Microlensing of x-ray pulsars: A method to detect primordial black hole dark matter
Abstract
Primordial black holes (PBHs) with a mass from 10-16 to 10-11 M⊙ may comprise 100% of dark matter. Due to a combination of wave and finite source size effects, the traditional microlensing of stars does not probe this mass range. Here, we point out that x-ray pulsars with higher photon energies and smaller source sizes are good candidate sources for microlensing for this mass window. Among the existing x-ray pulsars, the Small Magellanic Cloud (SMC) X-1 source is found to be the best candidate because of its apparent brightness and long distance from Earth. We have analyzed the existing observation data of SMC X-1 by the RXTE telescope (around 10 days) and found that PBH as 100% of dark matter is close to but not yet excluded. Lastly, future longer observation of this source by x-ray telescopes with larger effective areas such as AstroSat, Athena, Lynx, and eXTP can potentially close the last mass window where PBHs can make up all of dark matter.
- Authors:
-
[2]
- Univ. of Wisconsin, Madison, WI (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Univ. of Wisconsin, Madison, WI (United States)
- Publication Date:
- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1570845
- Alternate Identifier(s):
- OSTI ID: 1546269
- Report Number(s):
- arXiv:1812.01427; FERMILAB-PUB-19-516-T
Journal ID: ISSN 2470-0010; PRVDAQ; oai:inspirehep.net:1706804
- Grant/Contract Number:
- AC02-07CH11359; SC0017647
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 12; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Bai, Yang, and Orlofsky, Nicholas. Microlensing of x-ray pulsars: A method to detect primordial black hole dark matter. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.123019.
Bai, Yang, & Orlofsky, Nicholas. Microlensing of x-ray pulsars: A method to detect primordial black hole dark matter. United States. doi:10.1103/PhysRevD.99.123019.
Bai, Yang, and Orlofsky, Nicholas. Mon .
"Microlensing of x-ray pulsars: A method to detect primordial black hole dark matter". United States. doi:10.1103/PhysRevD.99.123019. https://www.osti.gov/servlets/purl/1570845.
@article{osti_1570845,
title = {Microlensing of x-ray pulsars: A method to detect primordial black hole dark matter},
author = {Bai, Yang and Orlofsky, Nicholas},
abstractNote = {Primordial black holes (PBHs) with a mass from 10-16 to 10-11 M⊙ may comprise 100% of dark matter. Due to a combination of wave and finite source size effects, the traditional microlensing of stars does not probe this mass range. Here, we point out that x-ray pulsars with higher photon energies and smaller source sizes are good candidate sources for microlensing for this mass window. Among the existing x-ray pulsars, the Small Magellanic Cloud (SMC) X-1 source is found to be the best candidate because of its apparent brightness and long distance from Earth. We have analyzed the existing observation data of SMC X-1 by the RXTE telescope (around 10 days) and found that PBH as 100% of dark matter is close to but not yet excluded. Lastly, future longer observation of this source by x-ray telescopes with larger effective areas such as AstroSat, Athena, Lynx, and eXTP can potentially close the last mass window where PBHs can make up all of dark matter.},
doi = {10.1103/PhysRevD.99.123019},
journal = {Physical Review D},
number = 12,
volume = 99,
place = {United States},
year = {2019},
month = {6}
}
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Works referenced in this record:
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Do globular clusters possess dark matter haloes? A case study in NGC 2419
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Black Holes in the Early Universe
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Origin of the Soft Excess in X‐Ray Pulsars
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Primordial black holes—perspectives in gravitational wave astronomy
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Gravitational microlensing by the galactic halo
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Study of measured pulsar masses and their possible conclusions
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Accretion onto Fast X‐Ray Pulsars
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A good long look at the black hole candidates LMC X-1 and LMC X-3
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Bump Cepheids in the Magellanic Clouds: Metallicities, the Distances to the LMC and SMC, and the Pulsation‐Evolution Mass Discrepancy
journal, May 2006
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Analysis of HST/COS spectra of the bare C–O stellar core H1504+65 and a high-velocity twin in the Galactic halo
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- Astronomy & Astrophysics, Vol. 584
Effect of pulse profile variations on measurement of eccentricity in orbits of Cen X-3 and SMC X-1
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- Monthly Notices of the Royal Astronomical Society, Vol. 401, Issue 3
Femtolensing by dark matter revisited
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- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 12
EXPERIMENTAL LIMITS ON PRIMORDIAL BLACK HOLE DARK MATTER FROM THE FIRST 2 YR OF KEPLER DATA
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Evidence Against dark Matter Halos Surrounding the Globular Clusters mgc1 and ngc 2419
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eXTP: Enhanced X-ray Timing and Polarization mission
conference, July 2016
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Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ?/? 3
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Extending the MACHO search to about 10 exp 6 solar masses
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Pulse‐Phase Spectroscopy of SMC X‐1 with Chandra and XMM‐Newton : Reprocessing by a Precessing Disk?
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Can lensed stars be regarded as pointlike for microlensing by MACHOs?
journal, July 1994
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The OGLE view of microlensing towards the Magellanic Clouds - IV. OGLE-III SMC data and final conclusions on MACHOs★: The OGLE-III view of microlensing towards the SMC
journal, August 2011
- Wyrzykowski, L.; Skowron, J.; Kozłowski, S.
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The finite source size effect and wave optics in gravitational lensing
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Superorbital Phase-Resolved Analysis of smc x-1
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- The Astrophysical Journal, Vol. 773, Issue 1
The Large Observatory for X-ray Timing (LOFT)
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Features in the spectra of gamma-ray bursts
journal, August 1993
- Stanek, Krzysztof Z.; Paczynski, Bohdan; Goodman, Jeremy
- The Astrophysical Journal, Vol. 413
Voyager 1 Further Constrain Primordial Black Holes as Dark Matter
journal, January 2019
- Boudaud, Mathieu; Cirelli, Marco
- Physical Review Letters, Vol. 122, Issue 4
The X-ray spectrum of SMC X-1 observed from the Ariel V satellite
journal, November 1981
- Coe, M. J.; Burnell, S. J. B.; Engel, A. R.
- Monthly Notices of the Royal Astronomical Society, Vol. 197, Issue 2
LMC X-4 - GINGA observations and search for orbital period changes
journal, November 1991
- Levine, A.; Rappaport, S.; Putney, A.
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New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts
journal, August 2012
- Barnacka, A.; Glicenstein, J. -F.; Moderski, R.
- Physical Review D, Vol. 86, Issue 4
Limits on the Mass and Abundance of Primordial Black Holes from Quasar Gravitational Microlensing
journal, February 2017
- Mediavilla, E.; Jiménez-Vicente, J.; Muñoz, J. A.
- The Astrophysical Journal, Vol. 836, Issue 2
Axion miniclusters and Bose stars
journal, November 1993
- Kolb, Edward W.; Tkachev, Igor I.
- Physical Review Letters, Vol. 71, Issue 19
A report on Type II X-ray bursts from SMC X-1
journal, December 2018
- Rai, Binay; Pradhan, Pragati; Paul, Bikash Chandra
- Research in Astronomy and Astrophysics, Vol. 18, Issue 12
Femtolensing of gamma-ray bursters
journal, February 1992
- Gould, Andrew
- The Astrophysical Journal, Vol. 386
Constraints on primordial black holes as dark matter candidates from capture by neutron stars
journal, June 2013
- Capela, Fabio; Pshirkov, Maxim; Tinyakov, Peter
- Physical Review D, Vol. 87, Issue 12
Globular Clusters and dark Satellite Galaxies Through the Stream Velocity
journal, July 2014
- Naoz, Smadar; Narayan, Ramesh
- The Astrophysical Journal, Vol. 791, Issue 1
New cosmological constraints on primordial black holes
journal, May 2010
- Carr, B. J.; Kohri, Kazunori; Sendouda, Yuuiti
- Physical Review D, Vol. 81, Issue 10
Phase Variation in the Pulse Profile of SMC X-1
journal, October 2004
- Neilsen, J.; Hickox, R. C.; Vrtilek, S. D.
- The Astrophysical Journal, Vol. 616, Issue 2
Dark matter triggers of supernovae
journal, September 2015
- Graham, Peter W.; Rajendran, Surjeet; Varela, Jaime
- Physical Review D, Vol. 92, Issue 6
SUZAKU X-RAY SPECTRA AND PULSE PROFILE VARIATIONS DURING THE SUPERORBITAL CYCLE OF LMC X-4
journal, August 2010
- Hung, Li-Wei; Hickox, Ryan C.; Boroson, Bram S.
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Athena: the X-ray observatory to study the hot and energetic Universe
journal, May 2015
- Barcons, X.; Nandra, K.; Barret, D.
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The Dark Matter halo of the Milky Way, AD 2013
journal, July 2013
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Limits on the Macho content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
journal, April 2007
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Dark quark nuggets
journal, March 2019
- Bai, Yang; Long, Andrew J.; Lu, Sida
- Physical Review D, Vol. 99, Issue 5
Understanding caustic crossings in giant arcs: Characteristic scales, event rates, and constraints on compact dark matter
journal, January 2018
- Oguri, Masamune; Diego, Jose M.; Kaiser, Nick
- Physical Review D, Vol. 97, Issue 2
Tracking the Orbital and Superorbital Periods of SMC X‐1
journal, November 2007
- Trowbridge, Sarah; Nowak, Michael A.; Wilms, Jorn
- The Astrophysical Journal, Vol. 670, Issue 1
A centrally heated dark halo for our Galaxy
journal, November 2016
- Cole, D. R.; Binney, James
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 1
The LOFT mission concept
journal, April 2018
- Vacchi, A.
- Nuclear and Particle Physics Proceedings, Vol. 297-299
Forty eclipsing binaries in the Small Magellanic Cloud: fundamental parameters and Cloud distance: SMC eclipsing binaries
journal, January 2005
- Hilditch, R. W.; Howarth, I. D.; Harries, T. J.
- Monthly Notices of the Royal Astronomical Society, Vol. 357, Issue 1
Gas-rich and gas-poor structures through the stream velocity effect
journal, May 2016
- Popa, Cristina; Naoz, Smadar; Marinacci, Federico
- Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 2
Microlensing of Kepler Stars as a Method of Detecting Primordial Black Hole Dark Matter
journal, December 2011
- Griest, Kim; Lehner, Matthew J.; Cieplak, Agnieszka M.
- Physical Review Letters, Vol. 107, Issue 23
MACHO Project Limits on Black Hole Dark Matter in the 1–30 [ITAL]M[/ITAL][TINF]⊙[/TINF] Range
journal, April 2001
- Alcock, C.; Allsman, R. A.; Alves, D. R.
- The Astrophysical Journal, Vol. 550, Issue 2
Ultraviolet diversity of Type Ia Supernovae
journal, June 2016
- Foley, Ryan J.; Pan, Yen-Chen; Brown, P.
- Monthly Notices of the Royal Astronomical Society, Vol. 461, Issue 2
Gravitational microlensing as a method of detecting disk dark matter and faint disk stars
journal, May 1991
- Griest, Kim; Alcock, Charles; Axelrod, Timothy S.
- The Astrophysical Journal, Vol. 372
Works referencing / citing this record:
The Large Observatory for X-ray Timing (LOFT)
journal, August 2011
- Feroci, M.; Stella, L.; van der Klis, M.
- Experimental Astronomy, Vol. 34, Issue 2
The LOFT mission concept
journal, April 2018
- Vacchi, A.
- Nuclear and Particle Physics Proceedings, Vol. 297-299
A good long look at the black hole candidates LMC X-1 and LMC X-3
journal, January 2001
- Nowak, M. A.; Wilms, J.; Heindl, W. A.
- Monthly Notices of the Royal Astronomical Society, Vol. 320, Issue 3
Study of measured pulsar masses and their possible conclusions
journal, January 2011
- Zhang, C. M.; Wang, J.; Zhao, Y. H.
- Astronomy & Astrophysics, Vol. 527
Analysis of HST/COS spectra of the bare C–O stellar core H1504+65 and a high-velocity twin in the Galactic halo
journal, November 2015
- Werner, K.; Rauch, T.
- Astronomy & Astrophysics, Vol. 584
Limits on the Macho content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
journal, April 2007
- Tisserand, P.; Le Guillou, L.; Afonso, C.
- Astronomy & Astrophysics, Vol. 469, Issue 2
Gravitational microlensing by the galactic halo
journal, May 1986
- Paczynski, B.
- The Astrophysical Journal, Vol. 304
LMC X-4 - GINGA observations and search for orbital period changes
journal, November 1991
- Levine, A.; Rappaport, S.; Putney, A.
- The Astrophysical Journal, Vol. 381
Extending the MACHO search to about 10 exp 6 solar masses
journal, June 1992
- Gould, Andrew
- The Astrophysical Journal, Vol. 392
Can lensed stars be regarded as pointlike for microlensing by MACHOs?
journal, July 1994
- Witt, Hans J.; Mao, Shude
- The Astrophysical Journal, Vol. 430
Gravitational microlensing as a method of detecting disk dark matter and faint disk stars
journal, May 1991
- Griest, Kim; Alcock, Charles; Axelrod, Timothy S.
- The Astrophysical Journal, Vol. 372
Femtolensing of gamma-ray bursters
journal, February 1992
- Gould, Andrew
- The Astrophysical Journal, Vol. 386
Features in the spectra of gamma-ray bursts
journal, August 1993
- Stanek, Krzysztof Z.; Paczynski, Bohdan; Goodman, Jeremy
- The Astrophysical Journal, Vol. 413
MACHO Project Limits on Black Hole Dark Matter in the 1–30 [ITAL]M[/ITAL][TINF]⊙[/TINF] Range
journal, April 2001
- Alcock, C.; Allsman, R. A.; Alves, D. R.
- The Astrophysical Journal, Vol. 550, Issue 2
Accretion onto Fast X‐Ray Pulsars
journal, May 2004
- Rappaport, S. A.; Fregeau, J. M.; Spruit, H.
- The Astrophysical Journal, Vol. 606, Issue 1
Origin of the Soft Excess in X‐Ray Pulsars
journal, October 2004
- Hickox, Ryan C.; Narayan, Ramesh; Kallman, Timothy R.
- The Astrophysical Journal, Vol. 614, Issue 2
Phase Variation in the Pulse Profile of SMC X-1
journal, October 2004
- Neilsen, J.; Hickox, R. C.; Vrtilek, S. D.
- The Astrophysical Journal, Vol. 616, Issue 2
Pulse‐Phase Spectroscopy of SMC X‐1 with Chandra and XMM‐Newton : Reprocessing by a Precessing Disk?
journal, November 2005
- Hickox, R. C.; Vrtilek, S. D.
- The Astrophysical Journal, Vol. 633, Issue 2
Bump Cepheids in the Magellanic Clouds: Metallicities, the Distances to the LMC and SMC, and the Pulsation‐Evolution Mass Discrepancy
journal, May 2006
- Keller, S. C.; Wood, P. R.
- The Astrophysical Journal, Vol. 642, Issue 2
Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ?/? 3
journal, January 2006
- Graham, Alister W.; Merritt, David; Moore, Ben
- The Astronomical Journal, Vol. 132, Issue 6
Tracking the Orbital and Superorbital Periods of SMC X‐1
journal, November 2007
- Trowbridge, Sarah; Nowak, Michael A.; Wilms, Jorn
- The Astrophysical Journal, Vol. 670, Issue 1
SUZAKU X-RAY SPECTRA AND PULSE PROFILE VARIATIONS DURING THE SUPERORBITAL CYCLE OF LMC X-4
journal, August 2010
- Hung, Li-Wei; Hickox, Ryan C.; Boroson, Bram S.
- The Astrophysical Journal, Vol. 720, Issue 2
Evidence Against dark Matter Halos Surrounding the Globular Clusters mgc1 and ngc 2419
journal, October 2011
- Conroy, Charlie; Loeb, Abraham; Spergel, David N.
- The Astrophysical Journal, Vol. 741, Issue 2
Superorbital Phase-Resolved Analysis of smc x-1
journal, July 2013
- Hu, Chin-Ping; Chou, Yi; Yang, Ting-Chang
- The Astrophysical Journal, Vol. 773, Issue 1
EXPERIMENTAL LIMITS ON PRIMORDIAL BLACK HOLE DARK MATTER FROM THE FIRST 2 YR OF KEPLER DATA
journal, April 2014
- Griest, Kim; Cieplak, Agnieszka M.; Lehner, Matthew J.
- The Astrophysical Journal, Vol. 786, Issue 2
Gravitational lenses
journal, February 1994
- Refsdal, S.; Surdej, J.
- Reports on Progress in Physics, Vol. 57, Issue 2
Primordial black holes—perspectives in gravitational wave astronomy
journal, February 2018
- Sasaki, Misao; Suyama, Teruaki; Tanaka, Takahiro
- Classical and Quantum Gravity, Vol. 35, Issue 6
The finite source size effect and wave optics in gravitational lensing
journal, January 2006
- Matsunaga, Norihito; Yamamoto, Kazuhiro
- Journal of Cosmology and Astroparticle Physics, Vol. 2006, Issue 01
The Dark Matter halo of the Milky Way, AD 2013
journal, July 2013
- Nesti, Fabrizio; Salucci, Paolo
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 07
Femtolensing by dark matter revisited
journal, December 2018
- Katz, Andrey; Kopp, Joachim; Sibiryakov, Sergey
- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 12
A report on Type II X-ray bursts from SMC X-1
journal, December 2018
- Rai, Binay; Pradhan, Pragati; Paul, Bikash Chandra
- Research in Astronomy and Astrophysics, Vol. 18, Issue 12
Athena: the X-ray observatory to study the hot and energetic Universe
journal, May 2015
- Barcons, X.; Nandra, K.; Barret, D.
- Journal of Physics: Conference Series, Vol. 610
Globular Clusters and dark Satellite Galaxies Through the Stream Velocity
journal, July 2014
- Naoz, Smadar; Narayan, Ramesh
- The Astrophysical Journal, Vol. 791, Issue 1
Black Holes in the Early Universe
journal, August 1974
- Carr, B. J.; Hawking, S. W.
- Monthly Notices of the Royal Astronomical Society, Vol. 168, Issue 2
The X-ray spectrum of SMC X-1 observed from the Ariel V satellite
journal, November 1981
- Coe, M. J.; Burnell, S. J. B.; Engel, A. R.
- Monthly Notices of the Royal Astronomical Society, Vol. 197, Issue 2
Do globular clusters possess dark matter haloes? A case study in NGC 2419
journal, November 2012
- Ibata, R.; Nipoti, C.; Sollima, A.
- Monthly Notices of the Royal Astronomical Society, Vol. 428, Issue 4
Gas-rich and gas-poor structures through the stream velocity effect
journal, May 2016
- Popa, Cristina; Naoz, Smadar; Marinacci, Federico
- Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 2
Ultraviolet diversity of Type Ia Supernovae
journal, June 2016
- Foley, Ryan J.; Pan, Yen-Chen; Brown, P.
- Monthly Notices of the Royal Astronomical Society, Vol. 461, Issue 2
A centrally heated dark halo for our Galaxy
journal, November 2016
- Cole, D. R.; Binney, James
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 1
New cosmological constraints on primordial black holes
journal, May 2010
- Carr, B. J.; Kohri, Kazunori; Sendouda, Yuuiti
- Physical Review D, Vol. 81, Issue 10
New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts
journal, August 2012
- Barnacka, A.; Glicenstein, J. -F.; Moderski, R.
- Physical Review D, Vol. 86, Issue 4
Constraints on primordial black holes as dark matter candidates from capture by neutron stars
journal, June 2013
- Capela, Fabio; Pshirkov, Maxim; Tinyakov, Peter
- Physical Review D, Vol. 87, Issue 12
Dark matter triggers of supernovae
journal, September 2015
- Graham, Peter W.; Rajendran, Surjeet; Varela, Jaime
- Physical Review D, Vol. 92, Issue 6
Primordial black holes as dark matter
journal, October 2016
- Carr, Bernard; Kühnel, Florian; Sandstad, Marit
- Physical Review D, Vol. 94, Issue 8
Understanding caustic crossings in giant arcs: Characteristic scales, event rates, and constraints on compact dark matter
journal, January 2018
- Oguri, Masamune; Diego, Jose M.; Kaiser, Nick
- Physical Review D, Vol. 97, Issue 2
Dark quark nuggets
journal, March 2019
- Bai, Yang; Long, Andrew J.; Lu, Sida
- Physical Review D, Vol. 99, Issue 5
Microlensing of Kepler Stars as a Method of Detecting Primordial Black Hole Dark Matter
journal, December 2011
- Griest, Kim; Lehner, Matthew J.; Cieplak, Agnieszka M.
- Physical Review Letters, Vol. 107, Issue 23
Voyager 1 Further Constrain Primordial Black Holes as Dark Matter
journal, January 2019
- Boudaud, Mathieu; Cirelli, Marco
- Physical Review Letters, Vol. 122, Issue 4
Axion miniclusters and Bose stars
journal, November 1993
- Kolb, Edward W.; Tkachev, Igor I.
- Physical Review Letters, Vol. 71, Issue 19
Forty eclipsing binaries in the Small Magellanic Cloud: fundamental parameters and Cloud distance: SMC eclipsing binaries
journal, January 2005
- Hilditch, R. W.; Howarth, I. D.; Harries, T. J.
- Monthly Notices of the Royal Astronomical Society, Vol. 357, Issue 1
Effect of pulse profile variations on measurement of eccentricity in orbits of Cen X-3 and SMC X-1
journal, January 2010
- Raichur, Harsha; Paul, Biswajit
- Monthly Notices of the Royal Astronomical Society, Vol. 401, Issue 3
The OGLE view of microlensing towards the Magellanic Clouds - IV. OGLE-III SMC data and final conclusions on MACHOs★: The OGLE-III view of microlensing towards the SMC
journal, August 2011
- Wyrzykowski, L.; Skowron, J.; Kozłowski, S.
- Monthly Notices of the Royal Astronomical Society, Vol. 416, Issue 4
eXTP: Enhanced X-ray Timing and Polarization mission
conference, July 2016
- Zhang, S. N.; Feroci, M.; Santangelo, A.
- SPIE Astronomical Telescopes + Instrumentation, SPIE Proceedings
Limits on the Mass and Abundance of Primordial Black Holes from Quasar Gravitational Microlensing
journal, February 2017
- Mediavilla, E.; Jiménez-Vicente, J.; Muñoz, J. A.
- The Astrophysical Journal, Vol. 836, Issue 2
Revisiting constraints on asteroid-mass primordial black holes as dark matter candidates
journal, August 2019
- Montero-Camacho, Paulo; Fang, Xiao; Vasquez, Gabriel
- Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 08
Primordial Black Holes as a Dark Matter Candidate Are Severely Constrained by the Galactic Center 511 keV -Ray Line
journal, December 2019
- Laha, Ranjan
- Physical Review Letters, Vol. 123, Issue 25
Gamma-ray burst lensing parallax: Closing the primordial black hole dark matter mass window
journal, February 2020
- Jung, Sunghoon; Kim, TaeHun
- Physical Review Research, Vol. 2, Issue 1