Integer and fractional quantum Hall effect in a strip of stripes

2013/05/31 by Jelena Klinovaja, Daniel Loss · 2 citations
Mathematics · Physics and Astronomy · #Composite fermion #Electron #Filling factor #Fractional quantum Hall effect #Ground state #Luttinger liquid #Magnetic field #Quantum Hall effect #Quantum and electron transport phenomena #Quantum spin Hall effect #Scattering #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1140/epjb/e2014-50395-6

published as Eur. Phys. J. B 87, 171 (2014)

arxiv created 2014/07/16 · openalex publication_date 2014/07/31 · arxiv updated 2014/08/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k_F. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We calculate the Hall conductance via the Streda formula and show that it is given by σ_H=νe²/h for all filling factors. We show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.

Citations

• Colloquium: Artificial gauge potentials for neutral atoms
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Cited by

• Quantum spin Hall effect in strip of stripes model
• Chiral and nonchiral edge states in quantum Hall systems with charge density modulation