Cover	1
	Title Page	5
	Copyright	6
	Contents	7
	Preface	15
	Chapter 1 Introduction	19
	1.1 Dimensionality	20
	1.2 Approaching Dimensionality from Outside and from Inside	22
	1.3 Dimensionality of Carbon: Solids	26
	1.3.1 Three?Dimensional Carbon: Diamond	28
	1.3.2 Two?Dimensional Carbon: Graphite and Graphene	28
	1.3.3 One?Dimensional Carbon: Cumulene, Polycarbyne, and Polyene	30
	1.3.4 Zero?Dimensional Carbon: Fullerene	31
	1.4 Something in Between: Topology	32
	1.5 More Peculiarities of Dimension: One Dimension	34
	1.6 Summary	37
	References	44
	Chapter 2 One?Dimensional Substances	47
	2.1 A15 Compounds	50
	2.2 Krogmann Salts	55
	2.3 Alchemists' Gold	58
	2.4 Bechgaard Salts and Other Charge?Transfer Compounds	60
	2.5 Polysulfurnitride	63
	2.6 Phthalocyanines and Other Macrocycles	65
	2.7 Transition Metal Chalcogenides and Halides	66
	2.8 Halogen?Bridged Mixed?Valence Transition Metal Complexes	68
	2.9 Returning to Carbon	70
	2.9.1 Conducting Polymers	71
	2.9.2 Carbon Nanotubes	73
	2.10 Perovskites	77
	2.11 Topological States	79
	2.12 What Did We Forget?	80
	2.12.1 Poly?deckers	80
	2.12.2 Polycarbenes	81
	2.12.3 Isolated, Freestanding Nanowires	81
	2.12.4 Templates and Filled Pores	82
	2.12.5 Asymmetric Growth Using Catalysts	83
	2.12.6 Gated Semiconductor Quantum Wires	84
	2.12.7 Few?Atom Metal Nanowires	84
	2.13 A Summary of Our Materials	86
	References	87
	Chapter 3 Order and Symmetry: The Lattice	93
	3.1 The Correlation Function	94
	3.2 The Real Space Crystal Lattice and Its Basis	95
	3.2.1 Using a Coordinate System	99
	3.2.2 Surprises in Two?Dimensional Lattices	104
	3.2.3 The One?Dimensional Lattice	109
	3.2.4 Polymers as One?Dimensional Lattices	110
	3.2.5 Carbon Nanotubes as One?Dimensional Lattices	111
	3.3 Bonding and Binding	112
	3.4 Spatial Symmetries Are Not Enough: Time Crystals	119
	3.5 Summary	120
	References	128
	Chapter 4 The Reciprocal Lattice1	129
	4.1 Describing Objects Using Momentum and Energy	129
	4.1.1 Constructing the Reciprocal Lattice	130
	4.1.2 The Unit Cell	132
	4.2 The Reciprocal Lattice and Scattering	134
	4.2.1 General Scattering	134
	4.2.2 Real Systems	138
	4.2.3 Applying This to Real One?Dimensional Systems	141
	4.3 A Summary of the Reciprocal Lattice	143
	References	146
	Chapter 5 The Dynamic Lattice	147
	5.1 Crystal Vibrations and Phonons	148
	5.1.1 A Simple One?Dimensional Model	151
	5.1.1.1 A Model	151
	5.1.1.2 Long Wavelength Vibrations	154
	5.1.1.3 Short Wavelength Vibrations	155
	5.1.1.4 More Atoms in the Basis	155
	5.1.2 More Dimensions	157
	5.2 Quantum Considerations with Phonons	161
	5.2.1 Conservation of Crystal Momentum	162
	5.2.2 General Scattering	162
	5.3 Phonons Yield Thermal Properties	165
	5.3.1 Internal Energy and Phonons	166
	5.3.2 Models of Energy Distribution: fp(?) and ?K,p	168
	5.3.2.1 DuLong and Petit: Equipartition of Energy	168
	5.3.2.2 Einstein and Quantum Statistics	169
	5.3.2.3 Debye and the Spectral Analysis	170
	5.3.3 The Debye Approximation	174
	5.3.4 Generalizations of the Density of States	177
	5.3.5 Other Thermal Properties: Thermal Transport	179
	5.4 Anharmonic Effects	180
	5.5 Summary of Phonons	186
	References	190
	Chapter 6 Electrons in Solids	191
	Evolving Pictures	192
	Superconductors	194
	6.1 Properties of Electrons: A Review	194
	6.1.1 Electrons Travel as Waves	194
	6.1.1.1 Delocalization	194
	6.1.1.2 Localization	196
	6.1.2 Electrons Arrive as Particles: Statistics	196
	6.1.3 The Fermi Surface	198
	6.2 On to the Models	199
	6.2.1 The Free?Electron Model	199
	6.2.2 Nearly Free Electrons, Energy Bands, Energy Gaps, Density of States	202
	6.2.2.1 Bloch's Theorem	203
	6.2.2.2 The Nearly Free 1D Model	203
	6.2.2.3 Analyzing the 1D Nearly Free Solutions	205
	6.2.2.4 Extending Dispersion Curves to 3D	208
	6.2.3 Tight Binding or Linear Combination of Atomic Orbitals	209
	6.2.3.1 The Formalism	211
	6.2.3.2 The s?Band	212
	6.2.3.3 s Bands in One Dimension	213
	6.2.3.4 s Bands in Two Dimensions	213
	6.2.3.5 s Bands in Three Dimensions	214
	6.2.4 What About Orbitals Other Than s?	215
	6.2.4.1 Building Bands in a Polymer	216
	6.2.4.2 Bonding and Antibonding States	216
	6.2.4.3 The Polyenes	217
	6.2.4.4 Translating to Bloch's Theorem	221
	6.2.5 Tight Binding with a Basis	224
	6.2.5.1 Hybridization	227
	6.2.5.2 Graphene: A Two?Dimensional Example	229
	6.2.5.3 Carbon Nanotubes	231
	6.3 Are We Done Yet?	233
	6.4 Summary	235
	References	241
	Chapter 7 Electrons in Solids Part II: Spatial Heterogeneity	243
	7.1 Heterogeneity: Band?Level Diagrams and the Contact	244
	7.2 Heterogeneity in Semiconductors	247
	7.2.1 Semiconductors: Bandgaps and Doping	248
	7.2.1.1 Band?Level Diagrams	248
	7.2.1.2 Doping	248
	7.2.1.3 Carrier Concentrations in Intrinsic and Doped Semiconductors	253
	7.2.1.4 The Fermi Level vs. the Chemical Potential	257
	7.2.1.5 Spectroscopy of the Dopant Levels	258
	7.2.1.6 Carbon Does Not ``Dope'' Like Si	260
	7.2.2 Junctions with Semiconductors	262
	7.3 Other Types of Heterogeneity	267
	7.4 Summary	269
	References	275
	Chapter 8 Electrons Moving in Solids	277
	8.1 Phenomenology of Electron Dynamics in a Material	277
	8.1.1 Free?Electron Metals	277
	8.1.2 The Free?Electron Metal as a Fluid	280
	8.1.3 Temperature and Conductivity	282
	8.2 The Semiclassical Approach: The Boltzmann Equation	285
	8.2.1 The Sources of Electron Scattering	285
	8.2.2 The Nonequilibrium Distribution Function	286
	8.2.3 The Relaxation Time ?	286
	8.2.4 The Differential Equation for g(r	286
	8.2.5 Introducing Collisions	287
	8.2.6 The Relaxation Time Approximation	288
	8.2.7 Isotropic Scattering from Stationary States	289
	8.2.8 A Simple Example: Ohm's Law	289
	8.2.9 Parabolic Bands	290
	8.2.10 Another Simple Example: AC Conductivity and Linear Response	291
	8.2.11 An Example with Anisotropy: ? &equals	291
	8.2.12 The Seebeck Effect and Thermopower	292
	8.2.13 A Final Example: Static E and B Applied but ? ???(r) and ?rT &equals	295
	8.2.14 The Hall Effect and Magnetotransport	297
	8.2.15 The Curious Case of Al	298
	8.3 Coherent Transport: The Landauer–Büttiker Approach	299
	8.4 General Remarks on Measurements	301
	8.4.1 Simple Conductivity	301
	8.4.2 Conductivity of Small Particles	305
	8.4.3 Conductivity of High Impedance Samples	306
	8.4.4 Conductivity Measurements Without Contacts	307
	8.5 Complications: Localization, Hopping, and General Bad Behavior	308
	8.6 Summary	311
	References	315
	Chapter 9 Polarons, Solitons, Excitons, and Conducting Polymers	319
	9.1 Distortions, Instabilities, and Transitions in One Dimension	321
	9.1.1 Coupling Charge with the Lattice	321
	9.1.2 Peierls Instability	323
	9.1.3 Results of Peierls in Real Systems	326
	9.1.3.1 Phonon Softening and the Kohn Anomaly	326
	9.1.3.2 Fermi Surface Warping	327
	9.2 Conjugation and the Double Bond	328
	9.3 Conjugational Defects	331
	9.4 The Soliton	335
	9.4.1 Doping	337
	9.4.2 Quasiparticles	338
	9.5 Generation of Solitons	343
	9.6 Nondegenerate Ground?State Polymers: Polarons	346
	9.7 Fractional Charges	350
	9.8 Soliton Lifetime	352
	9.9 Conductivity and Solitons	355
	9.10 Fibril Conduction	359
	9.11 Hopping Conductivity: Variable Range Hopping vs. Fluctuation?Assisted Tunneling	363
	9.12 Highly Conducting Polymers	371
	9.13 Magnetoresistance	372
	9.14 Organic Molecular Devices	378
	9.14.1 Molecular Switches	378
	9.14.2 LB Diodes	381
	9.14.3 Organic Light?Emitting Diodes	382
	9.14.3.1 Fundamentals of OLEDs	384
	9.14.3.2 Materials for OLEDs	388
	9.14.3.3 Designs for OLEDs	389
	9.14.3.4 Performance of OLEDs	390
	9.14.4 Field?Induced Organic Emitters	391
	9.14.5 Organic Lasers and Organic Light?Emitting Transistors	394
	9.14.5.1 Current Densities	397
	9.14.5.2 Contacts	397
	9.14.5.3 Polarons and Triplets	397
	9.14.6 Organic Solar Cells	398
	9.14.7 Organic Field?Effect Transistors	402
	9.14.8 Organic Thermoelectrics	403
	9.15 Summary	405
	References	408
	Chapter 10 Correlation and Coupling	421
	10.1 The Metal?to?Insulator Transition and the Mott Insulator	421
	10.1.1 The Hamiltonian	424
	10.1.2 The Lattice and Antiferromagnetic Ordering	425
	10.1.3 Other Considerations: The Particle?Hole Symmetry (PHS)	425
	10.1.4 The Hubbard Model in Lower Dimensions	426
	10.1.5 Real One?Dimensional Mott Systems	428
	10.2 The Superconductor	429
	10.2.1 The Basic Phenomena	429
	10.2.1.1 In What Compounds Has Superconductivity Been Observed?	433
	10.2.2 A Basic Model	433
	10.2.2.1 How Does an Attractive Potential Show Up Between Two Negatively Charged Particles?	434
	10.2.2.2 Cooper Pair Binding	436
	10.2.2.3 The BCS Ground State	438
	10.2.2.4 Supplementary Thoughts	443
	10.2.3 Superconductivity Measurements Are Tricky	446
	10.2.4 Superconductivity and Dimensionality	448
	10.2.5 More on Organic Superconductors	449
	10.2.5.1 One?Dimensional Organic Superconductors	450
	10.2.5.2 Two?Dimensional Organic Superconductors	453
	10.2.5.3 Three?Dimensional Organic Superconductors	454
	10.2.6 Trends	456
	10.3 The Charge Density Wave	458
	10.3.1 The Charge Density Wave and Peierls	458
	10.3.1.1 Modulation of the Electron and Mass Densities	459
	10.3.1.2 Starting with Polymers	459
	10.3.1.3 A Gap Is Introduced	460
	10.3.1.4 The Order Parameter	460
	10.3.1.5 Phase Dynamics, Pinning, Commensurability, and Solitons	460
	10.3.2 Peierls and Coulomb Interactions: Spin Interactions	464
	10.3.2.1 4kF Charge Density Waves	464
	10.3.2.2 Spin Peierls Waves	466
	10.3.2.3 Spin Density Waves	466
	10.3.3 Phonon Dispersion: Phase and Amplitude in CDWs	468
	10.3.4 More on Peierls–Fröhlich Mechanisms	470
	10.3.5 Spin Density Waves and the Quantized Hall Effect	471
	10.4 Plasmons	472
	10.4.1 The Drude Model and the Dielectric Function	472
	10.4.2 The Significance of the Plasma Frequency	473
	10.5 Composite Particles and Quasiparticles: A Summary	475
	References	476
	Chapter 11 Magnetic Interactions	485
	11.1 Magnetism of the Atom	487
	11.2 The Crystal Field	490
	11.3 Magnetism in Condensed Systems	492
	11.3.1 Paramagnetism	492
	11.3.1.1 Curie Paramagnets	494
	11.3.1.2 The Weiss Correction	495
	11.3.1.3 Free?Electron Magnets	496
	11.3.2 Diamagnetism	497
	11.4 Dia? and Para?Foundations of Other Magnets	499
	11.5 Mechanisms of Interaction: Spin Models	500
	11.5.1 The Mean Field Model	501
	11.5.2 Ising, Heisenberg, XY, and Hopfield	501
	11.5.2.1 Ising Models	501
	11.5.2.2 Heisenberg Models	503
	11.5.2.3 XY models	503
	11.5.2.4 Hopfield Models	505
	11.5.3 Spin Wave and Magnons	506
	11.5.3.1 Spin Waves	506
	11.5.3.2 Thermodynamics	509
	11.5.3.3 The Particle Nature of Magnons	511
	11.5.3.4 Stoner Excitations	512
	11.5.3.5 Coupling to the Electromagnetic Field: Magnon–Photon Coupling	512
	11.6 More Complicated Situations	512
	11.6.1 Double Exchange	512
	11.6.2 Super Exchange	514
	11.6.3 RKKY	514
	11.7 Time Reversal Symmetry	515
	11.8 Summary	516
	References	519
	Chapter 12 Polarization of Materials	521
	12.1 Simple Atomic Models	521
	12.1.1 Linearity in the Response	522
	12.1.2 Relating the Fields	525
	12.2 Temperature Dependence	527
	12.3 Time Dependence: ?(?)	528
	12.4 A Familiar Equation in Optics	531
	12.5 Understanding the Context	532
	12.6 The Dielectric Function and Metals	532
	12.7 Piezoelectrics, Pyroelectrics, and More	533
	12.7.1 The h?BN Example	536
	12.8 Summary	537
	References	541
	Chapter 13 Optical Interactions	543
	13.1 Maxwell and the Solid (Review)	545
	13.1.1 In a Vacuum	545
	13.1.2 In a Material	546
	13.1.3 A General Solution in the Solid	547
	13.1.3.1 A Fun Notational Fact	549
	13.2 Polarization Coupling: Polaritons	550
	13.2.1 Phonons with Electrical Polarization	550
	13.2.2 Phonons Meet Photons	552
	13.2.3 The Phonon–Polariton	553
	13.2.4 The Plasmon Polariton	556
	13.3 Optical Transitions, Excitons, and Exciton Polaritons	561
	13.3.1 Transitions	561
	13.3.2 Carbon Nanotubes: An Example	564
	13.3.3 Color Centers and Dopants	564
	13.3.4 Excitons	566
	13.3.5 Exciton Polaritons	567
	13.4 Kramers–Kronig	567
	13.5 Summary	569
	References	573
	Chapter 14 The End and the Beginning	575
	Reference	576
	Index	577
	EULA	592