Verfügbarkeit: Physics of condensed matter

Physics of condensed matter:

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1. Verfasser:	Misra, Prasanta K. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam [u.a] Elsevier 2012
Schlagworte:	Festkörperphysik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXIII, 664 S. Ill., graph. Darst.
ISBN:	9780123849540

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Datensatz im Suchindex

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adam_text	Contents Preface .......................................................................................xxi CHAPTER 1 Basic Properties of Crystals ..................................................1 1.1 Crystal Lattices .................................................................2 1.1.1 Primitive Cell .............................................................3 1.1.2 Unit Cell .................................................................3 1.1.3 Wigner-Seitz Cell ..........................................................3 1.1.4 Lattice Point Group ........................................................3 1.2 Bravais Lattices in Two and Three Dimensions ..................................4 1.2.1 Simple Cubic (sc) Lattice ...................................................4 1.2.2 Lattice Constants ..........................................................5 1.2.3 Coordination Numbers ......................................................5 1.2.4 Body-Centered Cubic (bcc) Lattice ...........................................5 1.2.5 Face-Centered Cubic (fee) Lattice ............................................7 1.2.6 Other Bravais Lattices ......................................................9 1.3 Lattice Planes and Miller Indices ...............................................11 1.4 Bravais Lattices and Crystal Structures .........................................13 1.4.1 Crystal Structure ..........................................................13 1.4.2 Lattice with a Basis .......................................................13 1.4.3 Packing Fraction ..........................................................14 1.5 Crystal Defects and Surface Effects ............................................14 1.5.1 Crystal Defects ...........................................................14 1.5.2 Surface Effects ...........................................................14 1.6 Some Simple Crystal Structures ................................................15 1.6.1 Sodium Chloride Structure .................................................15 1.6.2 Cesium Chloride Structure .................................................15 1.6.3 Diamond Structure ........................................................16 1.6.4 Zincblende Structure ......................................................17 1.6.5 Hexagonal Close-Packed (hep) Structure .....................................17 1.7 Bragg Diffraction ..............................................................19 1.8 Laue Method ..................................................................20 1.9 Reciprocal Lattice .............................................................21 1.9.1 Definition ................................................................21 1.9.2 Properties of the Reciprocal Lattice .........................................22 1.9.3 Alternative Formulation of the Laue Condition ................................25 VU viii Contents 1.10 Brillouin Zones ...............................................................27 1.10.1 Definition ...............................................................27 1.10.2 One-Dimensional Lattice ..................................................28 1.10.3 Two-Dimensional Square Lattice ...........................................28 1.10.4 bcc Lattice ..............................................................29 1.10.5 fee Lattice ..............................................................30 1.11 Diffraction by a Crystal Lattice with a Basis ...................................31 1.11.1 Theory .................................................................31 1.11.2 Geometrical Structure Factor ..............................................32 1.11.3 Application to bcc Lattice .................................................32 1.11.4 Application to fee Lattice .................................................33 1.11.5 The Atomic Scattering Factor or Form Factor ...............................33 Problems ......................................................................34 References ....................................................................35 CHAPTER 2 Phonons and Lattice Vibrations .............................................37 2.1 Lattice Dynamics ..............................................................37 2.1. 1 Theory ..................................................................37 2.1.2 Normal Modes of a One-Dimensional Monoatomic Lattice .....................41 2.1.3 Normal Modes of a One-Dimensional Chain with a Basis ......................44 2.2 Lattice Specific Heat ..........................................................48 2.2.1 Theory ..................................................................48 2.2.2 The Debye Model of Specific Heat ..........................................49 2.2.3 The Einstein Model of Specific Heat ........................................52 2.3 Second Quantization ...........................................................53 2.3.1 Occupation Number Representation .........................................53 2.3.2 Creation and Annihilation Operators .........................................54 2.3.3 Field Operators and the Hamiltonian ........................................58 2.4 Quantization of Lattice Waves .................................................61 2.4.1 Formulation ..............................................................61 2.4.2 Quantization of Lattice Waves ..............................................65 Problems ......................................................................66 References ....................................................................68 CHAPTER 3 Free Electron Model ........................................................71 3.1 The Classical (Drude) Model of a Metal .......................................71 3.2 Sommerfeld Model ............................................................73 3.2. і Introduction ..............................................................73 3.2.2 Fermi Distribution Function ................................................74 3.2.3 Density Operator ..........................................................75 3.2.4 Free Electron Fermi Gas ...................................................77 3.2.5 Ground-State Energy of the Electron Gas ....................................79 3.2.6 Density of Electron States ..................................................81 Contents ix 3.3 Fermi Energy and the Chemical Potential ......................................82 3.4 Specific Heat of the Electron Gas ..............................................84 3.5 DC Electrical Conductivity ....................................................86 3.6 The Hall Effect ................................................................87 3.7 Failures of the Free Electron Model ............................................89 Problems ......................................................................90 References ....................................................................93 CHAPTER 4 Nearly Free Electron Model. ................................................95 4.1 Electrons in a Weak Periodic Potential .........................................96 4.1.1 Introduction ..............................................................96 4.1.2 Plane Wave Solutions .....................................................97 4.2 Bloch Functions and Bloch Theorem ...........................................99 4.3 Reduced, Repeated (Periodic), and Extended Zone Schemes ...................99 4.3.1 Reduced Zone Scheme ...................................................100 4.3.2 Repeated Zone Scheme ...................................................100 4.3.3 Extended Zone Scheme ...................................................101 4.4 Band Index ..................................................................101 4.5 Effective Hamiltonian ........................................................102 4.6 Proof of Bloclťs Theorem from Trunslutional Symmetry ......................103 4.7 Approximate Solution Near a Zone Boundary .................................105 4.8 Different Zone Schemes ......................................................109 4.8.1 Reduced Zone Scheme ...................................................109 4.8.2 Extended Zone Scheme ...................................................110 4.8.3 Periodic Zone Scheme .................................................... Ill 4.9 Elementary Band Theory of Solids ........................................... Ill 4.9.1 Introduction ............................................................. Ill 4.9.2 Energy Bands in One Dimension ..........................................112 4.9.3 Number of States in a Band ...............................................112 4.10 Metals, Insulators, and Semiconductors .......................................112 4.11 Brillouin Zones ..............................................................117 4.12 Fermi Surface ................................................................119 4.12.1 Fermi Surface (in Two Dimensions) .......................................119 4.12.2 Fermi Surface (in Three Dimensions) ......................................121 4.12.3 Harrison s Method of Construction of the Fermi Surface .....................121 Problems ....................................................................124 References ...................................................................130 CHAPTER 5 Band-Structure Calculations ............................................... 131 5.1 Introduction ...........,......................................................131 5.2 Tight-Binding Approximation ................................................131 5.3 LCAO Method ...............................................................135 Contents 5.4 Wannier Functions........................................................... 140 5.5 Cellular Method ..............................................................142 5.6 Orthogonalized Plane-Wave (OPW) Method ..................................145 5.7 Pseudopotentials .............................................................147 5.8 Muffin-Tin Potential .........................................................149 5.9 Augmented Plane-Wave (APW) Method ......................................150 5.10 Green s Function (KKR) Method .............................................152 5.11 Model Pseudopotentials ......................................................156 5.12 Empirical Pseudopotentials ...................................................157 5.13 First-Principles Pseudopotentials ..............................................158 Problems ....................................................................160 References ...................................................................163 CHAPTER 6 Static and Transport Properties of Solids ...................................165 6.1 Band Picture .................................................................166 6.2 Bond Picture .................................................................167 6.3 Diamond Structure ...........................................................168 6.4 Si and Ge ....................................................................168 6.5 Zinc-Blende Semiconductors .................................................170 6.6 Ionic Solids ..................................................................172 6.7 Molecular Crystals ...........................................................174 6.7.1 Molecular Solids .........................................................174 6.7.2 Hydrogen-Bonded Structures ..............................................174 6.8 Cohesion of Solids ...........................................................174 6.8.1 Molecular Crystals: Noble Gases ...........................................174 6.8.2 Ionic Crystals ...........................................................176 6.8.3 Covalent Crystals ........................................................177 6.8.4 Cohesion in Metals ......................................................178 6.9 The Semiclassical Model .....................................................179 6.10 Liouville s Theorem ..........................................................182 6.11 Boltzmann Equation ..........................................................183 6.12 Relaxation Time Approximation ..............................................184 6.13 Electrical Conductivity .......................................................186 6.14 Thermal Conductivity ........................................................187 6.15 Weak Scattering Theory of Conductivity ......................................188 6.15.1 Relaxation Time and Scattering Probability ................................ Î88 6.15.2 The Collision Term .....................................................188 6.15.3 Impurity Scattering ..................................................... ł89 6.16 Resistivity Due to Scattering by Phonons .....................................192 Problems ....................................................................194 References ...................................................................196 Contents xi CHAPTER 7 Electron-Electron Interaction ..............................................199 7.1 Introduction ..................................................................199 7.2 Hartree Approximation .......................................................200 7.3 Hartree-Fock Approximation .................................................203 7.3.1 General Formulation .....................................................203 7.3.2 Hartree-Fock Theory for Jellium ...........................................204 7.4 Effect of Screening ...........................................................207 7.4.1 General Formulation .....................................................207 7.4.2 Thomas-Fermi Approximation .............................................208 7.4.3 Lindhard Theory of Screening .............................................209 7.5 Friedel Sum Rule and Oscillations ............................................214 7.6 Frequency and Wave-Number-Dependent Dielectric Constant ..................217 7.7 Mott Transition ..............................................................222 7.8 Density Functional Theory ...................................................223 7.8. 1 General Formulation .....................................................223 7.8.2 Local Density Approximation .............................................224 7.9 Fenrii Liquid Theory .........................................................225 7.9.1 Quasiparticles ...........................................................225 7.9.2 Energy Functional .......................................................227 7.9.3 Fermi Liquid Parameters .................................... ..............230 7.Î0 Green s Function Method ....................................................232 7.10.1 General Formulation ....................................................232 7.10.2 Finite-Temperature Green s Function Formalism for Interacting Bloch Electrons ..............................................................233 7.10.3 Exchange Self-Energy in the Band Model ..................................234 Problems ....................................................................235 References ...................................................................241 CHAPTER 8 Dynamics of Bloch Electrons ..............................................243 8.1 Semiclassical Model ..........................................................243 8.2 Velocity Operator ............................................................244 8.3 к · ρ Perturbation Theory .....................................................245 8.4 Quasiclassical Dynamics .....................................................246 8.5 Effective Mass ...............................................................247 8.6 Bloch Electrons in External Fields ............................................248 8.6. 1 Time Evolution of Bioch Electrons in an Electric Field .......................250 8.6.2 Alternate Derivation for Bloch Functions in an External Electric and Magnetic Field ......................................................252 8.6.3 Motion in an Applied DC Field ............................................253 8.7 Bloch Oscillations ............................................................254 8.8 Holes ........................................................................255 8.9 Zener Breakdown (Approximate Method) .....................................258 xii Contents 8.10 Rigorous Calculation of Zener Tunneling .....................................261 8.11 Electron-Phonon Interaction ..................................................264 Problems ....................................................................271 References ...................................................................274 CHAPTER 9 Semiconductors ..........................................................275 9.1 Introduction ..................................................................275 9.2 Electrons and Holes ..........................................................278 9.3 Electron and Hole Densities in Equilibrium ...................................279 9.4 Intrinsic Semiconductors .....................................................283 9.5 Extrinsic Semiconductors .....................................................284 9.6 Doped Semiconductors .......................................................285 9.7 Statistics of Impurity Levels in Thermal Equilibrium ..........................288 9.7.1 Donor Levels ...........................................................288 9.7.2 Acceptor Levels .........................................................288 9.7.3 Doped Semiconductors ...................................................289 9.8 Diluted Magnetic Semiconductors ............................................290 9.8.1 Introduction .............................................................290 9.8.2 Magnetization in Zero External Magnetic Field in DMS ......................291 9.8.3 Electron Paramagnetic Resonance Shift .....................................291 9.8.4 I?··?? Model ............................................................295 9.9 Zinc Oxide ..................................................................296 9.10 Amorphous Semiconductors ..................................................296 9.10.1 Introduction ............................................................296 9.10.2 Linear Combination of Hybrids Model for Tetrahedral Semiconductors ........297 Problems ....................................................................300 References ...................................................................303 CHAPTER 10 Electronics ...............................................................305 10.1 Introduction ..................................................................305 10.2 p -η Junction .................................................................306 10.2.1 Introduction ............................................................306 10.2.2 p -η Junction in Equilibrium ..............................................307 10.3 Rectification by a p -η Junction ...............................................311 10.3.1 Equilibrium Case .......................................................311 10.3.2 Nonequilibrium Case (V^0) ............................................313 10.4 Transistors ...................................................................318 10.4.1 Bipolar Transistors ......................................................318 10.4.2 Field-Effect Transistor ...................................................319 10.4.3 Single-Electron Transistor ................................................321 10.5 Integrated Circuits ............................................................325 Contents xiii 10.6 Optoelectronic Devices.......................................................325 10.7 Graphene....................................................................329 10.8 Graphene-Based Electronics..................................................332 Problems....................................................................333 References ...................................................................336 CHAPTER 11 Spintronics...............................................................339 11.1 Introduction.................................................................. 339 11.2 Magnetoresistance............................................................340 11.3 Giant Magnetoresistance......................................................340 11.3.1 Metallic Multilayers .....................................................340 11.4 Mott s Theory of Spin-Dependent Scattering of Electrons ......................342 11.5 Camley-Barnas Model .......................................................345 11.6 CPP-GMR ...................................................................348 11.6.1 Introduction ............................................................348 11.6.2 Theory of CPP-GMR of Multilayered Nanowires ...........................350 11.7 MTJ, TMR, and MRAM .....................................................352 11.8 Spin Transfer Torques and Magnetic Switching ...............................356 11.9 Spintronics with Semiconductors .............................................357 Π .9.1 Introduction ............................................................357 11.9.2 Theory of an FM-T-N Junction ...........................................358 11.9.3 Injection Coefficient ....................................................361 Problems ....................................................................364 References ...................................................................367 CHAPTER 12 Điamagnetism and Paramagnetism .........................................369 12.1 Introduction ..................................................................370 12.2 Atomic (or Ionic) Magnetic Susceptibilities ...................................371 12.2.1 General Formulation ....................................................371 12.2.2 Larmor Điamagnetism ...................................................372 12.2.3 Hund s Rules ..........................................................373 12.2.4 Van VIeck Paramagnetism ...............................................374 12.2.5 Lande g Factor .........................................................375 12.2.6 Curie s Law ............................................................377 12.3 Magnetic Susceptibility of Free Electrons in Metals ...........................378 12.3.1 General Formulation ....................................................378 12.3.2 Landau Điamagnetism and Pauli Paramagnetism ............................380 12.3.3 De Haas-van Alphen Effect ..............................................383 12.4 Many-Body Theory of Magnetic Susceptibility of Bloch Electrons in Solids. . . 388 12.4.1 Introduction ............................................................388 12.4.2 Equation of Motion in the Bloch Representation ............................388 xiv Contents 12.4.3 Thermodynamic Potential................................................390 12.4.4 General Formula for^................................................... 390 12.4.5 Exchange Self-Energy in the Band Model..................................393 12.4.6 Exchange Enhancement of xs .............................................394 12.4.7 Exchange and Correlation Effects onj0 ....................................395 12.4.8 Exchange and Correlation Effects on xso ...................................396 12.5 Quantum Hall Effect .........................................................396 12.5.1 Introduction ............................................................396 12.5.2 Two-Dimensional Electron Gas ...........................................396 12.5.3 Quantum Transport of a Two-Dimensional Electron Gas in a Strong Magnetic Field .........................................................397 12.5.4 Quantum Hall Effect from Gauge Invariance ...............................400 12.6 Fractional Quantum Hall Effect ...............................................400 Problems ....................................................................401 References ...................................................................407 CHAPTER 13 Magnetic Ordering ........................................................409 13.1 Introduction ..................................................................410 13.2 Magnetic Dipole Moments ...................................................411 13.3 Models for Ferromagnetism and Antiferromagnetism ..........................412 13.3.1 Introduction ............................................................412 13.3.2 Heitler-London Approximation ...........................................412 13.3.3 Spin Hamiitonian .......................................................414 13.3.4 Heisenberg Model ......................................................416 13.3.5 Direct, Indirect, and Superexchange .......................................416 13.3.6 Spin Waves in Ferromagnets: Magnons ....................................417 13.3.7 Schwinger Representation ................................................417 13.3.8 Application to the Heisenberg Hamiitonian.................................418 13.3.9 Spin Waves in Antiferromagnets ..........................................421 13.4 Ferromagnetism in Solids .....................................................422 13.4.1 Ferromagnetism Near the Curie Temperature ...............................422 13.4.2 Comparison of Spin-Wave Theory with the Weiss Field Model ...............424 13.4.3 Ferromagnetic Domains .................................................425 13.4.4 Hysteresis .............................................................426 13.4.5 Ising Model ............................................................427 13.5 Ferromagnetism in Transition Metals .........................................427 13.5.1 Introduction ............................................................427 13.5.2 Stoner Model ..........................................................428 13.5.3 Ferromagnetism in Fe, Co, and Ni from Stoner s Model and Konn-Snam Equations ..................................................430 13.5.4 Free Electron Gas Model ................................................431 13.5.5 Hubbard Model ........................................................433 Contents xv 13.6 Magnetization of Interacting Bloch Electrons ..................................434 13.6. ! Introduction ............................................................434 13.6.2 Theory of Magnetization .................................................434 13.6.3 The Quasiparticle Contribution to Magnetization ............................435 13.6.4 Contribution of Correlations to Magnetization ..............................436 13.6.5 Single-Particle Spectrum and the Criteria for Ferromagnetic Ground State ......437 13.7 The Kondo Effect ............................................................439 13.8 Anderson Model .............................................................439 13.9 The Magnetic Phase Transition ...............................................440 13.9.1 Introduction ............................................................440 13.9.2 The Order Parameter ....................................................441 13.9.3 Landau Theory of Second-Order Phase Transitions ..........................441 Problems ....................................................................443 References ...................................................................448 CHAPTER 14 Superconductivity .........................................................451 14.1 Properties of Superconductors ................................................452 14. 1 .1 Introduction ............................................................452 14.1.2 Type I and Type II Superconductors ......................................453 14.1.3 Second-Order Phase Transition ...........................................454 14.1.4 Isotope Effect ..........................................................454 14.1.5 Phase Diagram .........................................................454 14.2 Meissner-Ochsenfeld Effect ..................................................455 14.3 The London Equation ........................................................455 14.4 Ginzburg-Landau Theory ....................................................456 14.4. 1 Order Parameter ........................................................456 14.4.2 Boundary Conditions ....................................................457 14.4.3 Coherence Length ......................................................457 14.4.4 London Penetration Depth ...............................................458 14.5 Flux Quantization ............................................................459 14.6 Josephson Effect .............................................................460 14.6.1 Two Superconductors Separated by an Oxide Layer .........................460 14.6.2 AC and DC Josephson Effects ............................................462 14.7 Microscopic Theory of Superconductivity .....................................462 14.7.1 Introduction ............................................................462 14.7.2 Quasi-Electrons .........................................................463 14.7.3 Cooper Pairs ...........................................................464 14.7.4 BCS Theory ...........................................................466 14.7.5 Ground State of the Superconducting Electron Gas ..........................466 14.7.6 Excited States at Г=0 ..................................................469 14.7.7 Excited States al T^O ..................................................470 xvi Contents 14.8 Strong-Coupling Theory ......................................................472 14.8.1 Introduction ............................................................472 14.8.2 Upper Limit of the Critical Temperature, Tc ................................472 14.9 High-Temperature Superconductors ...........................................473 14.9.1 Introduction ............................................................473 14.9.2 Properties of Novel Superconductors (Cuprates) ............................474 14.9.3 Brief Review of s-, p-, and d-wave Pairing .................................474 14.9.4 Experimental Confirmation of d-wave Pairing ..............................476 14.9.5 Search for a Theoretical Mechanism of High Tc Superconductors .............481 Problems ....................................................................481 References ...................................................................485 CHAPTER 15 Heavy Fermions ...........................................................487 15.1 Introduction ..................................................................488 15.2 Kondo-Lattice, Mixed-Valence, and Heavy Fermions ..........................490 15.2.1 Periodic Anderson and Kondo-Lattice Models ..............................490 15.2.2 Mixed-Valence Compounds ..............................................492 15.2.3 Slave Boson Method ....................................................493 15.2.4 Cluster Calculations .....................................................494 15.3 Mean-Field Theories .........................................................498 15.3.1 The Local Impurity Self-Consistent Approximation ..........................498 15.3.2 Application of LISA to Periodic Anderson Model ...........................499 15.3.3 RKKY Interaction ......................................................500 15.3.4 Extended Dynamical Mean-field Theory ...................................501 15.4 Fermi-Liquid Models .........................................................502 15.4.1 Heavy Fermi Liquids ....................................................502 15.4.2 Fractionalized Fermi Liquids .............................................505 15.5 Metamagnetism in Heavy Fermions ...........................................506 15.6 Ce- and U-Based Superconducting Compounds ...............................508 15.6.1 Ce-Based Compounds ...................................................508 15.6.2 U-Based Superconducting Compounds ....................................509 15.7 Other Heavy-Fermion Superconductors .......................................513 15.7.1 PrtXtSb^ .............................................................513 15.7.2 PuCoGas ..............................................................513 15.7.3 PuRhGa5 ..............................................................515 15.7.4 Comparison between Cu and Pu Containing High-rf Superconductors .........516 15.8 Theories of Heavy-Fermion Superconductivity ................................516 15.9 Kondo Insulators .............................................................516 15.9.1 Brief Review ...........................................................516 15.9.2 Theory of Kondo Insulators ..............................................517 Problems ....................................................................519 References ...................................................................524 Contents xvü CHAPTER 16 Metallic Nanoclusters.....................................................527 16.1 Introduction ..................................................................528 16.1.1 Nanoscience and Nanoclusters............................................528 16.1.2 Liquid Drop Model.....................................................528 16.1.3 Size and Surface/Volume Ratio...........................................528 16.1.4 Geometrie and Electronic Shell Structures ..................................530 16.2 Electronic Shell Structure .....................................................531 16.2.1 Spherical Jellium Model (Phenomenological)...............................531 16.2.2 Self-Consistent Spherical Jellium Model...................................532 16.2.3 Ellipsoidal Shell Model..................................................535 16.2.4 Nonalkali Clusters ......................................................535 16.2.5 Large Clusters ..........................................................535 16.3 Geometrie Shell Structure.................................................... 537 16.3.1 Close-Packing ..........................................................537 16.3.2 Wulff Construction .....................................................537 16.3.3 Polyhedra ..............................................................538 16.3.4 Filling between Complete Shells ..........................................540 16.4 Cluster Growth on Surfaces ..................................................540 16.4.1 Monte Carlo Simulations, ...............................................540 16.4.2 Mean-Field Rate Equations ..............................................541 16.5 Structure of Isolated Clusters .................................................542 16.5.1 Theoretical Models .....................................................542 16.5.2 Structure of Some Isolated Clusters .......................................546 16.6 Magnetism in Clusters ........................................................ 547 16.6.1 Magnetism in Isolated Clusters ...........................................547 16.6.2 Experimental Techniques for Studying Cluster Magnetism ...................549 16.6.3 Magnetism in Embedded Clusters .........................................553 16.6.4 Graphite Surfaces .......................................................555 16.6.5 Study of Clusters by Scanning Tunneling Microscope .......................555 16.6.6 Clusters Embedded in a Matrix ...........................................557 16.7 Superconducting State of Nanoclusters ........................................558 16.7.1 Qualitative Analysis .....................................................558 16.7.2 Thermodynamie Green s Function Formalism for Nanoclusters ...............559 Problems ....................................................................562 References ...................................................................565 CHAPTER 17 Complex Structures .......................................................567 17.1 Liquids ......................................................................568 17.1.1 Introduction ............................................................568 17.1.2 Phase Diagram .........................................................568 17.1.3 Van Hove Pair Correlation Function ......................................569 17.1.4 Correlation Function for Liquids ..........................................570 xviii Contents 17.2 Superfluid 4He...............................................................570 17.2.1 Introduction ............................................................570 17.2.2 Phase Transition in 4He.................................................570 17.2.3 Two-Fluid Model for Liquid 4He.........................................571 17.2.4 Theory of Superfluidity in Liquid 4He.....................................571 17.3 Liquid 3He...................................................................573 17.3.1 Introduction ............................................................573 17.3.2 Possibility of Superfluidity in Liquid 3He ..................................574 17.3.3 Fermi Liquid Theory ....................................................574 17.3.4 Experimental Results of Superfluidity in Liquid 3He .........................575 17.3.5 Theoretical Model for the A and A¡ Phases .................................575 17.3.6 Theoretical Model for the В Phase ........................................577 17.4 Liquid Crystals ...............................................................578 17.4.1 Introduction ............................................................578 17.4.2 Three Classes of Liquid Crystals ..........................................578 17.4.3 The Order Parameter ....................................................580 17.4.4 Curvature Strains .......................................................581 17.4.5 Optical Properties of Cholesteric Liquid Crystals ............................581 17.5 Quasicrystals .................................................................583 17.5.1 Introduction ............................................................583 17.5.2 Penrose Tiles ...........................................................583 17.5.3 Discovery of Quasicrystals ...............................................584 17.5.4 Quasiperiodic Lattice ....................................................584 17.5.5 Phonon and Phason Degrees of Freedom ..................................586 17.5.6 Dislocation in the Penrose Lattice .........................................589 17.5.7 Icosahedral Quasicrystals ................................................589 17.6 Amorphous Solids ...........................................................590 17.6.1 Introduction ............................................................590 17.6.2 Energy Bands in One-Dimensional Aperiodic Potentials .....................591 17.6.3 Density of States .......................................................593 17.6.4 Amorphous Semiconductors ..............................................593 Problems ....................................................................594 References ...................................................................597 CHAPTER 18 Novel Materials ...........................................................599 18.1 Graphene ....................................................................600 18.1.1 Introduction ............................................................600 18.Í.2 Graphene Lattice .......................................................601 18.1.3 Tight-Binding Approximation ............................................602 18.1.4 Dirac Fermions .........................................................606 18.1.5 Comprehensive View of Graphene ........................................608 Contents xix 18.2 Fullerenes ....................................................................608 18.2.1 introduction ............................................................608 18.2.2 Discovery of Cbti .......................................................609 18.3 Fullerenes and Tubules .......................................................613 18.3.1 Introduction ............................................................613 18.3.2 Carbon Nanotubeles .....................................................614 18.3.3 Three Types of Carbon Nanotubes ........................................614 18.3.4 Symmetry Properties of Carbon Nanotubes .................................616 18.3.5 Band Structure of a Fullerene Nanotube ...................................617 18.4 Polymers ....................................................................617 18.4.1 Introduction ............................................................617 18.4.2 Saturated and Conjugated Polymers .......................................618 18.4.3 Transparent Metallic Polymers ............................................621 18.4.4 Electronic Polymers .....................................................621 18.5 Solitons in Conducting Polymers .............................................622 18.5.1 Introduction ............................................................622 18.5.2 Electronic Structure .....................................................623 18.5.3 Tight-Binding Model ....................................................623 18.5.4 Soliton Excitations ......................................................624 18.5.5 Solitons, Polarons, und Polarnu Excitations .................................626 18.6.6 Polarons and Bipolarons .................................................626 18.6 Photoinduced Electron Transfer ...............................................627 Problems ....................................................................627 References ...................................................................630 APPEHDIX A Elements of Group Theory .................................................633 A.1 Symmetry and Its Consequences ..............................................633 АЛЛ Symmetry of Crystals ....................................................633 A. 1.2 Definition of a Group ....................................................633 A. 1.3 Symmetry Operations in Crystal Lattices ...................................634 A.2 Space Groups ................................................................634 A.2.1 Introduction ............................................................634 A.2.2 Space Group Operations ..................................................634 A.3 Point Group Operations ......................................................636 A.3. 1 Introduction ............................................................636 A.3.2 Description of Point Groups ..............................................636 A.3.3 The Cubic Group O,, ....................................................638 APPENDIX В Massbauer Effect .........................................................641 B.1 Introduction ..................................................................641 B.2 Recoilless Fraction ...........................................................642 B.3 Average Transferred Energy ..................................................643 Reference ....................................................................644 xx Contents APPENDIX С Introduction to Renormalization Group Approach ............................645 СИ Critical Behavior .............................................................645 C.2 Theory for Scaling ...........................................................646 C.3 Renormalization Group Approach .............................................648 References ...................................................................649 Index ....................................................................................651
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