Part Ⅰ An Overview

1 Basic Principles Summarized

1.1 The Atomic Idea:From Elementary Particles to Solids

1.2 Permanent(i.e.,Equilibrium)Structures of Matter Correspond to the Minimum of Their(Free)Energy

1.3 Condensed Matter Tends to Collapse Under the Influence of Coulomb Potential Energy

1.4 Quantum Kinetic Energy Counterbalances Coulomb Potential Energy Leading to Stable Equilibrium Structures

1.4.1 Heisenberg's Uncertainty Principle and the Minimum Kinetic Energy

1.4.2 Pauli's Exclusion Principle and the Enhancement of the Minimum Kinetic Energy

1.4.3 Schr？dinger's Spectral Discreteness and the Rigidity of the Ground State

1.5 Dimensional Analysis

1.6 Key Points

1.7 Questions and Problems

2 Basic Principles in Action

2.1 Size and Energy Scale of Atoms

2.2 Why do Atoms Come Together to Form Molecules and Solids?

2.3 Ionic Motion:Small Oscillations

2.4 Why do the Specific Heats of Solids go to Zero as T→0K?

2.5 When is Classical Mechanics Adequate?

2.6 Estimating Magnitudes Through Dimensional Analysis

2.6.1 Atomic Radius,Rα

2.6.2 Volume per Atom,νa≡V/Na,in Solids

2.6.3 Mass Density,ρM

2.6.4 Cohesive Energy,Uc

2.6.5 Bulk Modulus,B,and Shear Modulus,μs

2.6.6 Sound Velocities in Solids,c0,cl,ct

2.6.7 Maximum Angular Frequency of Atomic Vibrations in Solids,ωmax

2.6.8 Melting Temperature,Tm

2.6.9 DC Electrical Resistivity,ρe

2.7 Key Points

2.8 Questions and Problems

3 A First Acquaintance with Condensed Matter

3.1 Various Kinds of Condensed Matter

3.1.1 Monocrystalline and Polycrystalline Atomic Solids

3.1.2 Atomic or Ionic Compounds and Alloys

3.1.3 Molecular Solids

3.1.4 Glasses

3.1.5 Polymers

3.1.6 Colloids

3.1.7 Gels

3.1.8 Liquid Crystals

3.1.9 Self-Assembled Soft Matter

3.1.1 0Artificial Structures

3.1.1 1Clusters and Other Finite Systems

3.2 Bonding Types and Resulting Properties

3.2.1 Simple Metals

3.2.2 Transition Metals and Rare Earths

3.2.3 Covalent Solids

3.2.4 Ionic Solids

3.2.5 Van der Waals Bonded Solids

3.2.6 Hydrogen Bonded Solids

3.3 A Short Introduction to Crystal Structures

3.3.1 Some Basic Definitions

3.3.2 Unit and Primitive Cells of Some Commonly Occurring 3-D Crystal Structures

3.3.3 Systems and Types of 3D Bravais Lattices

3.3.4 Crystal Planes and Miller Indices

3.4 Bloch Theorem,Reciprocal Lattice,Bragg Planes,and Brillouin Zones

3.4.1 Bloch Theorem

3.4.2 Reciprocal Lattice

3.4.3 Bragg Planes

3.4.4 Brillouin Zones

3.5 Key Points

3.6 Questions and Problems

Part Ⅱ Two Simple Models for Solids

4 The Jellium Model and Metals Ⅰ:Equilibrium Properties

4.1 Introduction

4.2 Electronic Eigenfunctions,Eigenenergies,Number of States

4.3 Kinetic and Potential Energy,Pressures,and Elastic Moduli

4.4 Acoustic Waves are the Ionic Eigenoscillations in the JM

4.5 Thermodynamic Quantities

4.5.1 General Formulas

4.5.2 Specific Heat,CV

4.5.3 Bulk Thermal Expansion Coefficient

4.6 Key Points

4.7 Problems

5 The Jellium Model and Metals Ⅱ:Response to External Perturbations

5.1 Response to Electric Field

5.2 The Dielectric Function

5.3 Static Electrical Conductivity

5.4 Phonon Contribution to Resistivity

5.5 Response in the Presence of a Static Uniform Magnetic Field

5.5.1 Magnetic Resonances

5.5.2 Hall Effect and Magnetoresistance

5.5.3 Magnetic Susceptibility,χm

5.6 Thermoelectric Response

5.7 Key Points

5.8 Problems

6 Solids as Supergiant Molecules:LCAO

6.1 Diversion:The Coupled Pendulums Model

6.2 Introductory Remarks Regarding the LCAO Method

6.3 A Single Band One-Dimensional Elemental“Metal”

6.4 One-Dimensional Ionic“Solid”

6.5 One-Dimensional Molecular“Solid”

6.6 Diversion:Eigenoscillations in One-Dimensional“solid”with two Atoms Per Primitive Cell

6.7 One-Dimensional Elemental sp1“Semiconductor”

6.8 One-Dimensional Compound sp1“Semiconductor”

6.9 Key Points

6.1 0Problems

7 Semiconductors and Other Tetravalent Solids

7.1 Lattice Structures:A Reminder

7.2 Band Edges and Gap

7.3 Differences Between the l-D and the 3-D Case and Energy Diagrams

7.4 Metals,Semiconductors,and Ionic Insulators

7.5 Holes

7.6 Effective Masses and DOS

7.7 Dielectric Function and Optical Absorption

7.8 Effective Hamiltonian

7.9 Impurity Levels

7.9.1 Impurity Levels:The General Picture

7.9.2 Impurity Levels:Doping

7.10 Concentration of Electrons and Holes at Temperature T

7.10.1 Intrinsic case

7.10.2 Extrinsic case

7.11 Band Structure and Electronic DOS

7.12 Eigenfrequencies,Phononic DOS,and Dielectric Function

7.13 Key Points

7.14 Problems

8 Beyond the Jellium and the LCAO:An Outline

8.1 Introductory Remarks

8.2 The Four Basic Approximations

8.3 Density Functional Theory

8.4 Outline of an Advanced Scheme for Calculating the Properties of Solids

8.5 Beyond the Four Basic Approximations

8.5.1 Periodicity Broken or Absent

8.5.2 Electron-Electron Correlations,Quasi-Particles,Magnetic Phases,and Superconductivity

8.5.3 Electron-Phonon Interactions,Transport Properties,Superconductivity,and Polarons

8.5.4 Phonon-Phonon Interactions,Thermal Expansion,Melting,Structural Phase Transitions,Solitons,Breathers

8.5.5 Disorder and Many Body Effects in Coexistence

8.5.6 Quantum Informatics and Solid State Systems

8.6 Key Points

8.7 Problems

Part Ⅲ More About Periodicity＆its Consequences

9 Crystal Structure and Ionic Vibrations

9.1 Experimental Determination of Crystal Structures

9.2 Determination of the Frequency vs.Wavevector

9.3 Theoretical Calculation of the Phonon Dispersion Relation

9.4 The Debye-Waller Factor and the Inelastic Cross-Section

9.5 Key Points

9.6 Problems

10 Electrons in Periodic Media.The Role of Magnetic Field

10.1 Introduction

10.2 Dispersion Relations,Surfaces of Constant Energy,and DOS:A Reminder

10.3 Effective Hamiltonian and Semiclassical Approximation

10.4 Semiclassical Trajectories in the Presence of a Magnetic Field

10.5 Two Simple but Elucidating TB Models

10.6 Cyclotron Resonance and the de Haas-van Alphen Effect

10.7 Hall Effect and Magnetoresistance

10.8 Key Points

10.9 Problems

11 Methods for Calculating the Band Structure

11.1 Introductory Remarks

11.2 Ionic and Total Pseudopotentials

11.3 Schr？dinger Equation,Plane Wave Expansion,and Bloch's Theorem

11.4 Plane Waves and Perturbation Theory

11.5 Muffin-Tin Potential

11.6 Schr？dinger Equation and the Augmented Plane Wave(APW)Method

11.7 Schr？dinger Equation and the Korringa-Kohn-Rostoker(KKR) Method

11.8 The κ·p Method of Band Structure Calculations

11.9 Key Points

11.1 0Problems

12 Pseudopotentials in Action

12.1 The One-Dimensional Case

12.2 The Two-Dimensional Square Lattice

12.2.1 Spaghetti Diagrams

12.2.2 Fermi Lines

12.3 Harrison's Construction

12.4 Second-Order Correction to the Total JM Energy

12.5 Ionic Interactions in Real Space

12.6 Phononic Dispersions in Metals

12.7 Scattering by Phonons,Mean Free Path,and the Dimensionless Constant λ in Metals

12.8 Key Points

12.9 Problems

Part Ⅳ Materials

13 Simple Metals and Semiconductors Revisited

13.1 Band Structure and Fermi Surfaces of Simple Metals

13.1.1 Alkali Metals

13.1.2 Alkaline Earths:Be,Mg,Ca,Sr,Ba,and Ra

13.1.3 Trivalent Metals

13.1.4 Tetravalent Metals

13.2 Band Structure of Semiconductors

13.3 The Jones Zone and the Disappearance of the Fermi Surface

13.4 Mechanical Properties of Semiconductors

13.5 Magnetic Susceptibility of Semiconductors

13.6 Optical and Transport Properties of Semiconductors

13.6.1 Excitons

13.6.2 Conductivity and Mobility in Semiconductors

13.7 Silicon Dioxide(SiO2)

13.8 Graphite and Graphene

13.9 Organic semiconductors

13.10 Key Points

13.11 Questions and Problems

14 Closed-Shell Solids

14.1 Van Der Waals Solids

14.2 Ionic Compounds Ⅰ:Types and Crystal Structures

14.3 Ionic Compounds Ⅱ:Mechanical Properties

14.4 Ionic Compounds Ⅲ:Optical Properties

14.5 Key Points

14.6 Problems

15 Transition Metals and Compounds

15.1 Experimental Data for the Transition Metals

15.2 Calculations Ⅰ:APW or KKR

15.3 Calculations Ⅱ:LCAO

15.4 Calculations Ⅲ:The Simple Friedel Model

15.5 Compounds of Transition Elements,Ⅰ:Perovskites

15.6 Compounds of Transition Elements,Ⅱ:High Tc Superconducting Materials

15.7 Compounds of Transition Metals,Ⅲ:Oxides,etc

15.8 Key Points

15.9 Problems

16 Artificial Periodic Structures

16.1 Semiconductor Superlattices

16.2 Photonic Crystals:An Overview

16.3 Photonic Crystals:Theoretical Considerations

16.4 Phononic Crystals

16.5 Left-Handed Metamaterials(LHMs)

16.6 Designing,Fabricating,and Measuring LHMs

16.7 Key Points

16.8 Problems

Part Ⅴ Deviations from Periodicity

17 Surfaces and Interfaces

17.1 Surface Preparation

17.2 Relaxation and Reconstruction

17.3 Surface States

17.4 Work Function

17.5 Measuring the Work Function

17.6 The p-n Homojunction in Equilibrium

17.7 The p-n Homojunction Under an External Voltage V

17.8 Some Applications of Interfaces

17.9 Key Points

17.10 Problems

18 Disordered and Other Nonperiodic Solids

18.1 Introductory Remarks

18.2 Alloys and the Hume-Rothery Rule

18.3 Glasses and other Amorphous Systems

18.4 Distribution and Correlation Functions

18.5 Quasi-Crystals

18.6 Electron Transport and Quantum Interference

18.7 Band Structure,Static Disorder,and Localization

18.7.1 3D Case

18.7.2 2D Case

18.7.3 1D and quasi 1D Systems

18.8 Calculation Techniques

18.8.1 Coherent Potential Approximation

18.8.2 Weak Localization due to Quantum Interference

18.8.3 Scaling Approach

18.8.4 Quasi-One-Dimensional Systems and Scaling

18.8.5 Potential Well Analogy

18.9 Quantum Hall Effect

18.10 Key Points

18.11 Problems

19 Finite Systems

19.1 Introduction

19.2 Metallic Clusters

19.3 Fullerenes

19.4 C60-Based Solids

19.5 Carbon Nanotubes

19.6 Other Clusters

19.7 Quantum Dots

19.7.1 An Overview

19.7.2 Optical Transitions

19.7.3 QDs and Coulomb Blockade

19.8 Key Points

19.9 Problems

Part Ⅵ Correlated Systems

20 Magnetic Materials,Ⅰ:Phenomenology

20.1 Which Property Characterizes These Materials?

20.2 Experimental Data for Ferromagnets

20.2.1 Saturation Magnetization vs Temperature for Simple Ferromagnets

20.2.2 Magnetic Susceptibility of Simple Ferromagnet for T>Tc

20.2.3 Saturation Magnetization vs Temperature for Ferrimagnets

20.2.4 Magnetic Susceptibility of Ferrimagnets vs Temperature(T>Tc)

20.3 Experimental Data for Antiferromagnets

20.3.1 Determination of the Antiferromagnetic Ordered Structure

20.3.2 Magnetic Susceptibility vs Temperature

20.4 Materials

20.4.1 Simple Ferromagnetic Materials

20.4.2 Ferrimagnetic Materials

20.4.3 Antiferromagnetic Materials

20.5 Thermodynamic Relations

20.5.1 Thermodynamic Potentials

20.5.2 Mean Field Approximation(Landau's Approach)

20.5.3 Why are Magnetic Domains Formed?

20.5.4 How Thick is the Bloch Wall?

20.5.5 Examples of Magnetic Domains

20.5.6 Thermodynamics of Antiferromagnets

20.6 Spintronics

20.7 Key Points

20.8 Problems

21 Magnetic Materials Ⅱ:Microscopic View

21.1 Introduction

21.2 Jellium model and el-el Coulomb Repulsion

21.2.1 Is There Ferromagnetic Order in the JM?

21.2.2 Magnetic Susceptibility Within the JM in the Presence of Electron-Electron Interactions

21.2.3 Is There Antiferromagnetic Order in the JM?

21.3 The Hubbard Model

21.4 The Heisenberg Model

21.4.1 The Hamiltonian

21.4.2 Mean Field Approximation

21.4.3 The Ferromagnetic Case,(Jij>0)and its spin waves

21.4.4 The AF Case

21.5 Key Points

21.6 Problems

22 Superconductivity,Ⅰ:Phenomenology

22.1 Materials

22.2 Properties of Superconductors

22.2.1 Zero DC Resistivity

22.2.2 Expulsion of the Magnetic Field B from the Interior of a Superconductor

22.2.3 Critical Value of the Magnetic Field Beyond Which Superconductivity Disappears

22.2.4 Specific Heat and Other Thermodynamic Quantities

22.2.5 Response to Microwave or Far Infrared EM Radiation

22.2.6 Ultrasound Attenuation

22.2.7 Tunneling Current in Metal/Insulator/Superconductor Junctions

22.2.8 Temperature Dependence of the Superconducting Gap

22.2.9 Isotope Effect

22.2.10 Relaxation Times for Nuclear Spin

22.2.11 Thermoelectric Coefficients

22.3 Thermodynamic Relations

22.4 London Equation

22.5 Pippard's Generalization

22.6 Ginzburg-Landau Theory

22.7 Quantization of the Magnetic Flux

22.8 Key Points

22.9 Problems

23 Superconductivity,Ⅱ:Microscopic Theory

23.1 Electron-Electron Indirect Attraction

23.2 Cooper Pairs

23.3 Comments

23.4 Corrected Binding Energy and the Critical Temperature

23.5 Further Corrections to the Formula for Tc

23.6 The Bardeen-Cooper-Schrieffer(BCS)Theory

23.7 Thermodynamic Quantities

23.8 Response to Electromagnetic Fields

23.9 Towards Material-Specific Calculations of Superconducting Quantities

23.10 Josephson Effects and SQUID

23.11 Key Points

23.12 Problems

Part Ⅶ Appendices

A Elements of Electrodynamics of Continuous Media

A.1 Field Vectors,Potentials,and Maxwell's Equations

A.2 Relations Among the Fields

B Elements of Quantum Mechanics

B.1 General Formalism

B.2 Bra and Ket Notation

B.3 Spherically Symmetric Potentials

B.4 Perturbation Results

B.5 Interaction of Matter with an External Electromagnetic Field

C Elements of Thermodynamics and Statistical Mechanics

C.1 Thermodynamic Relations

C.2 Basic Relations of Statistical Mechanics

C.3 Non-Interacting Particles

C.3.1 Non-Interacting Electrons

C.3.2 Phonons

D Dielectric Function,ε(κ,ω):Formulas and Uses

D.1 Uses

D.2 Expressions for ε(κ,ω)within the JM

D.3 Phenomenological Expressions for the Dielectric Function

E Waves in Continuous Elastic Media

E.1 Strains

E.2 Equations of Motion

E.3 Connecting Stress and Strain

E.4 The Elastic Wave Equation

F The Method LCAO Applied to Molecules

F.1 Formulation of the LCAO Method

F.2 Some Important Examples

F.2.1 Covalent Diatomic Molecule

F.2.2 Ionic Diatomic Molecule

F.3 Hybridization of Atomic Orbitals

F.3.1 sp1 Hybrid Atomic Orbitals

F.3.2 sp2 Hybrid Atomic Orbitals

F.3.3 sp3 Hybrid Atomic Orbitals

G Boltzmann's Equation

H Tables

Solutions of Selected Problems and Answers

General Reading

References

Index