Composite fermions /
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| Author / Creator: | Jain, Jainendra K. |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, 2007. |
| Description: | xvi, 543 p. : ill. ; 26 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6377331 |
Table of Contents:
- Preface
- List of symbols and abbreviations
- 1. Overview
- 1.1. Integral quantum Hall effect
- 1.2. Fractional quantum Hall effect
- 1.3. Strongly correlated state
- 1.4. Composite fermions
- 1.5. Origin of the FQHE
- 1.6. The composite fermion quantum fluid
- 1.7. An "ideal" theory
- 1.8. Miscellaneous remarks
- 2. Quantum Hall effect
- 2.1. The Hall effect
- 2.2. Two-dimensional electron system
- 2.3. The von Klitzing discovery
- 2.4. The von Klitzing constant
- 2.5. The Tsui-Stormer-Gossard discovery
- 2.6. Role of technology
- Exercises
- 3. Landau levels
- 3.1. Gauge invariance
- 3.2. Landau gauge
- 3.3. Symmetric gauge
- 3.4. Degeneracy
- 3.5. Filling factor
- 3.6. Wave functions for filled Landau levels
- 3.7. Lowest Landau level projection of operators
- 3.8. Gauge independent treatment
- 3.9. Magnetic translation operator
- 3.10. Spherical geometry
- 3.11. Coulomb matrix elements
- 3.12. Disk geometry/parabolic quantum dot
- 3.13. Torus geometry
- 3.14. Periodic potential: the Hofstadter butterfly
- 3.15. Tight binding model
- Exercises
- 4. Theory of the IQHE
- 4.1. The puzzle
- 4.2. The effect of disorder
- 4.3. Edge states
- 4.4. Origin of quantized Hall plateaus
- 4.5. IQHE in a periodic potential
- 4.6. Two-dimensional Anderson localization in a magnetic field
- 4.7. Density gradient and R[subscript xx]
- 4.8. The role of interaction
- 5. Foundations of the composite fermion theory
- 5.1. The great FQHE mystery
- 5.2. The Hamiltonian
- 5.3. Why the problem is hard
- 5.4. Condensed matter theory: solid or squalid?
- 5.5. Laughlin's theory
- 5.6. The analogy
- 5.7. Particles of condensed matter
- 5.8. Composite fermion theory
- 5.9. Wave functions in the spherical geometry
- 5.10. Uniform density for incompressible states
- 5.11. Derivation of v* and B*
- 5.12. Reality of the effective magnetic field
- 5.13. Reality of the [Lambda] levels
- 5.14. Lowest Landau level projection
- 5.15. Need for other formulations
- 5.16. Composite fermion Chern-Simons theory
- 5.17. Other CF based approaches
- Exercises
- 6. Microscopic verifications
- 6.1. Computer experiments
- 6.2. Relevance to laboratory experiments
- 6.3. A caveat regarding variational approach
- 6.4. Qualitative tests
- 6.5. Quantitative tests
- 6.6. What computer experiments prove
- 6.7. Inter-composite fermion interaction
- 6.8. Disk geometry
- 6.9. A small parameter and perturbation theory
- Exercises
- 7. Theory of the FQHE
- 7.1. Comparing the IQHE and the FQHE
- 7.2. Explanation of the FQHE
- 7.3. Absence of FQHE at v = 1/2
- 7.4. Interacting composite fermions: new fractions
- 7.5. FQHE and spin
- 7.6. FQHE at low fillings
- 7.7. FQHE in higher Landau levels
- 7.8. Fractions ad infinitum?
- Exercises
- 8. Incompressible ground states and their excitations
- 8.1. One-particle reduced density matrix
- 8.2. Pair correlation function
- 8.3. Static structure factor
- 8.4. Ground state energy
- 8.5. CF-quasiparticle and CF-quasihole
- 8.6. Excitations
- 8.7. CF masses
- 8.8. CFCS theory of excitations
- 8.9. Tunneling into the CF liquid: the electron spectral function
- Exercises
- 9. Topology and quantizations
- 9.1. Charge charge, statistics statistics
- 9.2. Intrinsic charge and exchange statistics of composite fermions
- 9.3. Local charge
- 9.4. Quantized screening
- 9.5. Fractionally quantized Hall resistance
- 9.6. Evidence for fractional local charge
- 9.7. Observations of the fermionic statistics of composite fermions
- 9.8. Leinaas-Myrheim-Wilczek braiding statistics
- 9.9. Non-Abelian braiding statistics
- 9.10. Logical order
- Exercises
- 10. Composite fermion Fermi sea
- 10.1. Geometric resonances
- 10.2. Thermopower
- 10.3. Spin polarization of the CF Fermi sea
- 10.4. Magnetoresistance at v = 1/2
- 10.5. Compressibility
- 11. Composite fermions with spin
- 11.1. Controlling the spin experimentally
- 11.2. Violation of Hund's first rule
- 11.3. Mean-field model of composite fermions with a spin
- 11.4. Microscopic theory
- 11.5. Comparisons with exact results: resurrecting Hund's first rule
- 11.6. Phase diagram of the FQHE with spin
- 11.7. Polarization mass
- 11.8. Spin-reversed excitations of incompressible states
- 11.9. Summary
- 11.10. Skyrmions
- Exercises
- 12. Non-composite fermion approaches
- 12.1. Hierarchy scenario
- 12.2. Composite boson approach
- 12.3. Response to Laughlin's critique
- 12.4. Two-dimensional one-component plasma (2DOCP)
- 12.5. Charged excitations at v = 1/m
- 12.6. Neutral excitations: Girvin-MacDonald-Platzman theory
- 12.7. Conti-Vignale-Tokatly continuum-elasticity theory
- 12.8. Search for a model interaction
- Exercises
- 13. Bilayer FQHE
- 13.1. Bilayer composite fermion states
- 13.2. 1/2 FQHE
- 13.3. v = 1: interlayer phase coherence
- 13.4. Composite fermion drag
- 13.5. Spinful composite fermions in bilayers
- Exercises
- 14. Edge physics
- 14.1. QHE edge = 1D system
- 14.2. Green's function at the IQHE edge
- 14.3. Bosonization in one dimension
- 14.4. Wen's conjecture
- 14.5. Experiment
- 14.6. Exact diagonalization studies
- 14.7. Composite fermion theories of the edge
- Exercises
- 15. Composite fermion crystals
- 15.1. Wigner crystal
- 15.2. Composite fermions at low v
- 15.3. Composite fermion crystal
- 15.4. Experimental status
- 15.5. CF charge density waves
- Appendixes
- A. Gaussian integral
- B. Useful operator identities
- C. Point flux tube
- D. Adiabatic insertion of a point flux
- E. Berry phase
- F. Second quantization
- G. Green's functions, spectral function, tunneling
- H. Off-diagonal long-range order
- I. Total energies and energy gaps
- J. Lowest Landau level projection
- K. Metropolis Monte Carlo
- L. Composite fermion diagonalization
- References
- Index
