Transport in multilayered nanostructures: the dynamical mean-field theory approach

James K. Freericks9781860947056, 1-86094-705-0

This novel book is the first comprehensive text on Dynamical Mean-Field Theory (DMFT), which has emerged over the past two decades as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, the volume develops the formalism of many-body Green’s functions using the equation of motion approach, which requires an undergraduate solid state physics course and a graduate quantum mechanics course as prerequisites. The DMFT is applied to study transport in multilayered nanostructures, which is likely to be one of the most prominent applications of nanotechnology in the coming years. The text is modern in scope focusing on exact numerical methods rather than the perturbation theory. Formalism is developed first for the bulk and then for the inhomogeneous multilayered systems. The science behind the metal-insulator transition, electronic charge reconstruction, and superconductivity are thoroughly described. The book covers complete derivations and emphasizes how to carry out numerical calculations, including discussions of parallel programing algorithms. Detailed descriptions of the crossover from tunneling to thermally activated transport, of the properties of Josephson junctions with barriers tuned near the metal-insulator transition, and of thermoelectric coolers and power generators are provided as applications of the theory.

---

Table of contents :
Contents……Page 12
Preface……Page 8
Acknowledgments……Page 10
1. Introduction to Multilayered Nanostructures……Page 16
1.1 Thin Film Growth and Multilayered Nanostructures……Page 17
1.2 Strongly Correlated Materials……Page 29
1.3 The Proximity Effect……Page 32
1.4 Electronic Charge Reconstruction at an Interface……Page 35
1.5 Roadmap to Real-Materials Calculations……Page 42
2.1 Models of Strongly Correlated Electrons……Page 46
2.2 Second Quantization……Page 54
2.3 Imaginary Time Green’s Functions……Page 61
2.4 Real Time Green’s Functions……Page 68
2.5 The Limit d -> oo and the Mapping onto a Time-Dependent Impurity Problem……Page 76
2.6 Impurity Problem Solvers……Page 82
2.7 Computational Algorithms……Page 92
2.8 Linear-Response dc-Transport in the Bulk……Page 95
2.9 Metal-Insulator Transitions within DMFT……Page 107
2.10 Bulk Charge and Thermal Transport……Page 114
3.1 Potthoff-Nolting Approach to Multilayered Nanostructures……Page 128
3.2 Quantum Zipper Algorithm (Renormalized Perturbation Expansion)……Page 131
3.3 Computational Methods……Page 134
3.4 Density of States for a Nanostructure……Page 137
3.5 Longitudinal Charge Transport Through a Nanostructure……Page 144
3.6 Charge Reconstruction (Schottky Barriers)……Page 155
3.7 Longitudinal Heat Transport Through a Nanostructure……Page 167
3.8 Superconducting Leads and Josephson Junctions……Page 187
3.9 Finite Dimensions and Vertex Corrections……Page 208
4.1 Heuristic Derivation of the Generalized Thouless Energy……Page 212
4.2 Thouless Energy in Metals……Page 214
4.3 Thouless Energy in Insulators……Page 221
4.4 Crossover from Tunneling to Incoherent Transport in Devices……Page 224
5.1 Introduction to Superconducting Electronics Devices……Page 230
5.2 Superconducting Proximity Effect……Page 234
5.3 Josephson Current……Page 239
5.4 Figure-of-Merit for a Josephson Junction……Page 245
5.5 Effects of Temperature……Page 249
5.6 Density of States and Andreev Bound States……Page 253
6.1 Electronic Charge Reconstruction Near a Metal-Insulator Transition……Page 264
6.2 Thermal Transport Through a Barrier Near the Metal-Insulator Transition……Page 268
7.1 Spintronics Devices……Page 276
7.2 Multiband Models for Real Materials……Page 280
7.3 Nonequilibrium Properties……Page 283
7.4 Summary……Page 285
A.l Jellium model……Page 286
A.2 Density of states for the hypercubic lattice in 1 2 3 and oo dimensions……Page 287
A.3 Noninteracting electron in a time-dependent potential……Page 288
A.4 Relation between imaginary-time summations and real-axis integrals……Page 289
A.6 Rigid-band approximation to the Falicov-Kimball model……Page 291
A.8 Imaginary-time Green’s functions……Page 293
A.10 Mapping the impurity in a field to an impurity coupled to a chain in the NRG approach……Page 294
A.11 Impurity Green’s function for the chain Hamiltonian in the NRG approach……Page 296
A.12 Solving the NRG many-body Hamiltonian for the chain……Page 297
A.14 Kramers-Kronig analysis for the Green’s function and the effect of the pole in the Mott insulator……Page 298
A.15 Metal-insulator transition on a simple cubic lattice……Page 299
A.16 DC conductivity for the simple cubic lattice……Page 302
A.17 Jonson-Mahan theorem……Page 303
A.18 Charge and thermal conductivity for the Falicov-Kimball model……Page 304
A.20 Non Fermi-liquid behavior of the Falicov-Kimball model……Page 306
A.22 U -> oo Green’s functions……Page 307
A.23 Determining GaB from the quantum zipper algorithm……Page 308
A.25 Efficient numerical evaluation of integrals via changes of variables……Page 309
A.26 Equilibrium solutions with charge reconstruction……Page 311
A.27 Local charge and heat current operators for a nanostructure……Page 312
A.29 BCS gap equation……Page 314
A.31 Spin one-half atom in a time-dependent normal and anomalous dynamical mean field……Page 315
A.32 Hilbert transformation in the Nambu-Gor’kov formalism……Page 316
A.33 Evaluating Hilbert transformation-like integrals needed for determining the bulk critical current on a simple-cubic lattice……Page 317
A.34 The single-plane Mott-insulating barrier……Page 319
A.35 Green’s functions of the particle-hole symmetric Falicov-Kimball model nanostructure……Page 320
A.37 Resistance and Thouless energy of a nanostructure……Page 321
Bibliography……Page 324
Index……Page 338