(Downloads - 0)
For more info about our services contact : help@bestpfe.com
Table of contents
1 Introduction
1.1 Fractional quantum Hall effect
1.2 Polarized electrons in the lowest Landau level
1.2.1 Laughlin’s wave function
1.2.2 Effective field theories
1.2.3 Composite fermions
1.2.4 Compressible state ν = 1/2
1.3 Second Landau level
1.3.1 The ν = 5/2 state
1.3.2 Conformal field theory approach
1.4 Multicomponent quantum Hall systems
1.4.1 Wide quantum wells
1.4.2 Quantum Hall bilayer
1.5 Multicomponent systems studied in this thesis
1.5.1 Quantum Hall bilayer at ν = 1
1.5.2 ν = 1/2
1.5.3 ν = 2/5
1.5.4 ν = 1/4
1.5.5 Graphene
2 Numerical studies of the FQHE
2.1 Exact diagonalization: Sphere
2.1.1 Example: Effect of finite thickness on the Laughlin ν = 1/3 state
2.1.2 Entanglement spectrum on the sphere
2.1.3 Example: Multicomponent states in the ν = 1/4 bilayer
2.2 Exact diagonalization: Torus
2.2.1 Example: Abelian vs. non-Abelian states on the torus
2.2.2 Example: Torus degeneracy of the 331 multicomponent state
2.3 Summary
3 Quantum disordering of the quantum Hall bilayer at ν = 1
3.1 Chern-Simons theory for the Halperin 111 state
3.2 Trial wave functions for the quantum Hall bilayer
3.3 Basic response of trial wave functions
3.4 Chern-Simons theory for the mixed states
3.4.1 Case 1
3.4.2 Case 2
3.4.3 Generalized states
3.5 Possibility for a paired intermediate phase in the bilayer
3.5.1 First-order corrections to the 111 state
3.5.2 Discussion
3.5.3 Numerical results
3.6 Conclusion
4 Transitions between two-component and non-Abelian states in bilayers with tunneling
4.1 Transition between 331 Halperin state and the Moore-Read Pfaffian
4.1.1 BCS model for half-filled Landau level
4.1.2 Exact diagonalization
4.1.3 Pfaffian signatures for intermediate tunneling and a proposal for the phase diagram
4.1.4 Generalized tunneling constraint
4.2 Transition from 332 Halperin to Jain’s state at ν = 2/5
4.2.1 The system under consideration
4.2.2 Exact diagonalizations
4.2.3 Intepretation of the results within an effective bosonic model
4.3 Conclusions
5 Wide quantum wells
5.1 Finite thickness and phase transitions between compressible and incompressible states
5.2 Two-subband model of the quantum well
5.2.1 Connection between the quantum-well model and the bilayer
5.3 ν = 1/2 in a quantum well
5.4 ν = 1/4 in a quantum well
5.5 Conclusion
6 Graphene as a multicomponent FQH system
6.1 Interaction model for graphene in a strong magnetic field
6.1.1 SU(4) symmetry
6.1.2 Effective interaction potential and pseudopotentials
6.2 Multicomponent trial wave functions for graphene
6.2.1 [m;m,m] wave functions
6.2.2 νG = 1/3 state in graphene
6.2.3 [m;m − 1,m] wave functions
6.2.4 [m;m − 1,m − 1] wave functions
6.3 Conclusions
7 Outlook
