Fluctuations and magnetoresistance oscillations near the half-filled Landau level
Abstract
We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level (ν = 1/2) that result from the presence of a periodic one-dimensional electrostatic potential. In this work, we use the Dirac composite fermion theory of Son, where the ν = 1/2 state is described by a (2 + 1)-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge-field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger-Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field–dependent mass for the Dirac composite fermions away from ν = 1/2. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.
- Authors:
-
- Univ. of California, Riverside, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Riverside, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Hellman Foundation; National Science Foundation (NSF)
- OSTI Identifier:
- 1803898
- Grant/Contract Number:
- SC0020007; PHY-1607611
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 16; 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; Materials Science; Physics
Citation Formats
Mitra, Amartya, and Mulligan, Michael. Fluctuations and magnetoresistance oscillations near the half-filled Landau level. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.165122.
Mitra, Amartya, & Mulligan, Michael. Fluctuations and magnetoresistance oscillations near the half-filled Landau level. United States. https://doi.org/10.1103/physrevb.100.165122
Mitra, Amartya, and Mulligan, Michael. Mon .
"Fluctuations and magnetoresistance oscillations near the half-filled Landau level". United States. https://doi.org/10.1103/physrevb.100.165122. https://www.osti.gov/servlets/purl/1803898.
@article{osti_1803898,
title = {Fluctuations and magnetoresistance oscillations near the half-filled Landau level},
author = {Mitra, Amartya and Mulligan, Michael},
abstractNote = {We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level (ν = 1/2) that result from the presence of a periodic one-dimensional electrostatic potential. In this work, we use the Dirac composite fermion theory of Son, where the ν = 1/2 state is described by a (2 + 1)-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge-field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger-Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field–dependent mass for the Dirac composite fermions away from ν = 1/2. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.},
doi = {10.1103/physrevb.100.165122},
journal = {Physical Review. B},
number = 16,
volume = 100,
place = {United States},
year = {Mon Oct 14 00:00:00 EDT 2019},
month = {Mon Oct 14 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
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:
Gauge-invariant response functions of fermions coupled to a gauge field
journal, December 1994
- Kim, Yong Baek; Furusaki, Akira; Wen, Xiao-Gang
- Physical Review B, Vol. 50, Issue 24
Field Theories of Condensed Matter Physics
book, January 2013
- Fradkin, Eduardo
- Cambridge University Press
Is the Composite Fermion a Dirac Particle?
journal, September 2015
- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3
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
Composite-fermion Hall conductance at ν=
journal, June 1997
- Kivelson, S. A.; Lee, D-H.; Krotov, Y.
- Physical Review B, Vol. 55, Issue 23
Ground State of Two-Dimensional Electrons in Strong Magnetic Fields and Quantized Hall Effect
journal, April 1983
- Yoshioka, D.; Halperin, B. I.; Lee, P. A.
- Physical Review Letters, Vol. 50, Issue 16
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
Chiral-symmetry breaking in three-dimensional electrodynamics
journal, May 1984
- Pisarski, Robert D.
- Physical Review D, Vol. 29, Issue 10
de Haas-van Alphen Effect and the Specific Heat of an Electron Gas
journal, September 1973
- Holstein, T.; Norton, R. E.; Pincus, P.
- Physical Review B, Vol. 8, Issue 6
Quark gap equation in an external magnetic field
journal, February 2014
- Watson, P.; Reinhardt, H.
- Physical Review D, Vol. 89, Issue 4
Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015
- Wang, Chong; Senthil, T.
- Physical Review X, Vol. 5, Issue 4
Mirror symmetry and the half-filled Landau level
journal, December 2015
- Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo
- Physical Review B, Vol. 92, Issue 23
On Gauge Invariance and Vacuum Polarization
journal, June 1951
- Schwinger, Julian
- Physical Review, Vol. 82, Issue 5
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
Signatures of a Novel Fermi Liquid in a Two-Dimensional Composite Particle Metal
journal, December 1994
- Manoharan, H. C.; Shayegan, M.; Klepper, S. J.
- Physical Review Letters, Vol. 73, Issue 24
Experimental evidence for composite fermions
journal, May 1997
- Willett, R. L.
- Semiconductor Science and Technology, Vol. 12, Issue 5
Higher-Spin Theory of the Magnetorotons
journal, November 2016
- Golkar, Siavash; Nguyen, Dung Xuan; Roberts, Matthew M.
- Physical Review Letters, Vol. 117, Issue 21
Composite Fermi liquids in the lowest Landau level
journal, December 2016
- Wang, Chong; Senthil, T.
- Physical Review B, Vol. 94, Issue 24
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
Higher-order corrections in (2+1)-dimensional QED
journal, June 1989
- Nash, Daniel
- Physical Review Letters, Vol. 62, Issue 26
Low-energy effective theory of Fermi surface coupled with U(1) gauge field in dimensions
journal, October 2009
- Lee, Sung-Sik
- Physical Review B, Vol. 80, Issue 16
Color superconductivity and nondecoupling phenomena in (2+1)-dimensional QCD
journal, June 2001
- Miransky, V. A.; Semenoff, G. W.; Shovkovy, I. A.
- Physical Review D, Vol. 64, Issue 2
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
Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations. II. Transport properties
journal, March 2005
- Gusynin, V. P.; Sharapov, S. G.
- Physical Review B, Vol. 71, Issue 12
Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory
journal, September 2018
- Kumar, Prashant; Mulligan, Michael; Raghu, S.
- Physical Review B, Vol. 98, Issue 11
Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order
journal, August 2010
- Metlitski, Max A.; Sachdev, Subir
- Physical Review B, Vol. 82, Issue 7
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( ) Dimensions
journal, June 2016
- Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
- Physical Review Letters, Vol. 117, Issue 1
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
Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
journal, April 2015
- Miransky, Vladimir A.; Shovkovy, Igor A.
- Physics Reports, Vol. 576
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
Critical Behavior in (2+1)-Dimensional QED
journal, June 1988
- Appelquist, Thomas; Nash, Daniel; Wijewardhana, L. C. R.
- Physical Review Letters, Vol. 60, Issue 25
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
Controlled expansion for certain non-Fermi-liquid metals
journal, July 2010
- Mross, David F.; McGreevy, John; Liu, Hong
- Physical Review B, Vol. 82, Issue 4
Composite fermion Hall conductivity and the half-filled Landau level
journal, June 2019
- Kumar, Prashant; Raghu, S.; Mulligan, Michael
- Physical Review B, Vol. 99, Issue 23
Emergent reflection symmetry from nonrelativistic composite fermions
journal, May 2019
- Kumar, Prashant; Mulligan, Michael; Raghu, S.
- Physical Review B, Vol. 99, Issue 20
The half-filled Landau level: The case for Dirac composite fermions
journal, April 2016
- Geraedts, S. D.; Zaletel, M. P.; Mong, R. S. K.
- Science, Vol. 352, Issue 6282
Landau band conductivity in a two-dimensional electron system modulated by an artificial one-dimensional superlattice potential
journal, March 1989
- Winkler, R. W.; Kotthaus, J. P.; Ploog, K.
- Physical Review Letters, Vol. 62, Issue 10
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
Landau level: Half-empty versus half-full
journal, February 2016
- Murthy, Ganpathy; Shankar, R.
- Physical Review B, Vol. 93, Issue 8
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
Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field
journal, March 1996
- Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A.
- Nuclear Physics B, Vol. 462, Issue 2-3
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
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
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
Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field
journal, April 2015
- Khalilov, V. R.; Mamsurov, I. V.
- The European Physical Journal C, Vol. 75, Issue 4
Specific heat and pairing of Dirac composite fermions in the half-filled Landau level
journal, October 2019
- Rombes, Nicholas; Chakravarty, Sudip
- Annals of Physics, Vol. 409
Weiss oscillations and particle-hole symmetry at the half-filled Landau level
journal, June 2017
- Cheung, Alfred K. C.; Raghu, S.; Mulligan, Michael
- Physical Review B, Vol. 95, Issue 23
Non-Abelian bosonization and modular transformation approach to superuniversality
journal, March 2019
- Hui, Aaron; Kim, Eun-Ah; Mulligan, Michael
- Physical Review B, Vol. 99, Issue 12
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
journal, November 2004
- Haldane, F. D. M.
- Physical Review Letters, Vol. 93, Issue 20
Quantum oscillations in graphene in the presence of disorder and interactions
journal, December 2008
- Goswami, Pallab; Jia, Xun; Chakravarty, Sudip
- Physical Review B, Vol. 78, Issue 24
Particle-Vortex Duality from 3D Bosonization
journal, September 2016
- Karch, Andreas; Tong, David
- Physical Review X, Vol. 6, Issue 3
Particle-hole symmetry in the anomalous quantum Hall effect
journal, May 1984
- Girvin, S. M.
- Physical Review B, Vol. 29, Issue 10
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
Radiative corrections to chiral separation effect in QED
journal, July 2013
- Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.
- Physical Review D, Vol. 88, Issue 2
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
journal, August 2017
- Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I.
- Physical Review X, Vol. 7, Issue 3
Quantum transport of a two-dimensional electron gas in a spatially modulated magnetic field
journal, January 1993
- Peeters, F. M.; Vasilopoulos, P.
- Physical Review B, Vol. 47, Issue 3
Appearance of enhanced Weiss oscillations in graphene: Theory
journal, March 2007
- Matulis, A.; Peeters, F. M.
- Physical Review B, Vol. 75, Issue 12
A controlled expansion for certain non-Fermi liquid metals
text, January 2010
- Mross, David F.; McGreevy, John; Liu, Hong
- arXiv
Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
text, January 1995
- Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A.
- arXiv