Semiconductor quantum dots in high magnetic fields: The composite-fermion view

Abstract

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called $\Lambda$ levels).

13 pages, 8 figures

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• Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3
• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories
• A fully quantal molecular description for the spectra of bosons and fermions in the lowest Landau level
• Quantal molecular description and universal aspects of the spectra of bosons and fermions in the lowest Landau level
• Emergent Fermi sea in a system of interacting bosons
• Microscopic study of the 2/5 fractional quantum Hall edge
• Effects of thickness in quantum dots at strong magnetic fields
• Universality of Many-Body States in Rotating Bose and Fermi Systems
• Hyperspherical theory of the quantum Hall effect: the role of exceptional degeneracy
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Few-body collective excitations beyond Kohn's theorem in quantum Hall systems
• Analytic results of the excited electronic states at $\upsilon =1/3$ and the Laughlin-Jain microscopic wave function approaches
• Path-integral Monte Carlo study of electronic states in quantum dots in an external magnetic field
• Proposal for bulk measurement of braid statistics in fractional quantum Hall effect