The Quantum Hall Effect Book

1	Discovery of the Quantum Hall Effect	1
1.1	Realization of Two-Dimensional Electron Systems	1
1.2	The Quantum Hall Effect	7
2	Two-Dimensional Electrons in a Magnetic Field	17
2.1	Electron Motion in Classical Mechanics	17
2.2	Motion of an Electron in Quantum Mechanics	20
2.3	Electrons in External Fields	28
2.4	Localization by Impurities	31
3	The Integer Quantum Hall Effect	37
3.1	Laughlin's Gedankenexperiment	37
3.2	Buttiker's Theory	41
3.3	Edge Current vs. Bulk Current	47
3.4	Deviations from the Quantized Value	49
4	The Fractional Quantum Hall Effect	53
4.1	General Considerations	53
4.2	Investigation by the Exact-Diagonalization Method	59
4.3	Investigation by the Variational Method	65
4.4	Comparison Between the Exact Ground State and the Laughlin State	72
4.5	Properties of the FQHE State	74
4.6	Comparison with Experiment	85
4.7	Order Parameter and Long-Range Order	90
5	Composite-Particle Mean-Field Theory	95
5.1	Berry Phase and Statistics of Quasiparticles	95
5.2	Composite-Boson Mean-Field Theory	102
5.3	Chern-Simons Ginzburg-Landau Theory	105
5.4	Composite-Fermion Mean-Field Theory	112
6	Spin and Pseudospin Freedom	117
6.1	The Ground State in the Presence of Spin Degeneracy	117
6.2	Excited States	122
6.3	Skyrmions	125
6.4	Bilayer Systems and Pseudospin Representation	130
6.5	Ground State of a Bilayer System	132
7	Even-Denominator States	139
7.1	Anomalous Phenomena at v = 1/2	139
7.2	Composite-Fermion Theory	142
7.3	Experimental Verification	143
7.4	A Remaining Problem: the Essence of the State at v = 1/2	148
8	Electron States at the Sample Edge	151
8.1	Edge States - Effect of the Long-Range Coulomb Interaction	151
8.2	Idealized Edge States - the Effect of Electron Correlation	155
9	Higher Landau Levels	173
9.1	New Ground States in Higher Landau Levels	173
9.2	The Hamiltonian in Higher Landau Levels	176
9.3	Pair States	178
9.4	Charge Density Wave States	181
	Answers to Exercises	189
	References	201
	Index	205