Sir Nevill Mott-70 years in physics

BCS and Eliashberg theories

BCS and Eliashberg theories

Introduction

Introduction

Model Hamiltonian with an effective electron attraction

Model Hamiltonian with an effective electron attraction

Instability of the normal state and emergence of the order parameter

Instability of the normal state and emergence of the order parameter

BCS wave function and its properties

BCS wave function and its properties

Low-lying excited states and Landau criterion for superfluidity

Low-lying excited states and Landau criterion for superfluidity

Finite-temperature properties and Ginzburg criterion

Finite-temperature properties and Ginzburg criterion

Meissner effect and conserving approximations

Meissner effect and conserving approximations

Eliashberg theory

Eliashberg theory

Precursor pairing correlations and pseudogaps

Precursor pairing correlations and pseudogaps

Introduction

Introduction

Pseudogap experiments

Pseudogap experiments

Survey of scenarios

Survey of scenarios

Pairing correlations above T_c

Pairing correlations above T_c

Pseudogap in s-wave models

Pseudogap in s-wave models

Commonly asked questions

Commonly asked questions

Phase fluctuations and T_c

Phase fluctuations and T_c

Pseudogaps in d-wave models

Pseudogaps in d-wave models

Open questions

Open questions

Conclusions

Conclusions

NMR in high-temperature superconductors

NMR in high-temperature superconductors

Introduction

Introduction

Spin-lattice and spin-spin relaxation, linewidths and lineshifts

Spin-lattice and spin-spin relaxation, linewidths and lineshifts

NMR/NQR in the normal state of high-T_c superconductors

NMR/NQR in the normal state of high-T_c superconductors

NQR/NMR in the superconducting state

NQR/NMR in the superconducting state

NQR and low-field NMR-spin pairing mechanism

NQR and low-field NMR-spin pairing mechanism

NMR and vortices

NMR and vortices

NMR evidence for phase separation and stripe phases

NMR evidence for phase separation and stripe phases

Concluding remarks

Concluding remarks

The Josephson effect: What it is-What it allows

The Josephson effect: What it is-What it allows

Introduction

Introduction

A Josephson effect primer

A Josephson effect primer

High-T_c superconductor junctions counterpart

High-T_c superconductor junctions counterpart

Symmetry of the order parameter and half-flux quantization in unconventional superconductors

Symmetry of the order parameter and half-flux quantization in unconventional superconductors

Heavy fermions

Heavy fermions

High-T_c cuprate superconductors

High-T_c cuprate superconductors

Conclusions

Conclusions

High-T_c superconductors: Insights from angle-resolved photoemission

High-T_c superconductors: Insights from angle-resolved photoemission

Introduction

Introduction

What does ARPES measure?

What does ARPES measure?

Spectral functions and sum rules

Spectral functions and sum rules

Experimental details

Experimental details

Experiments on sum rule and n(k)

Experiments on sum rule and n(k)

ARPES spectra: qualitative features

ARPES spectra: qualitative features

Normal state of optimally doped Bi2212

Normal state of optimally doped Bi2212

Extended saddle point singularity

Extended saddle point singularity

Bilayer splitting?

Bilayer splitting?

Superconducting gap and its anisotropy

Superconducting gap and its anisotropy

Pseudogap in the underdoped materials

Pseudogap in the underdoped materials

Conclusions

Conclusions

Angle-resolved photoemission study of high-temperature superconductors: Insulators, metals and supercondutors

Angle-resolved photoemission study of high-temperature superconductors: Insulators, metals and supercondutors

Angle-resolved photoemission as a tool to probe the electronic structure of novel materials

Angle-resolved photoemission as a tool to probe the electronic structure of novel materials

Doping-dependent electronic structure of cuprate materials

Doping-dependent electronic structure of cuprate materials

Photoemission study of the excitation gaps in the normal and superconducting state of underdoped Bi2Sr2CaCu2O(8+delta)

Photoemission study of the excitation gaps in the normal and superconducting state of underdoped Bi2Sr2CaCu2O(8+delta)

Antiferromagnetism and cuprate superconductivity

Antiferromagnetism and cuprate superconductivity

Models

Models

Mean-field approximation (MFA)

Mean-field approximation (MFA)

Spin wave excitations

Spin wave excitations

Spin fluctuation phase

Spin fluctuation phase

Spin fluctuation approaches

Spin fluctuation approaches

Limitations of the Fermi-liquid spin fluctuation approach

Limitations of the Fermi-liquid spin fluctuation approach

Fluctuation effects in underdoped cuprates

Fluctuation effects in underdoped cuprates

Photoemission spectra: k-, x-, and T-dependence of the normal phase

Photoemission spectra: k-, x-, and T-dependence of the normal phase

Delta-phase fluctuations in underdoped supercondutors

Delta-phase fluctuations in underdoped supercondutors

Delta-amplitude fluctuations

Delta-amplitude fluctuations

Pairing pseudogap

Pairing pseudogap

Conclusion

Conclusion

Strongly correlated models for the cuprate high-T_c superconductors

Strongly correlated models for the cuprate high-T_c superconductors

Introduction

Introduction

Electronic structure of cuprates: introduction of the t-J model

Electronic structure of cuprates: introduction of the t-J model

Properties of the t-J model in two dimensions

Properties of the t-J model in two dimensions

t-J ladders and cuprate ladder compounds

t-J ladders and cuprate ladder compounds

Conclusion

Conclusion

Superconductivity in correlated electron systems

Superconductivity in correlated electron systems

Introduction

Introduction

Acquired knowledge

Acquired knowledge

Two-dimensional systems

Two-dimensional systems

Phase diagram

Phase diagram

Electronic correlations

Electronic correlations

Feature in the density of states (DOS)

Feature in the density of states (DOS)

Symmetry of the condensed phase

Symmetry of the condensed phase

Linear resistivity at optimal doping

Linear resistivity at optimal doping

Controversial points

Controversial points

DOS features

DOS features

Role of the electron-phonon interaction

Role of the electron-phonon interaction

Phase separation

Phase separation

Superconducting phase

Superconducting phase

Pairing mechanism

Pairing mechanism

Theoretical models

Theoretical models

The p-d model

The p-d model

Correlation functions

Correlation functions

Results

Results

Normal-state charge transport properties of high-T_c cuprates

Normal-state charge transport properties of high-T_c cuprates

Introduction

Introduction

Generic phase diagram

Generic phase diagram

Systematic evolution of the temperature-dependent in-plane resistivity with doping

Systematic evolution of the temperature-dependent in-plane resistivity with doping

T-linear resistivity in the optimally doped superconductors

T-linear resistivity in the optimally doped superconductors

Normal-state gap and the in-plane resistivity

Normal-state gap and the in-plane resistivity

The out-of-plane transport

The out-of-plane transport

Anomalous temperature and carrier concentration dependence of the in-plane Hall effect

Anomalous temperature and carrier concentration dependence of the in-plane Hall effect

Summary

Summary

Raman spectroscopy experiments in high-T_c superconductors

Raman spectroscopy experiments in high-T_c superconductors

Introduction to Raman scattering

Introduction to Raman scattering

Vibrations in high-T_c's

Vibrations in high-T_c's

Lattice vibrations in YBa2Cu3O(7-delta) and related compounds

Lattice vibrations in YBa2Cu3O(7-delta) and related compounds

The Bi2Sr2Ca(n-1)Cu(n)O(2n+4) superconductor family

The Bi2Sr2Ca(n-1)Cu(n)O(2n+4) superconductor family

Electron-phonon interaction

Electron-phonon interaction

Self-energy effects in high-T_c's

Self-energy effects in high-T_c's

Above T_c effects

Above T_c effects

Summary

Summary

Experiments on the isotope effect

Experiments on the isotope effect

Introduction

Introduction

The isotope effect in doped cuprate high-T_c superconductors

The isotope effect in doped cuprate high-T_c superconductors

Doped YBa2Cu3O(7-delta)

Doped YBa2Cu3O(7-delta)

The isotope effect in oxygen-deficient YBa2Cu3O(7-delta)

The isotope effect in oxygen-deficient YBa2Cu3O(7-delta)

The isotope effect in La(2-x)Sr(x)CuO4

The isotope effect in La(2-x)Sr(x)CuO4

Discussion

Discussion

Oxygen-deficient YBa2Cu3O(7-delta)

Oxygen-deficient YBa2Cu3O(7-delta)

The La(1-x)Sr(x)CuO4 system

The La(1-x)Sr(x)CuO4 system

The isotope effect in the "Colossal Magneto-Resistance" compounds La(1-x)Ca(x)MnO3

The isotope effect in the "Colossal Magneto-Resistance" compounds La(1-x)Ca(x)MnO3

Conclusion

Conclusion

Bipolarons and high-T_c superconductivity

Bipolarons and high-T_c superconductivity

Introduction: Frohlich polarons

Introduction: Frohlich polarons

Frohlich bipolarons

Frohlich bipolarons

Introduction: history and main concepts

Introduction: history and main concepts

Path-integral treatment

Path-integral treatment

Stability of bipolarons

Stability of bipolarons

Stability of bipolarons in a magnetic field

Stability of bipolarons in a magnetic field

Magnetoabsorption of Frohlich bipolarons

Magnetoabsorption of Frohlich bipolarons

Polarons and the optical spectra of oxides

Polarons and the optical spectra of oxides

Many-polaron systems

Many-polaron systems

Many-polaron-bipolaron systems

Many-polaron-bipolaron systems

Intuitive approach

Intuitive approach

Polaron-bipolaron transitions and electron screening effects

Polaron-bipolaron transitions and electron screening effects

Bipolarons and high-T_c superconductivity

Bipolarons and high-T_c superconductivity

Appendix A - A note on the thermodynamics of an interacting Bose gas

Appendix A - A note on the thermodynamics of an interacting Bose gas

Polaronic and bipolaronic high-T_c superconductivity

Polaronic and bipolaronic high-T_c superconductivity

Introduction

Introduction

Bloch states and correlations in doped semiconductors

Bloch states and correlations in doped semiconductors

Effective mass approximation

Effective mass approximation

Tight-binding approximation and the generic Hamiltonian

Tight-binding approximation and the generic Hamiltonian

The multi-polaron problem

The multi-polaron problem

Small-polaron instability within the Migdal approach

Small-polaron instability within the Migdal approach

Exact solution of the multi-polaron problem for lambda to infinity

Exact solution of the multi-polaron problem for lambda to infinity

Polaron band

Polaron band

Electron Green's function and ARPES of polaronic systems

Electron Green's function and ARPES of polaronic systems

Polaronic and bipolaronic superconductivity

Polaronic and bipolaronic superconductivity

Cooper pairing of nonadiabatic carriers

Cooper pairing of nonadiabatic carriers

High-T_c polaronic superconductivity

High-T_c polaronic superconductivity

Coherent tunneling and repulsion of bipolarons

Coherent tunneling and repulsion of bipolarons

Bipolaron anisotropic flat bands in high-T_c copper oxides

Bipolaron anisotropic flat bands in high-T_c copper oxides

Pseudospin representation of the bipolaronic Hamiltonian

Pseudospin representation of the bipolaronic Hamiltonian

Superfluid vs. charged ordered ground state

Superfluid vs. charged ordered ground state

Excitation spectrum of the bipolaronic liquid

Excitation spectrum of the bipolaronic liquid

T-n phase diagram of the bipolaronic liquid

T-n phase diagram of the bipolaronic liquid

Bipolaron theory of high-T_c cuprates

Bipolaron theory of high-T_c cuprates

Hall density and the "boomerang" behavior of T_c with doping

Hall density and the "boomerang" behavior of T_c with doping

Temperature dependence of the Hall effect and the in-plane resistivity

Temperature dependence of the Hall effect and the in-plane resistivity

c-axis transport and normal-state gap

c-axis transport and normal-state gap

Violation of Kohler's rule

Violation of Kohler's rule

Thermodynamic vs. resistive transition in a magnetic field

Thermodynamic vs. resistive transition in a magnetic field

Conclusion

Conclusion

Infrared polaronic bands in cuprates and related perovskites

Infrared polaronic bands in cuprates and related perovskites

Introduction

Introduction

Optical conductivity of charges strongly coupled to a polar lattice

Optical conductivity of charges strongly coupled to a polar lattice

Charge density waves and polaron ordering

Charge density waves and polaron ordering

Modeling the optical conductivity of itinerant polarons

Modeling the optical conductivity of itinerant polarons

The small-polaron model

The small-polaron model

The large-polaron model

The large-polaron model

The Infrared Active Vibrations

The Infrared Active Vibrations

Fano lineshapes in the cuprates

Fano lineshapes in the cuprates

The optical conductivity of high-T_c superconductors in the normal phase

The optical conductivity of high-T_c superconductors in the normal phase

One-component and multi-component models for sigma(w)

One-component and multi-component models for sigma(w)

The polaron d-band at intermediate doping

The polaron d-band at intermediate doping

Polaron bands in CuO2 infinite-layer films

Polaron bands in CuO2 infinite-layer films

Polaron bands in the metallic phase of cuprates

Polaron bands in the metallic phase of cuprates

Conclusion

Conclusion

Large polarons and high-T_c superconductivity

Large polarons and high-T_c superconductivity

Introduction

Introduction

Frohlich polaron formation

Frohlich polaron formation

Screening effects in Frohlich polarons

Screening effects in Frohlich polarons

Screening and narrow-band effects in Frohlich polarons

Screening and narrow-band effects in Frohlich polarons

Many-body RPA approach to the polaron formation

Many-body RPA approach to the polaron formation

Infrared absorbtion spectra in high-T_c superconductors and large polarons

Infrared absorbtion spectra in high-T_c superconductors and large polarons

Large-bipolaron formation

Large-bipolaron formation

The boson-fermion model of superconductivity

The boson-fermion model of superconductivity

Conclusions

Conclusions

Small polarons

Small polarons

Introduction

Introduction

The model

The model

Internal structure of small polarons and their quasi-particle properties

Internal structure of small polarons and their quasi-particle properties

Correlated charge-deformation dynamics

Correlated charge-deformation dynamics

Summary

Summary

From localized to itinerant bi-polarons in high-T_c superconductors

From localized to itinerant bi-polarons in high-T_c superconductors

Introduction

Introduction

The boson-fermion model

The boson-fermion model

The pseudogap in high-To superconductors

The pseudogap in high-To superconductors

Various manifestations of the pseudogap

Various manifestations of the pseudogap

Discussion

Discussion

Superconducting and normal-state effects due to the breakdown of Migdal's theorem

Superconducting and normal-state effects due to the breakdown of Migdal's theorem

Introduction

Introduction

Migdal's theorem

Migdal's theorem

The vertex function

The vertex function

Electron mass isotope effects

Electron mass isotope effects

Small polaron

Small polaron

Vertex correction

Vertex correction

van Hove singularity

van Hove singularity

Conclusions and perspectives

Conclusions and perspectives

Vortex physics for superconductors from a two-dimensional perspective

Vortex physics for superconductors from a two-dimensional perspective

Introduction

Introduction

Vortices

Vortices

Coulomb gas model

Coulomb gas model

XY-model

XY-model

Properties of the Coulomb gas model

Properties of the Coulomb gas model

Charge unbinding transition

Charge unbinding transition

Dynamics

Dynamics

Non-linear I-V exponent

Non-linear I-V exponent

Comparison with experiments

Comparison with experiments

Coulomb gas scaling

Coulomb gas scaling

Complex impedance

Complex impedance

I-V characteristics

I-V characteristics

Anisotropic 3D XY-model

Anisotropic 3D XY-model

Plane decoupling

Plane decoupling

Non-linear I-V and critical current

Non-linear I-V and critical current

Comparison with experiments

Comparison with experiments

Anisotropic 3D XY-model in a magnetic field

Anisotropic 3D XY-model in a magnetic field

Concluding remarks

Concluding remarks

Elenco dei partecipanti

Elenco dei partecipanti