Kohn-Sham Theory of the Fractional Quantum Hall Effect

Hu, Yayun; Jain, J. K.

doi:10.1103/PhysRevLett.123.176802

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

Journal Article · 25 October 2019 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.123.176802 · OSTI ID:1606393

^[1];

^[2]

Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics; Penn State University
Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0005042

OSTI ID:: 1606393

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 17 Vol. 123; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (34)

Hohenberg-Kohn theory including spin magnetism and magnetic fields Kohn, Walter; Savin, Andreas; Ullrich, Carsten A. International Journal of Quantum Chemistry, Vol. 100, Issue 1 https://doi.org/10.1002/qua.20163	journal	January 2004
Hohenberg-Kohn theory including spin magnetism and magnetic fields Kohn, Walter; Savin, Andreas; Ullrich, Carsten A. International Journal of Quantum Chemistry, Vol. 101, Issue 5 https://doi.org/10.1002/qua.20303	journal	January 2004
Density functionals for coulomb systems Lieb, Elliott H. International Journal of Quantum Chemistry, Vol. 24, Issue 3 https://doi.org/10.1002/qua.560240302	journal	September 1983
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Constrained Density Functional Theory Kaduk, Benjamin; Kowalczyk, Tim; Van Voorhis, Troy Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200148b	journal	November 2011
Aharonov–Bohm interference of fractional quantum Hall edge modes Nakamura, J.; Fallahi, S.; Sahasrabudhe, H. Nature Physics, Vol. 15, Issue 6 https://doi.org/10.1038/s41567-019-0441-8	journal	March 2019
Uniform magnetic fields in density-functional theory Tellgren, Erik I.; Laestadius, Andre; Helgaker, Trygve The Journal of Chemical Physics, Vol. 148, Issue 2 https://doi.org/10.1063/1.5007300	journal	January 2018
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem Levy, M. Proceedings of the National Academy of Sciences, Vol. 76, Issue 12 https://doi.org/10.1073/pnas.76.12.6062	journal	December 1979
Magnetic-field density-functional theory Grayce, Christopher J.; Harris, Robert A. Physical Review A, Vol. 50, Issue 4 https://doi.org/10.1103/PhysRevA.50.3089	journal	October 1994
Strictly correlated electrons in density-functional theory Seidl, Michael; Perdew, John P.; Levy, Mel Physical Review A, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevA.59.51	journal	January 1999
Strong-interaction limit of density-functional theory Seidl, Michael Physical Review A, Vol. 60, Issue 6 https://doi.org/10.1103/PhysRevA.60.4387	journal	December 1999
Choice of basic variables in current-density-functional theory Tellgren, Erik I.; Kvaal, Simen; Sagvolden, Espen Physical Review A, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevA.86.062506	journal	December 2012
Some static and dynamical properties of a two-dimensional Wigner crystal Bonsall, Lynn; Maradudin, A. A. Physical Review B, Vol. 15, Issue 4 https://doi.org/10.1103/PhysRevB.15.1959	journal	February 1977
Edge structure of fractional quantum Hall systems from density-functional theory Ferconi, M.; Geller, M. R.; Vignale, G. Physical Review B, Vol. 52, Issue 23 https://doi.org/10.1103/PhysRevB.52.16357	journal	December 1995
Generalized Kohn-Sham schemes and the band-gap problem Seidl, A.; Görling, A.; Vogl, P. Physical Review B, Vol. 53, Issue 7 https://doi.org/10.1103/PhysRevB.53.3764	journal	February 1996
Formation of an edge striped phase in the ν = 1 3 fractional quantum Hall system Tsiper, E. V.; Goldman, V. J. Physical Review B, Vol. 64, Issue 16 https://doi.org/10.1103/PhysRevB.64.165311	journal	October 2001
Berry phases for composite fermions: Effective magnetic field and fractional statistics Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K. Physical Review B, Vol. 70, Issue 12 https://doi.org/10.1103/PhysRevB.70.125316	journal	September 2004
Density-Functional Theory for Strongly Interacting Electrons Gori-Giorgi, Paola; Seidl, Michael; Vignale, G. Physical Review Letters, Vol. 103, Issue 16 https://doi.org/10.1103/PhysRevLett.103.166402	journal	October 2009
Strong Correlation in Kohn-Sham Density Functional Theory Malet, Francesc; Gori-Giorgi, Paola Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.246402	journal	December 2012
Fractional Angular Momentum in Cold-Atom Systems Zhang, Yuhe; Sreejith, G. J.; Gemelke, N. D. Physical Review Letters, Vol. 113, Issue 16 https://doi.org/10.1103/PhysRevLett.113.160404	journal	October 2014
Density-Functional Theory of the Fractional Quantum Hall Effect Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish Physical Review Letters, Vol. 118, Issue 19 https://doi.org/10.1103/PhysRevLett.118.196802	journal	May 2017
Two-Dimensional Magnetotransport in the Extreme Quantum Limit Tsui, D. C.; Stormer, H. L.; Gossard, A. C. Physical Review Letters, Vol. 48, Issue 22 https://doi.org/10.1103/PhysRevLett.48.1559	journal	May 1982
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States Halperin, B. I. Physical Review Letters, Vol. 52, Issue 18 https://doi.org/10.1103/PhysRevLett.52.1583	journal	April 1984
Fractional Statistics and the Quantum Hall Effect Arovas, Daniel; Schrieffer, J. R.; Wilczek, Frank Physical Review Letters, Vol. 53, Issue 7 https://doi.org/10.1103/PhysRevLett.53.722	journal	August 1984
Composite-fermion approach for the fractional quantum Hall effect Jain, J. K. Physical Review Letters, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevLett.63.199	journal	July 1989
Ensemble Density Functional Theory of the Fractional Quantum Hall Effect Heinonen, O.; Lubin, M. I.; Johnson, M. D. Physical Review Letters, Vol. 75, Issue 22 https://doi.org/10.1103/PhysRevLett.75.4110	journal	November 1995
Orbital-dependent density functionals: Theory and applications Kümmel, Stephan; Kronik, Leeor Reviews of Modern Physics, Vol. 80, Issue 1 https://doi.org/10.1103/RevModPhys.80.3	journal	January 2008
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States Halperin, B. I. Physical Review Letters, Vol. 52, Issue 26 https://doi.org/10.1103/physrevlett.52.2390.4	journal	June 1984
Composite Fermions in Quantum Dots Jain, J. K.; Kawamura, T. Europhysics Letters (EPL), Vol. 29, Issue 4 https://doi.org/10.1209/0295-5075/29/4/009	journal	February 1995
Strong correlation in Kohn-Sham density functional theory Malet, Francesc; Gori-Giorgi, Paola arXiv https://doi.org/10.48550/arxiv.1207.2775	text	January 2012
The choice of basic variables in current-density functional theory Tellgren, Erik I.; Kvaal, Simen; Sagvolden, Espen arXiv https://doi.org/10.48550/arxiv.1210.2291	text	January 2012
Berry phases for composite fermions: effective magnetic field and fractional statistics Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K. arXiv https://doi.org/10.48550/arxiv.cond-mat/0407137	text	January 2004
Ensemble density functional theory of the fractional quantum Hall effect Heinonen, O.; Lubin, M. I.; Johnson, M. D. arXiv https://doi.org/10.48550/arxiv.cond-mat/9506141	text	January 1995

Similar Records

Crystalline solutions of the Kohn-Sham equations in the fractional quantum Hall regime

Journal Article · 2021 · Physical Review. B · OSTI ID:1842666

Hu, Yayun; Ge, Yang; Zhang, Jian-Xiao; +1 more

Density-Functional Theory of the Fractional Quantum Hall Effect

Journal Article · 2017 · Physical Review Letters · OSTI ID:1489116

Zhao, Jianyun; Thakurathi, Manisha; Jain, Manish; +2 more

Even denominator fractional quantum Hall states in higher Landau levels of graphene

Journal Article · 2018 · Nature Physics · OSTI ID:1489119

Kim, Youngwook; Balram, Ajit C.; Taniguchi, Takashi; +3 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Density Functional Theory
Kohn Sham
composite fermions

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

Citation Formats

References (34)

Similar Records

Related Subjects