Title Page

Indice

Preface

Gruppo fotografico dei partecipanti al Corso

Introduction to polaron physics: Basic concepts and models

Introduction

The Frohlich large polaron

Polarons in ionic crystals

Polarons in non-polar covalent materials

Polarons in metals

The Holstein small polaron

Self-trapping

Some early experimental insights

Bipolaron dissociation and recombination in WO 3-x

Photoinduced polaronic charge carriers in high-Tc cuprates

Bipolaronic charge ordering in Ti4O7

Summary

Frohlich polarons from 3D to 0D: Concepts and recent developments

The polaron concept

The Frohlich Hamiltonian

The structure of the polaron excitation spectrum and optical absorption by polarons

Optical absorption at weak coupling

Optical absorption at strong coupling

Optical absorption of continuum polarons at arbitrary coupling

Sum rules for the optical conductivity spectra

Scaling relations for Frohlich polarons

Check of the scaling relation for the path-integral Monte Carlo results for the polaron free energy

Magnetoabsorption spectra of polarons

Many-polaron systems

Ground state and the optical absorption spectra of many-polaron systems

Many-polaron cyclotron resonance in quantum wells

Interacting polarons in a quantum dot

Appendix. On the contributions of the N-phonon states to the polaron ground state

Effects of strong charge-lattice coupling on the optical conductivity of transition metal oxides

Introduction

Large-polaron absorption in high-Tc cuprates

Small-polaron absorption in nickelates

Jahn-Teller and Hund's effects on the optical conductivity of manganites

Fano resonances in cobaltates and cuprates

Infrared signatures of charge ordering in transition metal oxides

Conclusion

On the local lattice displacements in the correlated transition metal oxides

Introduction

EXAFS as a probe of local lattice displacements

Local lattice displacements in the copper oxide superconductors

Local Cu-O displacements as a function of doping

Critical role of Cu-O displacements

Characteristic Cu-O displacements in the copper oxides

Mn-O displacements in the charge-ordered and CMR manganese oxides

Large local displacements in the charge-ordered nickel oxides

Concluding remarks

Polarons in complex oxides: CMR manganites and HTSC cuprates

Introduction

Polarons in CMR manganites

Observation of spin-lattice polarons in manganites by neutron scattering and the percolative nature of metal-insulator transition

Ionic size effect

Phonons and nanoscale phase separation in the cuprates

Electron-phonon interaction in HTSC cuprates

Dynamic polarons in HTSC cuprates

ARPES observations

Two-component model

Conclusions

Variational approaches to polarons

Introduction

Models for e-ph coupling models

A variational method for the Frohlich model

A variational method for the Holstein model

Coherent state basis for the Holstein model

Conclusions

Polarons and bipolarons in Holstein and Holstein t-J models by dynamical mean-field theory

Introduction

The DMFT method

Introduction

Single-impurity action

Single-impurity Hamiltonian

Holstein model in infinte dimensions

DMFT-QMC method

DMFT-ED method

Quantities of interest

Single electron in Holstein and Holstein t-J models

T = 0 continued fraction for a single polaron

Holstein t-J model in infinite dimensions

Results

Half-filled Holstein model: spinless vs. spinful cases at T = 0

Adiabatic regime

Antiadiabatic regime

Results from DMFT-ED

Half-filled Holstein model: spinless vs. spinful cases at T > 0

Results from DMFT-QMC

Conclusions

Renormalization group approaches to strongly correlated electron-phonon systems

Polarons by exact Diagrammatic Monte Carlo and Stochastic Optimization methods

Introduction

Variety of polaron conceptions

Basic polaron models

Diagrammatic Monte Carlo and Stochastic Optimization methods for analytic continuation

Formal definitions of quantities giving information about quasi-particles

Diagrammatic Monte Carlo method

Stochastic optimization method for analytic continuation

Comparison of existing methods with the DMC-SO technique

Self-trapping: from simple systems to the high-Tc superconductors

Typical self-trapping phenomenon: the Rashba-Pekar exciton

One-dimensional exciton-polaron: quasidegenerate self-trapping

Spectral function of a hole interacting with phonons in the t-J model

Two-particle objects: exciton

Optical conductivity of the Frohlich polaron

Dynamical localization-delocalization transition in the Hubbard-Holstein model

Introduction

Hubbard-Holstein model

Atomic limit

One-electron Green's function

Three-point vertex function

Two-site system

Infinite-dimensional system

Dynamical mean-field theory

Expansion from the atomic limit

Calculation on the imaginary axis

Calculation on the real axis

Conclusion and discussion

Electron-phonon coupling in the presence of strong correlations

Introduction

The Hubbard-Holstein model in Dynamical Mean-Field Theory

The half-filled Hubbard-Holstein model close to the Mott transition

The effect of doping and the phase separation instability

Phase separation instability

A simpler approach: Slave-boson mean-field and variational Lang-Firsov

Conclusions

Exact numerical methods for electron-phonon problems

Introduction

Models

Methods

Exact diagonalization approach

Many-body Hilbert space and basis construction

Basis symmetrization

Phonon Hilbert space truncation

Variational ED method

Solving the eigenvalue problem

Lanczos diagonalization

Implementation of matrix vector multiplication

Algorithms for estimating spectral functions

Lanczos recursion method

Kernel polynomial method

Cluster perturbation theory (CPT)

Density matrix renormalization group approach

Renormalization group and density matrix

DMRG algorithms

Truncation errors

Methods for electron-phonon systems

Pseudo-site method

Optimal phonon basis

Dynamical DMRG

Calculation of excited states and dynamical properties

Dynamical correlation functions

Symmetries

Lanczos-DMRG

Correction vector DMRG

Dynamical DMRG method

Variational principle

DDMRG algorithm

Spectrum in the thermodynamic limit

Application to electron-phonon problems

Conclusion

Spectral signatures of Holstein polarons

Fundamentals

Self-trapping phenomenon

Holstein model

Ground-state properties

Photoemission spectra

Phonon spectra

Optical response

Many-polaron problem

Summary and open problems

Quantum phase transitions in one-dimensional electron-phonon systems

Introduction

Luttinger-liquid Peierls-insulator transition

Holstein model of spinless fermions

Luttinger-liquid parameters and charge structure factors

Phase diagram of the Holstein model of spinless fermions

Peierls-insulator Mott-insulator transition

Ground-state properties

Optical response

Photoemission spectra

Many-body excitation gaps

Summary

Localisation vs. self-trapping: Polaron formation in the Anderson-Holstein model

Problem

Modelling

Stochastic Green's function approach

Limiting cases

Anderson model

Holstein model

Infinite dimension

Anderson-Holstein model

Anderson regime

Holstein regime

Conclusions

From Cooper pairs to resonating bipolarons

Introduction

From amplitude to phase fluctuation controlled superconductivity

Weak-coupling adiabatic limit

Strong coupling anti-adiabatic limit

Macroscopic phase-locking in superconductivity

Resonating bipolarons

Local vs. non-local phase coherence in the Boson-Fermion model

Conclusion

Polarization catastrophe at low densities of polarons: From cuprates to metal-ammonia solutions

Introduction

The polarization catastrophe: Herzfeld 1927

The Mott transition: 1961

The role of polarons in the MIT mechanism

The Wigner crystal of polarons

Relevance of the polarization catastrophe scenario in real compounds

Cuprates

Polaron softening

Charge modulations

Metal-ammonia solutions

Other examples

Electron-phonon coupling in strongly correlated materials

Introduction

Sum rules

Phonon self-energy

Electron self-energy

Polarons in undoped cuprates

Adiabatic approximation

Core level case

Side band dispersion

Electron-phonon coupling strength. Undoped cuprates

Conclusions

Infrared absorption in polaronic systems

Introduction

Polaronic mean-field approach and fluctuations

Mean field

Self-energy beyond mean field

Optical conductivity

Charge ordering in 3D systems: phase diagram and optical conductivity

Phase diagram and optical conductivity in manganites

Conclusions

Electron-Phonon interaction in quantum dots: Beyond the independent boson model

Introduction

The model and the transformation

Part I: The two-state model

Solution of the model

Spectral function

Numerical results

Part II: The two-band model

Linear optical response

Numerical results

Summary

Appendix A. Gram-Schmidt orthonormalization

Appendix B. Electron-Hole transformation

Appendix C. Material parameters for a CdSe quantum dot

Thermodynamical and dynamical instabilities in the homogeneous large-polaron gas

Introduction

Instability of the large-polaron gas

Polaron plasmons

Acoustical phonons

Instability in time of the homogeneous polaron gas

Homogeneous polaron gas vs. structured phases

Clusters formation

Formation of the periodic phase

Discussion

Change of local lattice deformations by tuning of pair correlations

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