Electronic Structure of Strongly Correlated Materials (eBook)

Vladimir Anisimov, Yuri Izyumov (Autoren)

eBook Download: PDF

2010 | 2010
XIII, 291 Seiten
Springer Berlin (Verlag)
978-3-642-04826-5 (ISBN)

Infos

Electronic structure and physical properties of strongly correlated materials containing elements with partially filled 3d, 4d, 4f and 5f electronic shells is analyzed by Dynamical Mean-Field Theory (DMFT). DMFT is the most universal and effective tool used for the theoretical investigation of electronic states with strong correlation effects. In the present book the basics of the method are given and its application to various material classes is shown. The book is aimed at a broad readership: theoretical physicists and experimentalists studying strongly correlated systems. It also serves as a handbook for students and all those who want to be acquainted with fast developing filed of condensed matter physics.

Inhalt

Preface 8
Contents 10
List of Acrnomys 14
1 Introduction 15
1.1 Strongly Correlated Materials 15
1.2 Basic Models in Strongly Correlated Systems Theory 18
1.3 Methods for Models Investigation 20
1.4 Ab-initio Electronic Structure Calculation Methods 21
2 Electronic Structure Calculations in One-Electron Approximation 23
2.1 Density Functional Theory and Electronic Structure Calculations Methods 23
2.1.1 Density Functional Theory 23
2.1.2 Electronic Structure Calculations Methods Based on DFT 25
2.1.3 Breakdown of Local Density Approximation for Strongly Correlated Systems 28
2.1.4 Corrections for Electron–Electron Correlations 29
2.2 Determining Problem Hamiltonian from Density Functional Theory 32
2.2.1 Problem Definition 32
2.2.2 Coulomb Interaction Hamiltonian 33
2.2.3 Double-Counting Problem for Coulomb Interaction 34
2.2.4 Wannier Functions as Coulomb Interaction Hamiltonian Basis 35
2.2.5 Coulomb Parameter U Value from Constrain DFT Calculation 40
2.3 Static Mean-Field Approximation: LDA+U Method 44
2.4 LDA+U Method Applications 47
2.4.1 Mott Insulators: NiO, CoO, and CaCuO2 47
2.4.2 Charge Ordering: Fe3O4 49
2.4.3 Orbital Ordering: KCuF3 52
2.4.4 Orbital and Charge Ordering: Pr0.5Ca0.5MnO3 55
2.4.5 Spin Ordering: CaVnO2n+1 57
3 Hubbard Model in Dynamical Mean-Field Theory 60
3.1 Reducing Lattice Model to Effective Single Impurity Anderson Model 60
3.1.1 Electronic Green Function 60
3.1.2 Single Impurity Anderson Model 62
3.1.3 Basic DMFT Equations 66
3.1.4 DMFT Equations for Bethe Lattice 68
3.1.5 Methods for Solution of Single ImpurityAnderson Model 68
3.2 Quantum Monte Carlo Method as Single Impurity Anderson Model Solver 72
3.2.1 Hirsch–Fye Algorithm 72
3.2.2 Maximum Entropy Method for Spectral Function Calculation 79
3.2.3 QMC for Single Impurity Anderson Model with Orbital Degrees of Freedom 85
3.2.4 Projective Quantum Monte Carlo Method 86
3.2.5 Continuous-Time QMC 89
3.3 Hubbard Model Spectral Function in DMFTApproximation 95
3.3.1 Three Peak Spectral Structure for Half-Filling 95
3.3.2 Metal–Insulator Phase Transition 100
3.4 Hubbard Model with Deviation from Half-Filling 103
3.4.1 Quasiparticle Peak Evolution 103
3.4.2 Phase Diagram for T=0 103
3.4.3 Spin-Polarized Case 107
3.5 Antiferromagnetism 111
3.5.1 DMFT Equations with AntiferromagneticOrder Parameter 111
3.5.2 NRG Method Results for AFM Phase 114
3.6 Superconductivity in Two-Dimensional Hubbard Model 119
3.6.1 DMFT Equations for Superconducting State 119
3.6.2 Coexistence Problem for Superconducting and Antiferromagnetic Order Parameters 122
3.7 Transport Properties and Susceptibility 124
3.7.1 Optical Conductivity 124
3.7.2 Magnetic Susceptibility 127
4 DMFT Extensions 134
4.1 t-J Model as a Hubbard Model Limit 134
4.1.1 Hamiltonian and Green Function 134
4.1.2 DMFT Equations Derivation 136
4.1.3 Reformulation of DMFT Equations 138
4.1.4 Numerical Calculation Results 141
4.2 DMFT Extensions for Nonlocal Coulomb and Exchange Interaction Case 143
4.2.1 Hamiltonian and Green Function for ExtendedModel 143
4.2.2 EDMFT for Homogeneous System 145
4.2.3 EDMFT for the System with Two Sublattices 147
4.2.4 DMFT with Orbital Degeneracy 150
4.2.5 QMC Impurity Solver for the Problem with Orbital Degeneracy 152
4.2.6 Exchange Interactions in QMC 153
4.2.7 Continuous-Time QMC for Two-Orbital Model 154
4.3 Taking into Account Spatial Fluctuations 157
4.3.1 Heuristic Approach to DMFT Extension for Spatial Fluctuations 157
4.3.2 Dynamical Vertex Approximation 161
4.3.3 Pseudogap 164
4.3.4 Dynamical Cluster Method 170
4.4 Generating Functional for Green Functions 174
4.4.1 Baym-Kadanoff Functional 174
4.4.2 Total Energy 175
4.5 DMFT for Systems with Disorder 177
4.5.1 Anderson-Hubbard Model 177
4.5.2 Phase Diagram for Nonmagnetic State 178
4.5.3 Optical Conductivity 182
5 Periodic Anderson Model (PAM) 186
5.1 Early Studies for PAM 186
5.1.1 PAM as a Basic Model for Heavy Fermion Systems 186
5.1.2 Review of Early Analytical Studies for PAM 188
5.1.3 DMFT for PAM 191
5.2 PAM Studies by DMFT Method 193
5.2.1 DMFT(NRG) Results at T=0 193
5.3 Kondo Lattice 199
5.3.1 DMFT for Kondo Lattice 199
5.3.2 Numerical Renorm-Group Method for Single Impurity Kondo Problem Solution 200
5.3.3 Two Energy Scales 202
5.3.4 Photoemission Spectra Calculations by NRGMethod 204
5.3.5 Magnetic Ordering in Kondo Lattice Study by Continuous-Time QMC Method 206
5.4 Ferromagnetic Kondo Lattice 209
5.4.1 DMFT Equations for sd-Model with Classical Spin 209
5.4.2 Analysis of DMFT Equations Solution 211
6 Electronic Structure Calculations for Real Materials by LDA+DMFT Method 215
6.1 Combining Density Functional Theory and Dynamical Mean-Field Theory: LDA+DMFT method 215
6.1.1 Coulomb Interaction 215
6.1.2 Computation of Lattice and Local Green Functions in General Case 216
6.1.3 Total Energy Calculation in LDA+DMFT 218
6.2 Early Transition Metal Oxides: Mott Insulators and Strongly Correlated Metals 219
6.2.1 SrVO3: One Electron in Degenerate d-Band, Strongly Correlated Metal 220
6.2.2 V2O3: Two Electrons in d-Band with Trigonal Crystal-Field Splitting 226
6.2.3 LiV2O4: Heavy Fermion in d-Electron System 230
6.3 Late Transition Metal Oxides: Charge Transfer Insulators 232
6.3.1 NiO: Band Structure for Charge Transfer Insulator 232
6.3.2 MnO: Metal–Insulator Transition with Pressure and d-ion Magnetic Moment Collapse 236
6.4 f-Electron Systems: - Transition in Ce 241
6.5 Manganites 244
6.5.1 Manganites Physical Properties 244
6.5.2 Electronic Model for Manganites 246
6.5.3 QMC for Systems with Electron–Lattice Coupling 247
6.5.4 LDA+DMFT(QMC) Results for La1-xSrxMnO3 251
6.6 High-Tc Superconductors Based on Pnictides Compounds 256
6.7 The List of Strongly Correlated Materials Investigated by DMFT Method 261
7 Conclusion 264
A Functional Integral and Partition Function 267
B Green Functions Formalism 281
References 285
Index 297

Produkt-Details

• Erscheint lt. Verlag: 23.7.2010
• Reihe/Serie: Springer Series in Solid-State Sciences
• Zusatzinfo: XIII, 291 p. 156 illus., 47 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Condensed Matter • Correlation Effects • electronic structure • magnetism • Superconductivity
• ISBN-10: 3-642-04826-9 / 3642048269
• ISBN-13: 978-3-642-04826-5 / 9783642048265