2019/04/09 by Jingcheng Liang, J. Liang, George Simion +3 · 1 citation
Mathematics · Physics and Astronomy · #Combinatorics #Composite fermion #Condensed matter physics #Domain (mathematical analysis) #Electron #Fibonacci number #Fractional quantum Hall effect #Geometry #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Spin (aerodynamics) #Topological Materials and Phenomena #Topological quantum computer #Torus #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.100.075155
published as Phys. Rev. B 100, 075155 (2019) · 17 pages, 12 figures
arxiv created 2019/04/09 · openalex publication_date 2019/08/28 · arxiv updated 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall effect. Effective theory approach and exact diagonalization in a disk and torus geometries proves the existence of the counterpropagating edge modes with opposite spin polarizations at the boundary between the two neighboring regions of the two-dimensional electron liquid in spin-polarized and spin-unpolarized phases. By analytical and numerical analysis, we argue that these systems can host parafermions when coupled to an s-wave superconductor and are experimentally feasible. We investigate settings based on \ensuremathν=2/3,\phantom\rule4pt0ex4/3, and 5/3 spin transitions and analyze spin-flipping interactions that hybridize counterpropagating modes. Finally, we discuss spin-orbit interactions of composite fermions.