Tapash Chakraborty, Pekka Pietiläinen

The Quantum Hall Effects (eBook, PDF)

Integral and Fractional

• Format: PDF

Produktbeschreibung

The Fractional Quantum Hall Effect presents a general survery of most of the theoretical work on the subject and briefly reviews the experimental results on the excitation gap. Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. are added to render the monographic treatment up-to-date. To complete the picture this second edition includes three chapters on the integral quantum Hall effect.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 302
• Erscheinungstermin: 12. März 2013
• Englisch
• ISBN-13: 9783642793196
• Artikelnr.: 53106664

Inhaltsangabe

1. Quantum Hall Effect: The Basics.- 1.1 Two-Dimensional Electron Gas.- 1.2 Electrons in a Strong Magnetic Field.- 2. Integral Quantum Hall Effect.- 2.1 Experimental Work.- 2.2 Classical Hall Effect.- 2.3 Quantum Mechanical Approach.- 2.4 Integral Quantization: Theoretical Work.- 2.5 Kubo Formula Approach.- 2.6 The Gauge Invariance Approach.- 2.7 The Topological Invariance Approach.- 3. Other Developments.- 3.1 Electron Localization in the Quantum Hall Regime.- 3.2 Renormalization Group Approach.- 3.3 Current-Carrying Edge States.- 3.4 Transport in Edge Channels and Other Topics.- 4. Fractional Quantum Hall Effect: Introduction.- 5. Ground State.- 5.1 Finite-Size Studies: Rectangular Geometry.- 5.2 Laughlin's Theory.- 5.3 Spherical Geometry.- 5.4 Monte Carlo Results.- 5.5 Reversed Spins in the Ground State.- 5.6 Finite Thickness Correction.- 5.7 Liquid-Solid Transition.- 5.8 Magnetoluminescence.- 6. Elementary Excitations.- 6.1 Quasiholes and Quasiparticles.- 6.2 Finite-Size Studies: Rectangular Geometry.- 6.3 Spin-Reversed Quasiparticles.- 6.4 Spherical Geometry.- 6.5 Monte Carlo Results.- 6.6 Experimental Investigations of the Energy Gap.- 6.7 Fractional Statistics and the Anyons.- 6.8 The Hierarchy: Higher Order Fractions.- 6.9 Tilted-Field Effects and Reversed-Spin States.- 7. Collective Modes: Intra-Landau Level.- 7.1 Finite-Size Studies: Spherical Geometry.- 7.2 Rectangular Geometry: Translational Symmetry.- 7.3 Spin Waves.- 7.4 Single Mode Approximation: Magnetorotons.- 8. Collective Modes: Inter-Landau Level.- 8.1 Kohn's Theorem.- 8.2 Filled Landau Level.- 8.3 Fractional Filling: Single Mode Approximation.- 8.4 Fractional Filling. Finite-Size Studies.- 9. Further Topics.- 9.1 Effect of Impurities.- 9.2 Quantization Condition.- 9.3 Higher Landau Levels.- 9.4Even Denominator Filling Fractions.- 9.5 Multiple Layer Systems.- 9.6 Nature of Long-Range Order in the Laughlin State.- 10. Open Problems and New Directions.- Appendices.- A The Landau Wave Function in the Symmetric Gauge.- B Kubo Formalism for the Hall Conductivity.- C The Hypernetted-Chain Primer.- D Repetition of the Intra-Landau-level Mode in the Inter-Landau-level Mode.- E Characteristic Scale Values.- References.