Electronic and optical properties of D-band perovskites

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1.1 Introduction......Page 15
1.2 The perovskite structure......Page 17
1.3 Ionic model......Page 18
1.4 Madelung and electrostatic potentials......Page 20
1.5 Covalent mixing......Page 23
1.6 Energy bands......Page 26
1.7 Localized d electrons......Page 30
1.8 Magnetism in the perovskites......Page 31
1.9 Superconductivity......Page 32
1.10 Some applications of perovskite materials......Page 34
References......Page 38
Problems for Chapter 1......Page 39
2.1 The Hamiltonian......Page 41
2.2 The Slater determinant state......Page 42
2.3 Koopman's theorem......Page 43
2.4 Hartree–Fock equations......Page 44
2.5 Hartree–Fock potential......Page 46
2.6 Approximate exchange potential......Page 48
2.7 The LCAO method......Page 49
2.8 Orthogonalized atomic orbitals......Page 51
Suggested reference texts......Page 52
Problems for Chapter 2......Page 53
3.1 LCAO matrix elements......Page 55
3.2 Slater–Koster model......Page 56
3.3 Symmetry properties of the Löwdin orbitals......Page 62
Problems for Chapter 3......Page 66
4.1 The unit cell and Brillouin zone......Page 67
4.2 LCAO matrix equation for an infinite lattice......Page 70
4.3 LCAO matrix elements for the perovskite......Page 71
(a) Diagonal LCAO matrix elements......Page 72
4.4 LCAO eigenvalue equation for the cubic perovskites......Page 75
(a) Pi bands......Page 79
(b) Sigma bands......Page 84
4.6 Summary of the chapter results......Page 87
Problems for Chapter 4......Page 89
5.1 Energy bands at Gamma......Page 91
5.2 Energy bands at X......Page 95
5.3 Energy bands at M......Page 98
5.4 Energy bands at R......Page 100
5.5 Cluster electronic states......Page 104
(a) Block-diagonalizing the Hamiltonian using symmetry coordinates......Page 105
The a1g state......Page 108
The eg states......Page 110
The t2g states......Page 112
The t1u states......Page 113
The t2u states......Page 114
(d) Comparison of cluster states with energy band states......Page 115
Problems for Chapter 5......Page 119
6.1 Definitions......Page 121
6.2 DOS for the pi bands......Page 123
6.3 DOS for the sigma bands......Page 128
(a) Semiconducting perovskites......Page 137
(b) Metallic perovskites......Page 141
(c) Electronic properties of Nax WO3......Page 144
Specific heat of Nax WO3 as a function of x......Page 145
Magnetic susceptibility and effective mass of Nax WO3 as functions of x......Page 147
References......Page 150
Problems for Chapter 6......Page 151
7 Optical properties of the d-band perovskites......Page 152
7.1 Review of semiclassical theory......Page 153
7.2 Qualitative theory of Epsilon2(Omega)......Page 156
(a) Joint density of states......Page 158
(b) LCAO transition matrix elements......Page 161
(a) … interband transition......Page 167
(c) Tabulation of interband transition matrix elements......Page 169
7.4 Frequency dependence of Epsilon2(Omega) for insulating and semiconducting perovskites......Page 171
(a) Band-edge behavior of Epsilon2(Omega)......Page 172
(b) Frequency dependence of Epsilon2(Omega) from…......Page 176
7.5 Frequency dependence of Epsilon2(Omega) from…......Page 181
7.6 Frequency dependence of Epsilon2(Omega) from…......Page 184
7.7 …interband transitions......Page 187
References......Page 194
Problems for Chapter 7......Page 195
8 Photoemission from perovskites......Page 196
8.1 Qualitative theory of photoemission......Page 197
8.2 Partial density of states functions......Page 201
8.3 The XPS spectrum of SrTiO3......Page 203
8.4 NaxWO3......Page 206
8.5 Many-body effects in XPS spectra......Page 207
References......Page 210
Problems for Chapter 8......Page 211
9.1 Perturbations at a surface......Page 213
(a) The (001) surface......Page 216
(b) Pi(yz) surface energy bands......Page 218
Volume states......Page 220
Surface states......Page 222
(d) Pi(yz) density of surface states......Page 223
(e) Pi(xy) surface energy bands......Page 226
9.3 Self-consistent solutions for the band-gap surface states: SrTiO3......Page 227
(a) Other types of surface bands......Page 232
(b) Experimental results: SrTiO3, TiO2, and Nax WO3......Page 233
9.4 Surface–oxygen defect states......Page 235
(a) A line of oxygen vacancies on a type I (001) surface......Page 237
(b) Isolated vacancy states......Page 239
Problems for Chapter 9......Page 244
10.1 Displacive distortions: cubic-to-tetragonal phase transition......Page 245
(a) Pi-like tetragonal states......Page 250
(b) Sigma-like tetragonal states......Page 253
(a) Classification of tilting systems and space groups......Page 254
(c) Geometric considerations......Page 257
(d) Lattice energy calculations......Page 259
(e) Electronic structure considerations......Page 260
References......Page 261
Problems for Chapter 10......Page 262
11.1 Background......Page 263
11.2 Band theory and quasiparticles......Page 267
11.3 Effective Hamiltonians for low-energy excitations......Page 270
11.4 Angle-resolved photoemission......Page 271
11.5 Energy bands of the Cu–O2 layers......Page 274
(a) Filled valence bands: the pi bands......Page 276
(b) Sigma bands for the Cu–O2 layer......Page 277
(c) Effects of the oxygen–oxygen interactions......Page 280
(d) Extended singularity in the DOS......Page 282
(e) Comparison of the three-band results with Fermi surface experimental data......Page 285
(f) Possible role of the dz2 non-bonding band......Page 288
11.6 Chains in YBa2Cu3O6.95......Page 291
11.7 Summary......Page 293
References......Page 294
Problems for Chapter 11......Page 296
A.1 Selected physical constants......Page 299
A.2 The complete elliptic integral of the first kind......Page 300
Appendix B The delta function......Page 302
Appendix C Lattice Green's function......Page 305
C.1 Function GEpsilon(0)......Page 307
C.2 Function GEpsilon(1)......Page 308
(a) The pi-band lattice Green's function......Page 310
(b) Relation to the density of sates......Page 311
(c) Partial density of states......Page 312
(d) d-Orbital and p-orbital partial DOS functions......Page 313
(e) Covalency ratio......Page 314
Appendix D Surface and bulk Madelung potentials for the ABO3 structure......Page 316
References......Page 317
Index......Page 319