The Fractional Quantum Hall Effect: Properties of an Incompressible Quantum Fluid

ISBN-13: 9783642971037 / Angielski / Miękka / 2012 / 175 str.

Tapash Chakraborty; Pekka Pietil Inen

Opis

The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. It is more than thirty years since investigations of bulk semiconductors in very strong magnetic fields were begun. Under these conditions, only the lowest Landau level is occupied and the theory predicted a monotonic variation of the resistivity with increasing magnetic field, depending sensitively on the scattering mechanism. However, the ex perimental data could not be analyzed accurately since magnetic freeze-out effects and the transitions from a degenerate to a nondegenerate system complicated the interpretation of the data. For a two-dimensional electron gas, where the positive background charge is well separated from the two dimensional system, magnetic freeze-out effects are barely visible and an analysis of the data in the extreme quantum limit seems to be easier. First measurements in this magnetic field region on silicon field-effect transistors were not successful because the disorder in these devices was so large that all electrons in the lowest Landau level were localized. Consequently, models of a spin glass and finally of a Wigner solid were developed and much effort was put into developing the technology for improving the quality of semi conductor materials and devices, especially in the field of two-dimensional electron systems.

Spis treści

1. Introduction.- 2. Ground State.- 2.1 Finite-Size Studies: Rectangular Geometry.- 2.2 Laughlin’s Theory.- 2.3 Spherical Geometry.- 2.4 Monte Carlo Results.- 2.5 Reversed Spins in the Ground State.- 2.6 Finite Thickness Correction.- 2.7 Liquid-Solid Transition.- 3. Elementary Excitations.- 3.1 Quasiholes and Quasiparticles.- 3.2 Finite-Size Studies: Rectangular Geometry.- 3.3 Spin-Reversed Quasiparticles.- 3.4 Spherical Geometry.- 3.5 Monte Carlo Results.- 3.6 Experimental Investigations of the Energy Gap.- 3.7 The Hierarchy: Higher Order Fractions.- 4. Collective Modes: Intra-Landau Level.- 4.1 Finite-Size Studies: Spherical Geometry.- 4.2 Rectangular Geometry: Translational Symmetry.- 4.3 Spin Waves.- 4.4 Single Mode Approximation: Magnetorotons.- 5. Collective Modes: Inter-Landau Level.- 5.1 Filled Landau Level.- 5.2 Fractional Filling: Single Mode Approximation.- 5.3 Fractional Filling: Finite-Size Studies.- 6. Further Topics.- 6.1 Effect of Impurities.- 6.2 Higher Landau Levels.- 6.3 Even Denominator Filling Fractions.- 6.4 Half-Filled Landau Level in Multiple Layer Systems.- 7. Open Problems and New Directions.- Appendices.- A The Landau Wave Function in the Symmetric Gauge.- B The Hypernetted-Chain Primer.- C Repetition of the Intra-Mode in the Inter-Mode.- References.