Introduction to quantum Hall effect / Keshav N. Shrivastava.

Format:

Book

Author/Creator:

Shrivastava, Keshav Narain, 1943-

Contributor:

Anne and Joseph Trachtman Memorial Book Fund.

Language:

English

Subjects (All):

Quantum Hall effect.

Physical Description:

293 pages : illustrations ; 24 cm

Place of Publication:

New York : Nova Science Publishers, [2002]

Contents:

1.1 Coulomb's law 1

1.2 Gauss law 3

1.3 Biot and Savart law 9

1.4 Vector potential 13

1.5 Faraday's law 14

1.6 Maxwell's equations 17

1.7 Vector and scalar potentials 19

1.8 Atom in a magnetic field 22

2 Semiconductors 30

2.1 Periodic potential 30

2.2 Density of states and carrier concentration 37

2.3 Insulator-metal transition by doping 44

2.4 Heterostructures 47

2.5 Minigaps 52

3 Landau levels 56

3.1 Electrons in a magnetic lield 56

3.2 Electron spin-orbit resonance 71

3.3 InSb 84

4 Response function 88

4.1 Linear response 88

4.2 Goldstone theorem 97

4.3 Phase transition 97

5 Quantum Hall effect 103

5.1 Hall effect 103

5.2 Quantum Hall effect 110

5.3 Fractional quantum Hall effect 119

6 Interpretation of quantum Hall effect 123

6.1 The fractional effective charges 121

6.2 Grouping of charges into two each 130

6.3 Grouping of charges on both sides of n/2 131

6.4 Equality of masses 131

6.5 High Landau levels 132

6.6 Half-filled Landau levels 132

6.7 Energy divergence and phase transition at n/2 136

6.8 Flux tunneling mode similar to Goldstone mode 140

7 Experimental quantum Hall effect 145

7.1 Effective fractional charges 146

7.2 Goldstone modes 156

8 Physical properties in quantum Hall effect 162

8.1 Diamagnetic points 162

8.2 Two particle states and bound states 163

8.3 Rotons and light scattering 165

8.4 Ferromagnetism 167

8.5 Spin-polarized ground state at n/2 = 5/2 171

8.6 Quantum Hall luminescence 172

9 NMR in quantum Hall effect 174

9.1 Measurement of magnetic field by NMR 174

9.2 Field sweep rate in NMR in quantum Hall effect 181

9.3 Polarization from Knight shift 188

9.4 Experimental data of polarization 192

Appendix A Time reversal 198

A.1. Kramers time reversal operator 198

A.2. Time reversal invariance experiment 202

Appendix B Perturbation theory of k.p 204

Appendix C Radiation from a 1-d box 207

Appendix D Fractional charge experiments 211

D.1. Tunneling resistivity 211

D.2. Noise power 211

Appendix E Bose condensation 214

E.1. Bose condensation in two levels 214

E.2. Bose condensation in half-filled Landau level 216

Appendix F Plateau width and activation 221

F.1. Disappearence of the QHE 221

F.2. Activation energy 223

F.3. Non-Lande non-Zeeman resonances 226

Appendix G Elementary spin-orbit interaction 227

Appendix H Aharonov-Bohm phase 234

H.1. Phase 234

H.2. Quantized peak voltage and conductivity 239

Appendix I Spin-charge decoupling 243

I.1. Luttinger liquid 243

I.2. Laughlin's theory 245

I.3. Flux tubes and electrons 251

I.4. Composite fermions and inconsistencies 258

Appendix J What is quantum Hall effect 266

J.2. Bilayers 269

J.3. Measurement of h/m 275

J.4. Fractional charge 275

J.5. High fields 276

J.6. g-values 280.

Notes:

Includes bibliographical references and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

1590334191

OCLC:

50510767