Plasmaron

In physics, the plasmaron was proposed by Lundqvist in 1967 as a quasiparticle arising in a system that has strong plasmon-electron interactions.[1][2] In the original work, the plasmaron was proposed to describe a secondary peak (or satellite) in the photoemission spectral function of the electron gas. More precisely it was defined as an additional zero of the quasi-particle equation (ω−ϵH−Re[Σ(ω)]=0). The same authors pointed out, in a subsequent work, that this extra solution might be an artifact of the used approximations:[3]

> We want to stress again that the discussion we have given of the one-electron spectrum is based on the assumption that vertex corrections are small. As discussed in the next section recent work by Langreth [29] shows that vertex corrections in the core electron problem can have a quite large effect on the form of satellite structures, while their effect on the quasi particle properties seems to be small. Preliminary investigations by one of us (L.H.) show similar strong vertex effects on the conduction band satellite. The details of the plasmaron structure should thus not be taken very seriously.

A more mathematical discussion is provided.[4][5]

The plasmaron was also studied in more recent works in the literature.[6] It was shown, also with the support of the numerical simulations, that the plasmaron energy is an artifact of the approximation used to numerically compute the spectral function, e.g. solution of the dyson equation for the many body green function with a frequency dependent GW self-energy.[7] This approach give rise to a wrong plasmaron peak instead of the plasmon satellite which can be measured experimentally.

Despite this fact, experimental observation of a plasmaron was reported in 2010 for graphene.[8]

Also supported by earlier theoretical work.[9] However subsequent works discussed that the theoretical interpretation of the experimental measure was not correct,[10] in agreement with the fact that the plasmaron is only an artifact of the GW self-energy used with the Dyson equation. The artificial nature of the plasmaron peak was also proven via the comparison of experimental and numerical simulations for the photo-emission spectrum of bulk silicon.[11] Other works on plasmaron have been published in the literature.[12][13][14][15]

Observation of plasmaron peaks have also been reported in optical measurements of elemental bismuth[16] and in other optical measurements.[17]

## References

1. ↑ Hedin, L., Lundqvist, B. & Lundqvist, S. New structure in the single-particle spectrum of an electron gas. Solid State Commun. 5, 237-239 (1967).
2. ↑ Bengt Lundqvist (1967). "Single-particle spectrum of the degenerate electron gas". Physik der Kondensierten Materie 6 (3): 206–2017. doi:10.1007/BF02422717. Bibcode: 1967PKM.....6..206L. https://link.springer.com/article/10.1007/BF02422717.
3. ↑ L. Hedin, B. I. Lundqvist, and S. Lundqvist, J Res Natl Bur Stand A Phys Chem. 74A, 417-431 (1970)
4. ↑ Blomberg, Clas; Bergersen, Birger (1972). "Spurious Structure from Approximations to the Dyson Equation". Canadian Journal of Physics 50 (19): 2286–2293. doi:10.1139/p72-303. Bibcode: 1972CaJPh..50.2286B.
5. ↑ Bergersen, B.; Kus, F. W.; Blomberg, C. (1973). "Single Particle Green's Function in the Electron–Plasmon Approximation". Canadian Journal of Physics 51 (1): 102–110. doi:10.1139/p73-012. Bibcode: 1973CaJPh..51..102B.
6. ↑ P. von Allmen Phys. Rev. B 46, 13345 (1992)
7. ↑ F. Aryasetiawan, L. Hedin, and K. Karlsson, Phys. Rev. Lett. 77, 2268 (1996)
8. ↑ Bostwick et al. (2010-05-21). "Observation of Plasmarons in Quasi-Freestanding Doped Graphene". Science 328 (5981): 999–1002. doi:10.1126/science.1186489. PMID 20489018. Bibcode: 2010Sci...328..999B. http://edoc.mpg.de/534644.
9. ↑ Polini, Marco; Asgari, Reza; Borghi, Giovanni; Barlas, Yafis; Pereg-Barnea, T.; MacDonald, A. H. (2008). "Plasmons and the spectral function of graphene". Physical Review B 77 (8). doi:10.1103/physrevb.77.081411. Bibcode: 2008PhRvB..77h1411P.
10. ↑ Lischner, Johannes; Vigil-Fowler, Derek; Louie, Steven G. (2013). "Physical Origin of Satellites in Photoemission of Doped Graphene: AnAb Initio<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:math>Plus Cumulant Study". Physical Review Letters 110 (14). doi:10.1103/physrevlett.110.146801. PMID 25167020.GWPlus+Cumulant+Study&rft.jtitle=Physical+Review+Letters&rft.aulast=Lischner&rft.aufirst=Johannes&rft.au=Lischner, Johannes&rft.au=Vigil-Fowler, Derek&rft.au=Louie, Steven+G.&rft.date=2013&rft.volume=110&rft.issue=14&rft_id=info:doi/10.1103/physrevlett.110.146801&rft_id=info:pmid/25167020&rfr_id=info:sid/en.wikibooks.org:Physics:Plasmaron">
11. ↑ Matteo Guzzo (2011). "Valence Electron Photoemission Spectrum of Semiconductors: Ab Initio Description of Multiple Satellites.". Phys. Rev. Lett. 107 (16). doi:10.1103/PhysRevLett.107.166401. PMID 22107408. Bibcode: 2011PhRvL.107p6401G.
12. ↑ Dial, O. E.; Ashoori, R. C.; Pfeiffer, L. N.; West, K. W. (2012). "Observations of plasmarons in a two-dimensional system: Tunneling measurements using time-domain capacitance spectroscopy". Physical Review B 85 (8). doi:10.1103/physrevb.85.081306. Bibcode: 2012PhRvB..85h1306D.
13. ↑ Yamase, Hiroyuki; Bejas, Matías; Greco, Andrés (2023). "Plasmarons in high-temperature cuprate superconductors". Communications Physics 6 (1): 168. doi:10.1038/s42005-023-01276-z. Bibcode: 2023CmPhy...6..168Y.
14. ↑ Zhuravlev, A. S.; Kuznetsov, V. A.; Kulik, L. V.; Bisti, V. E.; Kirpichev, V. E.; Kukushkin, I. V.; Schmult, S. (2016). "Artificially Constructed Plasmarons and Plasmon-Exciton Molecules in 2D Metals". Physical Review Letters 117 (19). doi:10.1103/physrevlett.117.196802. ISSN 0031-9007. PMID 27858449. Bibcode: 2016PhRvL.117s6802Z.
15. ↑ Pramanik, Arindam; Thakur, Sangeeta; Singh, Bahadur; Willke, Philip; Wenderoth, Martin; Hofsäss, Hans; Di Santo, Giovanni; Petaccia, Luca et al. (2022). "Anomalies at the Dirac Point in Graphene and Its Hole-Doped Compositions". Physical Review Letters 128 (16). doi:10.1103/physrevlett.128.166401. PMID 35522498. Bibcode: 2022PhRvL.128p6401P.
16. ↑ Riccardo Tediosi; N. P. Armitage; E. Giannini; D. van der Marel (1971-09-13). "Charge Carrier Interaction with a Purely Electronic Collective Mode: Plasmarons and the Infrared Response of Elemental Bismuth". Phys. Rev. Lett. 27 (11): 711–714. doi:10.1103/PhysRevLett.99.016406. PMID 17678175. Bibcode: 2007PhRvL..99a6406T. http://archive-ouverte.unige.ch/unige:24322.
17. ↑ Ban, W J; Wu, D S; Xu, B; Luo, J L; Xiao, H (2019). "Revealing 'plasmaron' feature in DySb by optical spectroscopy study". Journal of Physics: Condensed Matter 31 (40): 405701. doi:10.1088/1361-648x/ab2d1a. PMID 31242466. Bibcode: 2019JPCM...31N5701B. http://doc.rero.ch/record/327018/files/xu_rpf.pdf.

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