Hamiltonian theory of the fractional quantum Hall effect: Effect of Landau level mixing

2002/01/07 by Ganpathy Murthy, R. Shankar
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Composite fermion #Condensed matter physics #Electron #Fermi gas #Fractional quantum Hall effect #Graphene research and applications #Hamiltonian (control theory) #Landau quantization #Mathematics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum oscillations #Quantum spin Hall effect #Shubnikov–de Haas effect #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.65.245309

arxiv created 2002/01/07 · openalex publication_date 2002/06/05 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05

Abstract

We derive an effective Hamiltonian in the lowest Landau level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy, \ensuremathκ=(e²/\ensuremathεl)/\ensuremathω_c. We then transcribe the Hamiltonian to the composite fermion basis using our Hamiltonian approach, and compute the effect of LL mixing on transport gaps.

Citations

• On the theory of identical particles
• Hamiltonian theory of the fractional quantum Hall effect: Conserving approximation for incompressible fractions
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Fractional quantum Hall effect and Chern-Simons gauge theories
• Composite fermions and Landau-level mixing in the fractional quantum Hall effect