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Title: Kohn-Sham Theory of the Fractional Quantum Hall Effect

Abstract

We formulate the Kohn-Sham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Self-consistent solutions of the KS equations demonstrate that our formulation captures not only configurations with nonuniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. Lastly, this method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, screening, and of fractional quantum Hall effect in mesoscopic devices.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1606393
Grant/Contract Number:  
SC0005042
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 123; Journal Issue: 17; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Kohn Sham; Density Functional Theory; composite fermions

Citation Formats

Hu, Yayun, and Jain, J. K. Kohn-Sham Theory of the Fractional Quantum Hall Effect. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.123.176802.
Hu, Yayun, & Jain, J. K. Kohn-Sham Theory of the Fractional Quantum Hall Effect. United States. https://doi.org/10.1103/PhysRevLett.123.176802
Hu, Yayun, and Jain, J. K. Fri . "Kohn-Sham Theory of the Fractional Quantum Hall Effect". United States. https://doi.org/10.1103/PhysRevLett.123.176802. https://www.osti.gov/servlets/purl/1606393.
@article{osti_1606393,
title = {Kohn-Sham Theory of the Fractional Quantum Hall Effect},
author = {Hu, Yayun and Jain, J. K.},
abstractNote = {We formulate the Kohn-Sham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Self-consistent solutions of the KS equations demonstrate that our formulation captures not only configurations with nonuniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. Lastly, this method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, screening, and of fractional quantum Hall effect in mesoscopic devices.},
doi = {10.1103/PhysRevLett.123.176802},
journal = {Physical Review Letters},
number = 17,
volume = 123,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 8 works
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Figures / Tables:

FIG. 1 FIG. 1: Density profile for 1/3 droplets. This figure shows the density of a system of $N$ composite fermions. $ρ$0 is the density for Laughlin’s 1/3 wave function, and $ρ$ED is obtained from exact diagonalization (ED) of the Coulomb interaction at total angular momentum $L$total = 3$N$($N$ - 1)/2. Themore » density $ρ$DFT is calculated from the solution of the KS equations for composite fermions in an external potential produced by a uniform positively charged disk of radius $R$ so that $πR$2$ρ_b$ = $N$ . The total angular momentum of the CF state is $L^{*}_{tot}$, which is related to the total angular momentum of the electron state by $L$tot =$L^{*}_{tot}$ + $N$($N$ -1). The CF-DFT solution produces $L^{*}_{tot}$ = $N$($N$ -1)/2, which is consistent with $L$tot = 3$N$($N$ -1)/2. All densities are quoted in units of (2$πl^{2}_{B}$)-1, the density at $ν$ = 1. We take $ρ_b$ = 1/3.« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.