Weiss oscillations and particle-hole symmetry at the half-filled Landau level
Abstract
Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ± e2/2h at half filling. Here, we study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015)]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. We find an approximate “sum rule” obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.
- Authors:
-
- Stanford Univ., CA (United States). Dept. of Physics
- Stanford Univ., CA (United States). Dept. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Univ. of California, Riverside, CA (United States). Dept. of Physics and Astronomy
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Natural Sciences and Engineering Research Council of Canada (NSERC)
- OSTI Identifier:
- 1369390
- Alternate Identifier(s):
- OSTI ID: 1364077
- Grant/Contract Number:
- AC02-76SF00515; PHY-11-25915
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Cheung, Alfred K. C., Raghu, S., and Mulligan, Michael. Weiss oscillations and particle-hole symmetry at the half-filled Landau level. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.95.235424.
Cheung, Alfred K. C., Raghu, S., & Mulligan, Michael. Weiss oscillations and particle-hole symmetry at the half-filled Landau level. United States. https://doi.org/10.1103/PhysRevB.95.235424
Cheung, Alfred K. C., Raghu, S., and Mulligan, Michael. Thu .
"Weiss oscillations and particle-hole symmetry at the half-filled Landau level". United States. https://doi.org/10.1103/PhysRevB.95.235424. https://www.osti.gov/servlets/purl/1369390.
@article{osti_1369390,
title = {Weiss oscillations and particle-hole symmetry at the half-filled Landau level},
author = {Cheung, Alfred K. C. and Raghu, S. and Mulligan, Michael},
abstractNote = {Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal ± e2/2h at half filling. Here, we study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son [Son, Phys. Rev. X 5, 031027 (2015)]. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field the oscillations occur symmetrically as the electron density is varied about half filling. We find an approximate “sum rule” obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long-wavelength physics.},
doi = {10.1103/PhysRevB.95.235424},
journal = {Physical Review B},
number = 23,
volume = 95,
place = {United States},
year = {Thu Jun 15 00:00:00 EDT 2017},
month = {Thu Jun 15 00:00:00 EDT 2017}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 18 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Is the Composite Fermion a Dirac Particle?
journal, September 2015
- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3
Universal Conductivity at the Quantum Hall Liquid to Insulator Transition
journal, May 1995
- Shahar, D.; Tsui, D. C.; Shayegan, M.
- Physical Review Letters, Vol. 74, Issue 22
Composite-fermion Hall conductance at ν=
journal, June 1997
- Kivelson, S. A.; Lee, D-H.; Krotov, Y.
- Physical Review B, Vol. 55, Issue 23
Universality and phase diagram around half-filled Landau levels
journal, December 1996
- Wong, L. W.; Jiang, H. W.; Schaff, W. J.
- Physical Review B, Vol. 54, Issue 24
Theory of magnetotransport in two-dimensional electron systems with unidirectional periodic modulation
journal, June 1990
- Zhang, Chao; Gerhardts, Rolf R.
- Physical Review B, Vol. 41, Issue 18
What Determines the Fermi Wave Vector of Composite Fermions?
journal, November 2014
- Kamburov, D.; Liu, Yang; Mueed, M. A.
- Physical Review Letters, Vol. 113, Issue 19
Particle-hole symmetry and electromagnetic response of a half-filled Landau level
journal, March 2017
- Levin, Michael; Son, Dam Thanh
- Physical Review B, Vol. 95, Issue 12
Evidence for Charge-Flux Duality near the Quantum Hall Liquid-to-Insulator Transition
journal, October 1996
- Shahar, D.; Tsui, D. C.; Shayegan, M.
- Science, Vol. 274, Issue 5287
Incompressible Paired Hall State, Stripe Order, and the Composite Fermion Liquid Phase in Half-Filled Landau Levels
journal, May 2000
- Rezayi, E. H.; Haldane, F. D. M.
- Physical Review Letters, Vol. 84, Issue 20
Linear response theory revisited III: One‐body response formulas and generalized Boltzmann equations
journal, February 1982
- Charbonneau, M.; van Vliet, K. M.; Vasilopoulos, P.
- Journal of Mathematical Physics, Vol. 23, Issue 2
dc Transport of Composite Fermions in Weak Periodic Potentials
journal, May 1998
- Smet, J. H.; von Klitzing, K.; Weiss, D.
- Physical Review Letters, Vol. 80, Issue 20
Novel magnetoresistance oscillations in a periodically modulated two-dimensional electron gas
journal, March 1989
- Gerhardts, R. R.; Weiss, D.; Klitzing, K. v.
- Physical Review Letters, Vol. 62, Issue 10
Experimental evidence for composite fermions
journal, October 1997
- Willett, Robert L.
- Advances in Physics, Vol. 46, Issue 5
Commensurability Oscillations of Composite Fermions Induced by the Periodic Potential of a Wigner Crystal
journal, August 2016
- Deng, H.; Liu, Y.; Jo, I.
- Physical Review Letters, Vol. 117, Issue 9
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016
- Metlitski, Max A.; Vishwanath, Ashvin
- Physical Review B, Vol. 93, Issue 24
Composite Fermions in Modulated Structures: Transport and Surface Acoustic Waves
journal, May 1998
- von Oppen, Felix; Stern, Ady; Halperin, Bertrand I.
- Physical Review Letters, Vol. 80, Issue 20
Positive Magnetoresistance of Composite Fermion Systems with a Weak One-Dimensional Density Modulation
journal, September 1999
- Zwerschke, S. D. M.; Gerhardts, R. R.
- Physical Review Letters, Vol. 83, Issue 13
Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions
journal, October 2015
- Balram, Ajit C.; Tőke, Csaba; Jain, J. K.
- Physical Review Letters, Vol. 115, Issue 18
Commensurability Oscillations of Hole-Flux Composite Fermions
journal, December 2012
- Kamburov, D.; Shayegan, M.; Pfeiffer, L. N.
- Physical Review Letters, Vol. 109, Issue 23
A duality web in dimensions and condensed matter physics
journal, November 2016
- Seiberg, Nathan; Senthil, T.; Wang, Chong
- Annals of Physics, Vol. 374
Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field
journal, May 2008
- Tahir, M.; Sabeeh, K.
- Physical Review B, Vol. 77, Issue 19
Recent progress in the theory of composite fermions near even-denominator filling factors
journal, July 1996
- Read, N.
- Surface Science, Vol. 361-362
Metallic phase of the quantum Hall system at even-denominator filling fractions
journal, October 1992
- Kalmeyer, Vadim; Zhang, Shou-Cheng
- Physical Review B, Vol. 46, Issue 15
Mirror symmetry and the half-filled Landau level
journal, December 2015
- Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo
- Physical Review B, Vol. 92, Issue 23
Transport anomalies in the lowest Landau level of two-dimensional electrons at half-filling
journal, December 1989
- Jiang, H. W.; Stormer, H. L.; Isui, D. C.
- Physical Review B, Vol. 40, Issue 17
Theory of the half-filled Landau level
journal, March 1993
- Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
- Physical Review B, Vol. 47, Issue 12
Magnetoresistance Oscillations in a Two-Dimensional Electron Gas Induced by a Submicrometer Periodic Potential
journal, January 1989
- Weiss, D.; Klitzing, K. V.; Ploog, K.
- Europhysics Letters (EPL), Vol. 8, Issue 2
How real are composite fermions?
journal, December 1993
- Kang, W.; Stormer, H. L.; Pfeiffer, L. N.
- Physical Review Letters, Vol. 71, Issue 23
Commensurate Composite Fermions in Weak Periodic Electrostatic Potentials: Direct Evidence of a Periodic Effective Magnetic Field
journal, September 1999
- Smet, J. H.; Jobst, S.; von Klitzing, K.
- Physical Review Letters, Vol. 83, Issue 13
Emergent particle-hole symmetry in the half-filled Landau level
journal, August 2016
- Mulligan, Michael; Raghu, S.; Fisher, Matthew P. A.
- Physical Review B, Vol. 94, Issue 7
Velocity Shift of Surface Acoustic Waves due to Interaction with Composite Fermions in a Modulated Structure
journal, August 1998
- Mirlin, A.; Wölfle, P.; Levinson, Y.
- Physical Review Letters, Vol. 81, Issue 5
Particle-hole symmetry and the composite Fermi liquid
journal, October 2015
- Barkeshli, Maissam; Mulligan, Michael; Fisher, Matthew P. A.
- Physical Review B, Vol. 92, Issue 16
Electrical and thermal properties of a two-dimensional electron gas in a one-dimensional periodic potential
journal, August 1992
- Peeters, F. M.; Vasilopoulos, P.
- Physical Review B, Vol. 46, Issue 8
Quasiclassical calculation of magnetoresistance oscillations of a two-dimensional electron gas in spatially periodic magnetic and electrostatic fields
journal, April 1996
- Gerhardts, Rolf R.
- Physical Review B, Vol. 53, Issue 16
Geometric Resonance of Composite Fermion Cyclotron Orbits with a Fictitious Magnetic Field Modulation
journal, September 1999
- Willett, R. L.; West, K. W.; Pfeiffer, L. N.
- Physical Review Letters, Vol. 83, Issue 13
Two-dimensional gas of massless Dirac fermions in graphene
journal, November 2005
- Novoselov, K. S.; Geim, A. K.; Morozov, S. V.
- Nature, Vol. 438, Issue 7065, p. 197-200
Experimental evidence for composite fermions
journal, May 1997
- Willett, R. L.
- Semiconductor Science and Technology, Vol. 12, Issue 5
dc Transport of Composite Fermions in Weak Periodic Potentials
text, January 1998
- Smet, J. H.; Klitzing, Klaus von; Weiss, Dieter
- Universität Regensburg
Commensurate Composite Fermions in Weak Periodic Electrostatic Potentials: Direct Evidence of a Periodic Effective Magnetic Field
text, January 1999
- Smet, J. H.; Jobst, S.; Klitzing, Klaus von
- Universität Regensburg
Magnetoresistance Oscillations in a Two-Dimensional Electron Gas Induced by a Submicrometer Periodic Potential
text, January 1989
- Weiss, Dieter; Klitzing, Klaus von; Ploog, K.
- Universität Regensburg
How real are composite fermions?
journal, May 1995
- Kang, W.; Stormer, H. L.; Pfeiffer, L. N.
- Physica B: Condensed Matter, Vol. 211, Issue 1-4
Novel Magnetoresistance Oscillations in a Periodically Modulated Two-Dimensional Electron Gas
text, January 1989
- Gerhardts, R.; Weiss, Dieter; Klitzing, Klaus von
- Universität Regensburg
Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field
text, January 2007
- Tahir, M.; Sabeeh, K.
- arXiv
Mirror symmetry and the half-filled Landau level
text, January 2015
- Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo
- arXiv
Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
text, January 2015
- Balram, Ajit C.; Tőke, Csaba; Jain, J. K.
- arXiv
Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
text, January 2015
- Wang, Chong; Senthil, T.
- arXiv
Particle-hole symmetry and electromagnetic response of a half-filled Landau level
text, January 2016
- Levin, Michael; Son, Dam Thanh
- arXiv
Evidence for charge-flux duality near the quantum Hall liquid to insulator transition
text, January 1995
- Shahar, D.; Tsui, D. C.; Shayegan, M.
- arXiv
Universality and Phase Diagram around Half-filled Landau Level
text, January 1997
- Wong, L. W.; Jiang, H. W.; Schaff, W. J.
- arXiv
Velocity shift of surface acoustic waves due to interaction with composite fermions in a modulated structure
text, January 1998
- Mirlin, A. D.; Woelfle, P.; Levinson, Y.
- arXiv
Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
text, January 1999
- Rezayi, E. H.; Haldane, F. D. M.
- arXiv
Commensurate Composite Fermions in weak periodic electrostatic potentials: Direct evidence of a periodic effective magnetic field
text, January 1999
- Smet, J.; Jobst, S.; Klitzing, K.
- Universität Regensburg
Works referencing / citing this record:
Thermopower and Nernst measurements in a half-filled lowest Landau level
journal, June 2018
- Liu, Xiaoxue; Li, Tingxin; Zhang, Po
- Physical Review B, Vol. 97, Issue 24
Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing
journal, August 2018
- Pu, Songyang; Fremling, Mikael; Jain, J. K.
- Physical Review B, Vol. 98, Issue 7
Lattice Monte Carlo for Quantum Hall States on a Torus
text, January 2017
- Wang, Jie; Geraedts, Scott D.; Rezayi, E. H.
- arXiv
Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
text, January 2018
- Pu, Songyang; Fremling, Mikael; Jain, J. K.
- arXiv