Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions
Abstract
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.
- Authors:
-
- 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)
- Publication Date:
- Research Org.:
- Purdue Univ., West Lafayette, IN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1656751
- Alternate Identifier(s):
- OSTI ID: 1559081; OSTI ID: 1611445
- Grant/Contract Number:
- SC0010544
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Parafermions; Topological superconductivity; Domain walls; Quantum Hall effect; Anyons; Composite fermions; Edge states; Fractional quantum Hall effect; Majorana bound states; Proximity effect; Quantum phase transitions; Spin-orbit coupling; Symmetry protected topological states; Topological quantum computing; Topological superconductors; Materials Science; Physics
Citation Formats
Liang, Jingcheng, Simion, George, and Lyanda-Geller, Yuli. Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.075155.
Liang, Jingcheng, Simion, George, & Lyanda-Geller, Yuli. Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions. United States. https://doi.org/10.1103/physrevb.100.075155
Liang, Jingcheng, Simion, George, and Lyanda-Geller, Yuli. 2019.
"Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions". United States. https://doi.org/10.1103/physrevb.100.075155. https://www.osti.gov/servlets/purl/1656751.
@article{osti_1656751,
title = {Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions},
author = {Liang, Jingcheng and Simion, George and Lyanda-Geller, Yuli},
abstractNote = {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.},
doi = {10.1103/physrevb.100.075155},
url = {https://www.osti.gov/biblio/1656751},
journal = {Physical Review. B},
issn = {2469-9950},
number = 7,
volume = 100,
place = {United States},
year = {Wed Aug 28 00:00:00 EDT 2019},
month = {Wed Aug 28 00:00:00 EDT 2019}
}
Web of Science
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