Transport In Multilayered Nanostructures: The Dynamical Mean-field Theory Approach (Second Edition)

by James K Freericks

Overview

Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and:A series of over 50 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field.

Product Details

ISBN-13:	9781783268573
Publisher:	Imperial College Press
Publication date:	05/20/2016
Pages:	430
Product dimensions:	6.30(w) x 9.20(h) x 0.90(d)

Table of Contents

Preface to the Second Edition vii

Preface to the First Edition ix

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 28

2 Dynamical Mean-Field Theory in the Bulk 33

2.1 Models of Strongly Correlated Electrons 33

2.2 Second Quantization 41

2.3 Imaginary Time Green's Functions 48

2.4 Real Time Green's Fund ions 55

2.5 The Limit d → ∞ and the Mapping onto a Time-Dependent Impurity Problem 63

2.6 Impurity Problem Solvers 70

2.7 Computational Algorithms 80

2.8 Linear-Response dc-Transport in the Bulk 83

2.9 Metal-Insulator Transitions within DMFT 95

2.10 Bulk Charge and Thermal Transport 102

3 Dynamical Mean-Field Theory of a Multilayered Nanostructure 117

3.1 Potthoff-Nolting Approach to Multilayered Nanostructures 117

3.2 Quantum Zipper Algorithm (Renormalized Perturbation Expansion) 120

3.3 Computational Methods 124

3.4 Density of States for a Nanostructure described by the Falicov-Kimball Model 127

3.5 Density of States for a Nanostructure described by the Hubbard Model 134

3.6 Longitudinal Charge Transport Through a Nanostructure 140

3.7 Charge Reconstruction (Schottky Barriers) 151

3.8 Longitudinal Heat Transport Through a Nanostructure 163

3.9 Current Parallel to the Planes 184

3.10 Superconducting Leads and Josephson Junctions 196

3.11 Vertex Corrections 218

3.12 Finite Dimensions 228

4 Thouless Energy and Normal-State Transport 231

4.1 Heuristic Derivation of the Generalized Thouless Energy 231

4.2 Thouless Energy in Metals 233

4.3 Thouless Energy in Insulators 241

4.4 Crossover from Tunneling to Incoherent Transport in Devices 243

5 Josephson Junctions and Superconducting Transport 249

5.1 Introduction to Superconducting Electronics Devices 249

5.2 Superconducting Proximity Effect 253

5.3 Josephsou Current 258

5.4 Figure-Of-Merit for a Josephsou Junction 263

5.5 Effects of Temperature 269

5.6 Density of States and Andreev Bound States 272

6 Thermal Transport 285

6.1 Electronic Charge Reconstruction Near a Metal-Insulator Transition 285

6.2 Thermal Transport Through a Barrier Near the Metal-Insulator Transition 289

7 Many-body Effects on Capacitance 297

7.1 Introduction 297

7.2 Formalism for Capacitance 299

7.3 Results 307

7.4 Future Prospects 313

8 Nonequilibrium Effects in Multilayers 315

8.1 Introduction to Nonequilibriurn Properties 315

8.2 General Formalism for the Nonequilibrium Many-Body Problem in the Bulk 317

8.3 Noninteracting Nonequilibriurn Green's Functions in the Bulk 322

8.4 Formalism for the Steady-State Response of a Multilayer 331

8.5 Results for Noninteracting Case 347

8.6 Future Work 348

9 Future Directions 351

9.1 Spintronics and Topological Insulating Devices 351

9.2 Multiband Models for Real Materials 355

9.3 Summary 358

Appendix A Problems 359

A.1 Jellium model 359

A.2 Density of states for the hypercubic lattice in 1, 2, 3, and ∞ dimensions 360

A.3 Noninteracting electron in a time-dependent potential 362

A.4 Relation between imaginary-time summations and real-axis integrals 363

A.5 The Green's functions of a local Fermi liquid 364

A.6 Rigid-band approximation to the Falicov-Kimball model 365

A.7 Comparing the spectral formula to the Hilbert transform 366

A.8 Imaginary-time Green's functions 367

A.9 Partition function for a spinless electron in a general time-dependent field 367

A.10 Mapping the impurity in a field to an impurity coupled to a chain in the NRG approach 368

A.11 Impurity Green's function for the chain Hamiltonian in the NRG approach 370

A.12 Solving the NRG many-body Hamiltonian for the chain 370

A.13 Metal-insulator transition in the half-filled Falicov-Kimball model 371

A.14 Kramers-Kronig analysis for the Green's function, and the effect of the pole in the Mott insulator 372

A.15 Met ah insulator transition on a simple cubic lattice 373

A.16 DC conductivity for the simple cubic lattice 375

A.17 Jonson-Mahan theorem 377

A.18 Charge and thermal conductivity for the Falicov-Kimball model 379

A.19 The particle-hole asymmetric metal-insulator transition 380

A.20 Non Fermi-liquid behavior of the Falicov-Kimball model 381

A.21 Thermopower of the Falicov-Kimball model and the figure of-merit 381

A.22 U^FK ∞ Green's functions 382

A.23 Determining G_αβ from the quantum zipper algorithm 382

A.24 The stability of the left, and right recursion relations of the quantum zipper algorithm 383

A.25 Efficient numerical evaluation of integrals via changes of variables 384

A.26 Hybridization parameter of a metal-Hubbard model-metal multilayered device 386

A.27 Equilibrium solutions with charge reconstruction 387

A.28 Local charge and heat current operators for a nanostructure 387

A.29 Operator identity for the Jonson-Mahan theorem 389

A.30 Alternative derivation of the transport density of states in two dimensions 390

A.31 Comparison of the resistance for longitudinal versus trans-verse transport 391

A.32 BCS gap equation 392

A.33 Equations of motion needed for the Nambu-Gor'kov formalism 393

A.34 Spin one-half atom in a time-dependent normal and anomalous dynamical mean field 393

A.35 Hilbert transformation in the Nambu-Gor'kov formalism 394

A.36 Evaluating Hubert transformation-like integrals needed for determining the bulk critical current on a simple-cubic lattice 395

A.37 The single-plane Mott-insulating barrier 397

A.38 Green's functions of the particle-hole symmetric Falicov-Kimball model nanostructure 398

A.39 Parallel implementation for the resistance calculation of a nanostructure 399

A.40 Resistance and Thouless energy of a nanostructure 399

A.41 Determining the irreducible charge vertex for the Falicov-Kimball model from the Ward identity 400

A.42 Deriving formulas for the capacitance of a multilayered device 400

A.43 Electronic charge reconstruction for the capacitor problem 401

A.44 Joint density of states for non equilibrium dynamical mean-field theory on a hypercubic lattice in d = ∞ dimensions with a field along the hypereube diagonal 402

A.45 Hilbert transform for the d = ∞ hypereubic lattice 402

A.46 Extraction of different real time Green's functions from the contour-ordered Green's function and other identities 403

A.47 Converting the contour-ordered Dyson equation to the Larkin-Ovchinnikov format 403

A.48 General form for the nonequilibrium retarded Green's function in a spatially uniform electric field 405

A.49 Transient density of states of a driven noninteracting system 406

A.50 Steady state weights of the Wannier-Stark ladder for a driven noninteracting system 406

A.51 Deriving the quantum zipper algorithm in the Larkin-Ovchinnikov form from the contour-ordered form 407

A.52 Calculate the local nonequilibrium density of states and lesser Green's function for noninteracting electrons on a simple cubic lattice with a nonzero constant vector potential A₀ in the axial direction 407

Bibliography 409

Index 427