skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1];  [2]; ORCiD logo [3]
  1. Purdue University, West Lafayette, IN (United States); University of California at San Diego, La Jolla, CA (United States)
  2. Purdue University, West Lafayette, IN (United States); IMEC, Leuven (Belgium)
  3. 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Sharp and smooth boundaries of quantum Hall liquids
journal, March 1994


Parafermionic edge zero modes in Z n -invariant spin chains
journal, November 2012


Topological transitions in Berry’s phase interference effects
journal, August 1993


Edge states in the fractional-quantum-Hall-effect regime
journal, January 1990


Edge Reconstruction in the ν = 2 / 3 Fractional Quantum Hall State
journal, December 2013


Ground State of Two-Dimensional Electrons in Strong Magnetic Fields and 1 3 Quantized Hall Effect
journal, April 1983


Solitons in Polyacetylene
journal, June 1979


Evidence for a spin transition in the ν=2/3 fractional quantum Hall effect
journal, April 1990


Ising Ferromagnetism and Domain Morphology in the Fractional Quantum Hall Regime
journal, March 2001


Exotic non-Abelian anyons from conventional fractional quantum Hall states
journal, January 2013


Magnetic Flux, Angular Momentum, and Statistics
journal, April 1982


New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012


Unpaired Majorana fermions in quantum wires
journal, October 2001


Effective action of a compressible quantum Hall state edge: Application to tunneling
journal, July 2001


Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures
journal, January 2010


Edge channels for the fractional quantum Hall effect
journal, January 1990


Mesoscopic Transport in Electrostatically Defined Spin-Full Channels in Quantum Hall Ferromagnets
journal, July 2017


Electrostatic control of quantum Hall ferromagnetic transition: A step toward reconfigurable network of helical channels
journal, August 2016


Non-Abelian statistics and topological quantum information processing in 1D wire networks
journal, February 2011


Ising Ferromagnetism and Domain Morphology in the Fractional Quantum Hall Regime
text, January 2001


Topological phase transition in the ν=2/3 quantum Hall effect
journal, June 1996


Topological orders and edge excitations in fractional quantum Hall states
journal, October 1995


Spin Transition in the ν = 8 / 3 Fractional Quantum Hall Effect
journal, May 2012


Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
journal, March 2014


The Two-Eigenvalue Problem and Density¶of Jones Representation of Braid Groups
journal, June 2002


Topological Phases with Parafermions: Theory and Blueprints
journal, March 2016


Microscopic study of edge excitations of spin-polarized and spin-unpolarized ν = 2 / 3 fractional quantum Hall effect
journal, September 2012


Fractional quantum Hall effect in a dilute magnetic semiconductor
journal, September 2014


Nonabelions in the fractional quantum hall effect
journal, August 1991


Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
text, January 2018


Edge excitations of the ν= spin-singlet quantum Hall state
journal, March 1997


Ground state and edge excitations of a quantum Hall liquid at filling factor 2/3
journal, December 2008


Theory of the edge States in Fractional Quantum hall Effects
journal, May 1992


Composite edges in the ν=2/3 fractional quantum Hall effect
journal, October 1991


Manipulating Majorana zero modes on atomic rings with an external magnetic field
journal, January 2016


Non-Abelian statistics in the fractional quantum Hall states
journal, February 1991


Non-Abelian Statistics of Half-Quantum Vortices in p -Wave Superconductors
journal, January 2001


Magnetic field spectral crossings of Luttinger holes in quantum wells
journal, November 2014


On the theory of identical particles
journal, January 1977


Non-Abelian anyons and topological quantum computation
journal, September 2008


Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
journal, March 2018


Resources required for topological quantum factoring
journal, June 2010


Impurity-generated non-Abelions
journal, June 2018


Structure of fractional edge states: A composite-fermion approach
journal, April 1995


Novel symmetry of a random matrix ensemble: Partially broken spin rotation invariance
journal, March 1994


Fractional quantum Hall effect in a dilute magnetic semiconductor
text, January 2014


Non-Abelian Anyons and Topological Quantum Computation
text, January 2007


Resources Required for Topological Quantum Factoring
text, January 2010


Works referencing / citing this record:

Model wave functions for an interface between lattice Laughlin and Moore-Read states
journal, May 2021