Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
Abstract
Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons ω0 is close to the energy gap EG, but |ω0 – EG| is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor S(ω,k) of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit k → 0. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densitiesmore »
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Chicago, IL (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1776992
- Alternate Identifier(s):
- OSTI ID: 1821660
- Grant/Contract Number:
- FG02-13ER41958; SC0009924
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 3 Journal Issue: 2; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Fractional quantum Hall effect; Topological phases of matter; Strongly correlated systems; Two-dimensional electron system; Effective field theory
Citation Formats
Nguyen, Dung Xuan, and Son, Dam Thanh. Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering. United States: N. p., 2021.
Web. doi:10.1103/PhysRevResearch.3.023040.
Nguyen, Dung Xuan, & Son, Dam Thanh. Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering. United States. https://doi.org/10.1103/PhysRevResearch.3.023040
Nguyen, Dung Xuan, and Son, Dam Thanh. Tue .
"Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering". United States. https://doi.org/10.1103/PhysRevResearch.3.023040.
@article{osti_1776992,
title = {Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering},
author = {Nguyen, Dung Xuan and Son, Dam Thanh},
abstractNote = {Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons ω0 is close to the energy gap EG, but |ω0 – EG| is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor S(ω,k) of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit k → 0. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes. We propose that Raman scattering provides a way to probe the bulk of the ν = 5/2 quantum Hall state to determine its nature.},
doi = {10.1103/PhysRevResearch.3.023040},
journal = {Physical Review Research},
number = 2,
volume = 3,
place = {United States},
year = {Tue Apr 13 00:00:00 EDT 2021},
month = {Tue Apr 13 00:00:00 EDT 2021}
}
https://doi.org/10.1103/PhysRevResearch.3.023040
Works referenced in this record:
Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982
- Tsui, D. C.; Stormer, H. L.; Gossard, A. C.
- Physical Review Letters, Vol. 48, Issue 22
Is the Composite Fermion a Dirac Particle?
journal, September 2015
- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3
Theory of the disordered quantum thermal Hall state: Emergent symmetry and phase diagram
journal, April 2018
- Lian, Biao; Wang, Juven
- Physical Review B, Vol. 97, Issue 16
Comment on “Interpretation of thermal conductance of the edge”
journal, October 2018
- Feldman, D. E.
- Physical Review B, Vol. 98, Issue 16
Inelastic Light Scattering from Semiconductor Plasmas in a Magnetic Field
journal, February 1970
- Blum, F. A.
- Physical Review B, Vol. 1, Issue 3
Particle-hole symmetry and composite fermions in fractional quantum Hall states
journal, May 2018
- Nguyen, Dung Xuan; Golkar, Siavash; Roberts, Matthew M.
- Physical Review B, Vol. 97, Issue 19
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983
- Laughlin, R. B.
- Physical Review Letters, Vol. 50, Issue 18
Bimetric Theory of Fractional Quantum Hall States
journal, November 2017
- Gromov, Andrey; Son, Dam Thanh
- Physical Review X, Vol. 7, Issue 4
Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
journal, October 2018
- Liu, Zhao; Gromov, Andrey; Papić, Zlatko
- Physical Review B, Vol. 98, Issue 15
Chiral Gravitons in Fractional Quantum Hall Liquids
journal, September 2019
- Liou, Shiuan-Fan; Haldane, F. D. M.; Yang, Kun
- Physical Review Letters, Vol. 123, Issue 14
Interpretation of thermal conductance of the edge
journal, March 2018
- Simon, Steven H.
- Physical Review B, Vol. 97, Issue 12
Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
journal, July 2018
- Mross, David F.; Oreg, Yuval; Stern, Ady
- Physical Review Letters, Vol. 121, Issue 2
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States
journal, April 1984
- Halperin, B. I.
- Physical Review Letters, Vol. 52, Issue 18
Light scattering by collective excitations in the fractional quantum hall regime
journal, June 1998
- Pinczuk, A.; Dennis, B. S.; Pfeiffer, L. N.
- Physica B: Condensed Matter, Vol. 249-251
Dispersion of the Excitations of Fractional Quantum Hall States
journal, April 2009
- Kukushkin, I. V.; Smet, J. H.; Scarola, V. W.
- Science, Vol. 324, Issue 5930
Factorization Of Hard Processes In QCD
book, July 1989
- Mueller, A. H.; Collins, John C.; Soper, Davison E.
- Perturbative QCD
Magnetic Flux, Angular Momentum, and Statistics
journal, April 1982
- Wilczek, Frank
- Physical Review Letters, Vol. 48, Issue 17
Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory
journal, May 1956
- Luttinger, J. M.
- Physical Review, Vol. 102, Issue 4
Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
journal, April 2017
- Yang, Bo; Hu, Zi-Xiang; Lee, Ching Hua
- Physical Review Letters, Vol. 118, Issue 14
Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
journal, February 2019
- Ma, Ken K. W.; Feldman, D. E.
- Physical Review B, Vol. 99, Issue 8
Inelastic Light Scattering by Gap Excitations of Fractional Quantum Hall States at
journal, January 2000
- Kang, Moonsoo; Pinczuk, A.; Dennis, B. S.
- Physical Review Letters, Vol. 84, Issue 3
Non-Abelian anyons and topological quantum computation
journal, September 2008
- Nayak, Chetan; Simon, Steven H.; Stern, Ady
- Reviews of Modern Physics, Vol. 80, Issue 3
Partial Equilibration of the Anti-Pfaffian Edge due to Majorana Disorder
journal, March 2020
- Simon, Steven H.; Rosenow, Bernd
- Physical Review Letters, Vol. 124, Issue 12
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect
journal, April 2000
- Read, N.; Green, Dmitry
- Physical Review B, Vol. 61, Issue 15
Magneto-roton theory of collective excitations in the fractional quantum Hall effect
journal, February 1986
- Girvin, S. M.; MacDonald, A. H.; Platzman, P. M.
- Physical Review B, Vol. 33, Issue 4
Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
journal, January 2016
- Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.
- Journal of High Energy Physics, Vol. 2016, Issue 1
Particle-Hole Symmetry and the Pfaffian State
journal, December 2007
- Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
- Physical Review Letters, Vol. 99, Issue 23
Landau Level Mixing and the Ground State of the Quantum Hall Effect
journal, July 2017
- Rezayi, Edward H.
- Physical Review Letters, Vol. 119, Issue 2
Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly
journal, February 2018
- Wiegmann, P.
- Physical Review Letters, Vol. 120, Issue 8
Geometrical Description of the Fractional Quantum Hall Effect
journal, September 2011
- Haldane, F. D. M.
- Physical Review Letters, Vol. 107, Issue 11
Particle-Hole Symmetry and the Quantum Hall State
journal, December 2007
- Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan
- Physical Review Letters, Vol. 99, Issue 23
Higher-Spin Theory of the Magnetorotons
journal, November 2016
- Golkar, Siavash; Nguyen, Dung Xuan; Roberts, Matthew M.
- Physical Review Letters, Vol. 117, Issue 21
Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers
journal, February 2021
- Liu, Zhao; Balram, Ajit C.; Papić, Zlatko
- Physical Review Letters, Vol. 126, Issue 7
Effective field theory for fractional quantum Hall systems near
journal, November 2020
- Hsin, Po-Shen; Lin, Ying-Hsuan; Paquette, Natalie M.
- Physical Review Research, Vol. 2, Issue 4
Quantum coherence and Skyrmions in a bilayer quantum Hall system
journal, March 1997
- Ezawa, Z. F.
- Physical Review B, Vol. 55, Issue 12
Topological order from disorder and the quantized Hall thermal metal: Possible applications to the state
journal, July 2018
- Wang, Chong; Vishwanath, Ashvin; Halperin, Bertrand I.
- Physical Review B, Vol. 98, Issue 4
Observation of half-integer thermal Hall conductance
journal, June 2018
- Banerjee, Mitali; Heiblum, Moty; Umansky, Vladimir
- Nature, Vol. 559, Issue 7713
Nonabelions in the fractional quantum hall effect
journal, August 1991
- Moore, Gregory; Read, Nicholas
- Nuclear Physics B, Vol. 360, Issue 2-3