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Contents 1 Classical models for electrons in solids 9 1.1 Lorentz oscillator model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Drude model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Sommerfeld theory 23 2.1 The problems with Drude theory . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Free electron gas in three-dimensions . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 Fermi surface, and density of states . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4 Thermal properties of the electron gas . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Screening and Thomas-Fermi theory . . . . . . . . . . . . . . . . . . . . . . . . 27 3 From atoms to solids 33 3.1 The binding of crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Complex matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 The description of periodic solids . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 The reciprocal lattice and diffraction . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5 Diffraction conditions and Brillouin zones . . . . . . . . . . . . . . . . . . . . . . 45 3.6 Lattice dynamics and phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Lattice specific heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4 Electronic structure 55 4.1 Schrödinger equation in a periodic potential . . . . . . . . . . . . . . . . . . . . 55 4.2 Bloch’s theorem from discrete translational symmetry . . . . . . . . . . . . . . . 57 4.3 Nearly free electron theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4 Tight binding: Linear combination of atomic orbitals . . . . . . . . . . . . . . . 65 4.5 Pseudopotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5 Bandstructure of real materials 73 3
Page 1: Quantum Condensed Matter Physics Pa
Page 5 and 6: CONTENTS 5 Preface Books There are
Page 7 and 8: CONTENTS 7 Outline “Any new disco
Page 9 and 10: Chapter 1 Classical models for elec
Page 11 and 12: 1.1. LORENTZ OSCILLATOR MODEL 11 Im
Page 13 and 14: 1.2. DRUDE MODEL 13 Im(ε) Permitti
Page 15 and 16: 1.2. DRUDE MODEL 15 ! # " Figure 1.
Page 17 and 18: 1.2. DRUDE MODEL 17 1. Rather than
Page 19 and 20: 1.2. DRUDE MODEL 19 We neglect B fo
Page 21 and 22: 1.2. DRUDE MODEL 21 Figure 1.9: The
Page 23 and 24: Chapter 2 Sommerfeld theory - elect
Page 25 and 26: 2.3. FERMI SURFACE, AND DENSITY OF
Page 27 and 28: 2.5. SCREENING AND THOMAS-FERMI THE
Page 33 and 34: Chapter 3 From atoms to solids What
Page 35 and 36: 3.1. THE BINDING OF CRYSTALS 35 •
Page 37 and 38: 3.2. COMPLEX MATTER 37 the other io
Page 39 and 40: 3.2. COMPLEX MATTER 39 liquid cryst
Page 41 and 42: 3.2. COMPLEX MATTER 41 Figure 3.5:
Page 43 and 44: 3.3. THE DESCRIPTION OF PERIODIC SO
Page 45 and 46: 3.5. DIFFRACTION CONDITIONS AND BRI
Page 47 and 48: 3.5. DIFFRACTION CONDITIONS AND BRI
Page 49 and 50: 3.6. LATTICE DYNAMICS AND PHONONS 4
Page 51 and 52: 3.6. LATTICE DYNAMICS AND PHONONS 5
Page 53 and 54:
3.7. LATTICE SPECIFIC HEAT 53 The i
Page 55 and 56:
Chapter 4 Electrons in a periodic p
Page 57 and 58:
4.2. BLOCH’S THEOREM FROM DISCRET
Page 59 and 60:
4.2. BLOCH’S THEOREM FROM DISCRET
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4.3. NEARLY FREE ELECTRON THEORY 61
Page 63 and 64:
4.3. NEARLY FREE ELECTRON THEORY 63
Page 65 and 66:
4.4. TIGHT BINDING: LINEAR COMBINAT
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
4.5. PSEUDOPOTENTIALS 71 4.5 Pseudo
Page 73 and 74:
Chapter 5 Bandstructure of real mat
Page 75 and 76:
5.1. BANDS AND BRILLOUIN ZONES 75 w
Page 77 and 78:
5.1. BANDS AND BRILLOUIN ZONES 77 1
Page 79 and 80:
5.2. EXAMPLES OF BAND STRUCTURES 79
Page 81 and 82:
5.3. SEMICLASSICAL DYNAMICS 81 Figu
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Chapter 6 Experimental probes of th
Page 89 and 90:
6.2. PHOTOEMISSION 89 &" ## -.-&" ,
Page 91 and 92:
6.3. QUANTUM OSCILLATIONS - DE HAAS
Page 93 and 94:
! Energy of the orbit (for spherica
Page 95 and 96:
6.4. TUNNELLING 95 experiments are
Page 97 and 98:
6.4. TUNNELLING 97 Figure 6.9: Diff
Page 99 and 100:
Chapter 7 Semiconductors 7.1 Semico
Page 101 and 102:
7.2. INTRINSIC CARRIER CONCENTRATIO
Page 103 and 104:
7.3. DOPED SEMICONDUCTORS 103 small
Page 105 and 106:
Chapter 8 Semiconductor devices We
Page 107 and 108:
8.2. P-N JUNCTION 107 Figure 8.2: .
Page 109 and 110:
8.2. P-N JUNCTION 109 p (acceptor-d
Page 111 and 112:
8.3. SOLAR CELL 111 them separately
Page 113 and 114:
8.3. SOLAR CELL 113 -I load I d (V)
Page 115 and 116:
8.4. FIELD EFFECT TRANSISTOR 115 p
Page 117 and 118:
ucture ose, Gate discussed 1 of ver
Page 119 and 120:
8.5. COMPOUND SEMICONDUCTOR HETEROS
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8.5. COMPOUND SEMICONDUCTOR HETEROS
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Chapter 9 Electronic instabilities
Page 125 and 126:
Condensed matter systems have colle
Page 127 and 128:
9.1. CHARGE DENSITY WAVES 127 9.1 C
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9.1. CHARGE DENSITY WAVES 129 0.3 0
Page 131 and 132:
9.1. CHARGE DENSITY WAVES 131 Figur
Page 133 and 134:
9.1. CHARGE DENSITY WAVES 133 Figur
Page 135 and 136:
9.2. MAGNETISM 135 We obtain for th
Page 137 and 138:
9.2. MAGNETISM 137 Here, E Coul loo
Page 139 and 140:
9.2. MAGNETISM 139 2 ∆E ~ − t /
Page 141 and 142:
9.2. MAGNETISM 141 Multiplying the
Page 143 and 144:
9.2. MAGNETISM 143 Figure 9.11: . I
Page 145 and 146:
Chapter 10 Fermi liquid theory 10.1
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10.2. COLLECTIVE EXCITATIONS 147 "
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10.3. TOTAL ENERGY EXPANSION FOR LA
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
10.4. FERMI LIQUIDS AT THE LIMIT: H
Page 157 and 158:
10.4. FERMI LIQUIDS AT THE LIMIT: H
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