Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions

Liang, Jingcheng; Simion, George; Lyanda-Geller, Yuli

doi:10.1103/physrevb.100.075155

Title: Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions

Journal Article · Wed Aug 28 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.075155· OSTI ID:1656751

Liang, Jingcheng ^[1]; Simion, George ^[2];

^[3]

Purdue University, West Lafayette, IN (United States); University of California at San Diego, La Jolla, CA (United States)
Purdue University, West Lafayette, IN (United States); IMEC, Leuven (Belgium)
Purdue University, West Lafayette, IN (United States)

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 counter-propagating 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 $$\nu=\frac{2}{3}$$, $$\nu=\frac{4}{3}$$ and $$\nu=\frac{5}{3}$$ spin transitions and analyze spin-flipping interactions that hybridize counter-propagating modes. Lastly, we discuss spin-orbit interactions of composite fermions.

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Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0010544

OSTI ID:: 1656751

Alternate ID(s):: OSTI ID: 1559081; OSTI ID: 1611445

Journal Information:: Physical Review. B, Vol. 100, Issue 7; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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Title: Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions

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