1．Introduction to Multilayered Nanostructures 1
1.1 Thin Film Growth and Multilayered Nanostructures 2
1.2 Strongly Correlated Materials 14
1.3 The Proximity Effect 17
1.4 Electronic Charge Reconstruction at an Interface 20
1.5 Roadmap to Real-Materials Calculations 27
2．Dynamical Mean-Field Theory in the Bulk 31
2.1 Models of Strongly Correlated Electrons 31
2.2 Second Quantization 39
2.3 Imaginary Time Green's Functions 46
2.4 Real Time Green's Functions 53
2.5 The Limit d→∞and the Mapping onto a Time-Dependent Impurity Problem 61
2.6 Impurity Problem Solvers 67
2.7 Computational Algorithms 77
2.8 Linear-Response dc-Transport in the Bulk 80
2.9 Metal-Insulator Transitions within DMFT 92
2.10 Bulk Charge and Thermal Transport 99
3．Dynamical Mean-Field Theory of a Multilayered Nanostructure 113
3.1 Potthoff-Nolting Approach to Multilayered Nanostructures 113
3.2 Quantum Zipper Algorithm （Renormalized Perturbation Expansion） 116
3.3 Computational Methods 119
3.4 Density of States for a Nanostructure 122
3.5 Longitudinal Charge Transport Through a Nanostructure 129
3.6 Charge Reconstruction（Schottky Barriers） 140
3.7 Longitudinal Heat Transport Through a Nanostructure 152
3.8 Superconducting Leads and Josephson Junctions 172
3.9 Finite Dimensions and Vertex Corrections 193
4．Thouless Energy and Normal-State Transport 197
4.1 Heuristic Derivation of the Generalized Thouless Energy 197
4.2 Thouless Energy in Metals 199
4.3 Thouless Energy in Insulators 206
4.4 Crossover from Tunneling to Incoherent Transport in Devices 209
5．Josephson Junctions and Superconducting Transport 215
5.1 Introduction to Superconducting Electronics Devices 215
5.2 Superconducting Proximity Effect 219
5.3 Josephson Current 224
5.4 Figure-of-Merit for a Josephson Junction 230
5.5 Effects of Temperature 234
5.6 Density of States and Andreev Bound States 238
6．Thermal Transport 249
6.1 Electronic Charge Reconstruction Near a Metal-Insulator Transition 249
6.2 Thermal Transport Through a Barrier Near the Metal-Insulator Transition 253
7．Future Directions 261
7.1 Spintronics Devices 261
7.2 Multiband Models for Real Materials 265
7.3 Nonequilibrium Properties 268
7.4 Summary 270
Appendix A Problems 271
A.1 Jellium model 271
A.2 Density of states for the hypercubic lattice in 1,2,3,and ∞ dimensions 272
A.3 Noninteracting electron in a time-dependent potential 273
A.4 Relation between imaginary-time summations and real-axis integrals 274
A.5 The Green's functions of a local Fermi liquid 276
A.6 Rigid-band approximation to the Falicov-Kimball model 276
A.7 Comparing the spectral formula to the Hilbert transform 278
A.8 Imaginary-time Green's functions 278
A.9 Partition function for a spinless electron in a general time-dependent field 279
A.10 Mapping the impurity in a field to an impurity coupled to a chain in the NRG approach 279
A.11 Impurity Green's function for the chain Hamiltonian in the NRG approach 281
A.12 Solving the NRG many-body Hamiltonian for the chain 282
A.13 Metal-insulator transition in the half-filled Falicov-Kimball model 283
A.14 Kramers-Kronig analysis for the Green's function,and the effect of the pole in the Mott insulator 283
A.15 Metal-insulator transition on a simple cubic lattice 284
A.16 DC conductivity for the simple cubic lattice 287
A.17 Jonson-Mahan theorem 288
A.18 Charge and thermal conductivity for the Falicov-Kimball model 290
A.19 The particle-hole asymmetric metal-insulator transition 291
A.20 Non Fermi-liquid behavior of the Falicov-Kimball model 291
A.21 Thermopower of the Falicov-Kimball model and the figure-of-merit 292
A.22 U→∞ Green's functions 292
A.23 Determining Gαβ from the quantum zipper algorithm 293
A.24 The stability of the left and right recursion relations of the quantum zipper algorithm 294
A.25 Efficient numerical evaluation of integrals via changes of variables 294
A.26 Equilibrium solutions with charge reconstruction 296
A.27 Local charge and heat current operators for a nanostructure 297
A.28 Operator identity for the Jonson-Mahan theorem 299
A.29 BCS gap equation 299
A.30 Equations of motion needed for the Nambu-Gor'kov formalism 300
A.31 Spin one-half atom in a time-dependent normal and anomalous dynamical mean field 300
A.32 Hilbert transformation in the Nambu-Gor'kov formalism 301
A.33 Evaluating Hilbert transformation-like integrals needed for determining the bulk critical current on a simple-cubic lattice 302
A.34 The single-plane Mott-insulating barrier 304
A.35 Green's functions of the particle-hole symmetric Falicov-Kimball model nanostructure 305
A.36 Parallel implementation for the resistance calculation of a nanostructure 306
A.37 Resistance and Thouless energy of a nanostructure 306
Bibliography 309
Index 323