The Dirac composite fermion of the fractional quantum Hall effect

Son, Dam Thanh

doi:10.1093/ptep/ptw133

Title: The Dirac composite fermion of the fractional quantum Hall effect

Journal Article · Wed Nov 09 00:00:00 EST 2016 · Progress of Theoretical and Experimental Physics

DOI:https://doi.org/10.1093/ptep/ptw133· OSTI ID:1465696

Son, Dam Thanh ^[1]

Univ. of Chicago, IL (United States). Kadanoff Center for Theoretical Physics

We review the recently proposed Dirac composite fermion theory of the half-filled Landau level. This paper is based on a talk given at the Nambu Symposium at the University of Chicago, March 11–13, 2016.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); US Army Research Office (ARO); National Science Foundation (NSF); Simons Foundation (United States)

Grant/Contract Number:: FG02-13ER41958; SC0009924

OSTI ID:: 1465696

Journal Information:: Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12; ISSN 2050-3911

Publisher:: Physical Society of JapanCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

References (52)

Experimental observation of the quantum Hall effect and Berry's phase in graphene Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L. Nature, Vol. 438, Issue 7065, p. 201-204 https://doi.org/10.1038/nature04235	journal	November 2005
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
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions Mross, David F.; Alicea, Jason; Motrunich, Olexei I. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.016802	journal	June 2016
Composite-fermion Hall conductance at ν= Kivelson, S. A.; Lee, D-H.; Krotov, Y. Physical Review B, Vol. 55, Issue 23 https://doi.org/10.1103/PhysRevB.55.15552	journal	June 1997
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
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M. Journal of Mathematical Physics, Vol. 56, Issue 10 https://doi.org/10.1063/1.4932967	journal	October 2015
Fields and fluids on curved non-relativistic spacetimes Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M. Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)042	journal	August 2015
What Determines the Fermi Wave Vector of Composite Fermions? Kamburov, D.; Liu, Yang; Mueed, M. A. Physical Review Letters, Vol. 113, Issue 19 https://doi.org/10.1103/PhysRevLett.113.196801	journal	November 2014
Baryons, monopoles and dualities in Chern-Simons-matter theories Aharony, Ofer Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)093	journal	February 2016
The half-filled Landau level: The case for Dirac composite fermions Geraedts, S. D.; Zaletel, M. P.; Mong, R. S. K. Science, Vol. 352, Issue 6282 https://doi.org/10.1126/science.aad4302	journal	April 2016
Nambu at work Freund, Peter G. O. Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 7 https://doi.org/10.1093/ptep/ptw054	journal	June 2016
$ν = \frac{1}{2}$ Landau level: Half-empty versus half-full Murthy, Ganpathy; Shankar, R. Physical Review B, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevB.93.085405	journal	February 2016
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators Metlitski, Max A.; Vishwanath, Ashvin Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245151	journal	June 2016
Gapped symmetry preserving surface state for the electron topological insulator Wang, Chong; Potter, Andrew C.; Senthil, T. Physical Review B, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevB.88.115137	journal	September 2013
Lowest-Landau-level theory of the quantum Hall effect: The Fermi-liquid-like state of bosons at filling factor one Read, N. Physical Review B, Vol. 58, Issue 24 https://doi.org/10.1103/PhysRevB.58.16262	journal	December 1998
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions Karthik, Nikhil; Narayanan, Rajamani Physical Review D, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevD.93.045020	journal	February 2016
Effective-Field-Theory Model for the Fractional Quantum Hall Effect Zhang, S. C.; Hansson, T. H.; Kivelson, S. Physical Review Letters, Vol. 62, Issue 1 https://doi.org/10.1103/PhysRevLett.62.82	journal	January 1989
A time-reversal invariant topological phase at the surface of a 3D topological insulator Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09 https://doi.org/10.1088/1742-5468/2013/09/P09016	journal	September 2013
A dipole interpretation of the state Pasquier, V.; Haldane, F. D. M. Nuclear Physics B, Vol. 516, Issue 3 https://doi.org/10.1016/S0550-3213(98)00069-8	journal	April 1998
Symmetry enforced non-Abelian topological order at the surface of a topological insulator Chen, Xie; Fidkowski, Lukasz; Vishwanath, Ashvin Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165132	journal	April 2014
Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A. Physical Review B, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevB.92.125111	journal	September 2015
Anomalous sound propagation at ν=1/2 in a 2D electron gas: Observation of a spontaneously broken translational symmetry? Willett, R. L.; Paalanen, M. A.; Ruel, R. R. Physical Review Letters, Vol. 65, Issue 1 https://doi.org/10.1103/PhysRevLett.65.112	journal	July 1990
Theory of the half-filled Landau level Halperin, B. I.; Lee, Patrick A.; Read, Nicholas Physical Review B, Vol. 47, Issue 12 https://doi.org/10.1103/PhysRevB.47.7312	journal	March 1993
Particle-Hole Symmetry and the Pfaffian State Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236806	journal	December 2007
Towards a Field Theory of Fractional Quantum Hall States Shankar, R.; Murthy, Ganpathy Physical Review Letters, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevLett.79.4437	journal	December 1997
Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids Wang, Chong; Senthil, T. Physical Review B, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevB.93.085110	journal	February 2016
How real are composite fermions? Kang, W.; Stormer, H. L.; Pfeiffer, L. N. Physical Review Letters, Vol. 71, Issue 23 https://doi.org/10.1103/PhysRevLett.71.3850	journal	December 1993
Particle-Hole Symmetry and the $ν = \frac{5}{2}$ Quantum Hall State Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236807	journal	December 2007
Fractional quantum Hall effect and Chern-Simons gauge theories Lopez, Ana; Fradkin, Eduardo Physical Review B, Vol. 44, Issue 10 https://doi.org/10.1103/PhysRevB.44.5246	journal	September 1991
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property Haldane, F. D. M. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.206602	journal	November 2004
Statistical mechanics of anyons Arovas, Daniel P.; Schrieffer, Robert; Wilczek, Frank Nuclear Physics B, Vol. 251 https://doi.org/10.1016/0550-3213(85)90252-4	journal	January 1985
Particle-hole symmetry and the composite Fermi liquid Barkeshli, Maissam; Mulligan, Michael; Fisher, Matthew P. A. Physical Review B, Vol. 92, Issue 16 https://doi.org/10.1103/PhysRevB.92.165125	journal	October 2015
Phase Transition in a Lattice Model of Superconductivity Dasgupta, C.; Halperin, B. I. Physical Review Letters, Vol. 47, Issue 21 https://doi.org/10.1103/PhysRevLett.47.1556	journal	November 1981
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
Mandelstam-'t Hooft duality in abelian lattice models Peskin, Michael E. Annals of Physics, Vol. 113, Issue 1 https://doi.org/10.1016/0003-4916(78)90252-X	journal	July 1978
Detection of composite fermions by magnetic focusing Goldman, V. J.; Su, B.; Jain, J. K. Physical Review Letters, Vol. 72, Issue 13 https://doi.org/10.1103/PhysRevLett.72.2065	journal	March 1994
Two-dimensional gas of massless Dirac fermions in graphene Novoselov, K. S.; Geim, A. K.; Morozov, S. V. Nature, Vol. 438, Issue 7065, p. 197-200 https://doi.org/10.1038/nature04233	journal	November 2005
Effective-Field-Theory Model for the Fractional Quantum Hall Effect Zhang, S. C.; Hansson, T. H.; Kivelson, S. Physical Review Letters, Vol. 62, Issue 8 https://doi.org/10.1103/physrevlett.62.980.3	journal	February 1989
How real are composite fermions? Kang, W.; Stormer, H. L.; Pfeiffer, L. N. Physica B: Condensed Matter, Vol. 211, Issue 1-4 https://doi.org/10.1016/0921-4526(94)01076-d	journal	May 1995
Particle-hole symmetry and the Pfaffian state Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd arXiv https://doi.org/10.48550/arxiv.0707.0483	text	January 2007
Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator Wang, Chong; Potter, Andrew C.; Senthil, T. arXiv https://doi.org/10.48550/arxiv.1306.3223	text	January 2013
A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1306.3230	text	January 2013
Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator Chen, Xie; Fidkowski, Lukasz; Vishwanath, Ashvin arXiv https://doi.org/10.48550/arxiv.1306.3250	text	January 2013
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh arXiv https://doi.org/10.48550/arxiv.1502.03446	text	January 2015
Fields and fluids on curved non-relativistic spacetimes Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M. arXiv https://doi.org/10.48550/arxiv.1503.02680	text	January 2015
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M. arXiv https://doi.org/10.48550/arxiv.1503.02682	text	January 2015
Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids Wang, Chong; Senthil, T. arXiv https://doi.org/10.48550/arxiv.1507.08290	text	January 2015
The half-filled Landau level: the case for Dirac composite fermions Geraedts, Scott D.; Zaletel, Michael P.; Mong, Roger S. K. arXiv https://doi.org/10.48550/arxiv.1508.04140	text	January 2015
Baryons, monopoles and dualities in Chern-Simons-matter theories Aharony, Ofer arXiv https://doi.org/10.48550/arxiv.1512.00161	text	January 2015
Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene Zhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0509355	text	January 2005
Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets Metlitski, Max A.; Fidkowski, Lukasz; Chen, Xie arXiv https://doi.org/10.48550/arxiv.1406.3032	preprint	January 2014

Cited By (7)

Thermopower and Nernst measurements in a half-filled lowest Landau level Liu, Xiaoxue; Li, Tingxin; Zhang, Po Physical Review B, Vol. 97, Issue 24 https://doi.org/10.1103/physrevb.97.245425	journal	June 2018
Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing Pu, Songyang; Fremling, Mikael; Jain, J. K. Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/physrevb.98.075304	journal	August 2018
Laughlin states and gauge theory Nekrasov, Nikita Arnold Mathematical Journal, Vol. 5, Issue 1 https://doi.org/10.1007/s40598-019-00113-y	journal	March 2019
Geometric resonance of four-flux composite fermions Hossain, Md. Shafayat; Ma, Meng K.; Mueed, M. A. Physical Review B, Vol. 100, Issue 4 https://doi.org/10.1103/physrevb.100.041112	journal	July 2019
Universal collective modes in two-dimensional chiral superfluids Hsiao, Wei-Han Physical Review B, Vol. 100, Issue 9 https://doi.org/10.1103/physrevb.100.094510	journal	September 2019
Boundary central charge from bulk odd viscosity: Chiral superfluids Golan, Omri; Hoyos, Carlos; Moroz, Sergej Physical Review B, Vol. 100, Issue 10 https://doi.org/10.1103/physrevb.100.104512	journal	September 2019
Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing Pu, Songyang; Fremling, Mikael; Jain, J. K. arXiv https://doi.org/10.48550/arxiv.1805.09237	text	January 2018

Similar Records

The Dirac Composite Fermion of the Fractional Quantum Hall Effect

Journal Article · Sat Mar 10 00:00:00 EST 2018 · Annual Review of Condensed Matter Physics · OSTI ID:1465696

Son, Dam Thanh

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

Journal Article · Wed May 02 00:00:00 EDT 2018 · Physical Review B · OSTI ID:1465696

Nguyen, Dung Xuan; Gromov, Andrey; Son, Dam Thanh

Particle-hole symmetry and composite fermions in fractional quantum Hall states

Journal Article · Tue May 29 00:00:00 EDT 2018 · Physical Review B · OSTI ID:1465696

Nguyen, Dung Xuan; Golkar, Siavash; Roberts, Matthew M.; +1 more

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
quantum Hall effect

Title: The Dirac composite fermion of the fractional quantum Hall effect

Citation Formats

References (52)

Cited By (7)

Similar Records

Related Subjects