Advertisement

Many-Body Calculations of Plasmon and Phonon Satellites in Angle-Resolved Photoelectron Spectra Using the Cumulant Expansion Approach

  • Fabio Caruso
  • Carla Verdi
  • Feliciano GiustinoEmail author
Reference work entry
  • 9 Downloads

Abstract

The interaction of electrons with crystal lattice vibrations (phonons) and collective charge-density fluctuations (plasmons) influences profoundly the spectral properties of solids revealed by photoemission spectroscopy experiments. Photoemission satellites, for instance, are a prototypical example of quantum emergent behavior that may result from the strong coupling of electronic states to plasmons and phonons. The existence of these spectral features has been verified over energy scales spanning several orders of magnitude (from 50 meV to 15–20 eV) and for a broad class of compounds such as simple metals, semiconductors, and highly doped oxides. During the past few years, the cumulant expansion approach, alongside with the GW approximation and the theory of electron-phonon and electron-plasmon coupling in solids, has evolved into a predictive and quantitatively accurate approach for the description of the spectral signatures of electron-boson coupling entirely from first principles, and it has thus become the state-of-the-art theoretical tool for the description of these phenomena. In this chapter we introduce the fundamental concepts needed to interpret plasmon and phonon satellites in photoelectron spectra, and we review recent progress on first-principles calculations of these features using the cumulant expansion method.

References

  1. Allen PB, Heine V (1976) Theory of the temperature dependence of electronic band structures. J Phys C 9:2305ADSCrossRefGoogle Scholar
  2. Antonius G, Poncé S, Lantagne-Hurtubise E, Auclair G, Gonze X, Côté M (2015) Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure. Phys Rev B 92:085137ADSCrossRefGoogle Scholar
  3. Aryasetiawan F, Hedin L, Karlsson K (1996) Multiple plasmon satellites in Na and Al spectral functions from ab initio cumulant expansion. Phys Rev Lett 77:2268–2271ADSCrossRefGoogle Scholar
  4. Aryasetiawan F, Gunnarson O (1998) The GW method. Rep Prog Phys 61:237–312ADSCrossRefGoogle Scholar
  5. Aulbur WG, Jonsson L, Wilkins JW (2000) Quasiparticle calculations in solids. In: Ehrenreich H, Spaepen F (eds) Solid state physics, vol 54. Academic Press, New York, pp 1–218Google Scholar
  6. Baer Y, Busch G (1973) X-ray photoemission from aluminum. Phys Rev Lett 30:280–282ADSCrossRefGoogle Scholar
  7. Bostwick A, Speck F, Seyller T, Horn K, Polini M, Asgari R, MacDonald AH, Rotenberg E (2010) Observation of plasmarons in quasi-freestanding doped graphene. Science 328:999–1002ADSCrossRefGoogle Scholar
  8. Cancellieri C, Mishchenko AS, Aschauer U, Filippetti A, Faber C, Barišić OS, Rogalev VA, Schmitt T, Nagaosa N, Strocov VN (2016) Polaronic metal state at the LaAlO3/SrTiO3 interface. Nat Commun 7:10386ADSCrossRefGoogle Scholar
  9. Caruso F, Giustino F (2015) Spectral fingerprints of electron-plasmon coupling. Phys Rev B 92:045123ADSCrossRefGoogle Scholar
  10. Caruso F, Giustino F (2016) Theory of electron-plasmon coupling in semiconductors. Phys Rev B 94:115208ADSCrossRefGoogle Scholar
  11. Caruso F, Rinke P, Ren X, Rubio A, Scheffler M (2013) Self-consistent GW: all-electron implementation with localized basis functions. Phys Rev B 88:075105ADSCrossRefGoogle Scholar
  12. Caruso F, Lambert H, Giustino F (2015) Band structures of plasmonic polarons. Phys Rev Lett 114:146404ADSCrossRefGoogle Scholar
  13. Caruso F, Dauth M, van Setten MJ, Rinke P (2016) Benchmark of GW approaches for the GW100 test set. J Chem Theory Comput 12:5076–5087CrossRefGoogle Scholar
  14. Caruso F, Verdi C, Poncé S, Giustino F (2018) Electron-plasmon and electron-phonon satellites in the angle-resolved photoelectron spectra of n-doped anatase TiO2. Phys Rev B 97:165113ADSCrossRefGoogle Scholar
  15. Chang YJ, Bostwick A, Kim YS, Horn K, Rotenberg E (2010) Structure and correlation effects in semiconducting SrTiO3. Phys Rev B 81:235109ADSCrossRefGoogle Scholar
  16. Chen C, Avila J, Frantzeskakis E, Levy A, Asensio MC (2015) Observation of a two-dimensional liquid of Fröhlich polarons at the bare SrTiO3 surface. Nat Commun 6:8585ADSCrossRefGoogle Scholar
  17. Damascelli A, Hussain Z, Shen ZX (2003) Angle-resolved photoemission studies of the cuprate superconductors. Rev Mod Phys 75:473ADSCrossRefGoogle Scholar
  18. Eiguren A, Hellsing B, Reinert F, Nicolay G, Chulkov EV, Silkin VM, Hüfner S, Echenique PM (2002) Role of bulk and surface phonons in the decay of metal surface states. Phys Rev Lett 88:066805ADSCrossRefGoogle Scholar
  19. Fröhlich H (1954) Electrons in lattice fields. Adv Phys 3:325ADSzbMATHCrossRefGoogle Scholar
  20. Giustino F (2017) Electron-phonon interactions from first principles. Rev Mod Phys 89:015003ADSMathSciNetCrossRefGoogle Scholar
  21. Giustino F, Cohen ML, Louie SG (2007) Electron-phonon interaction using Wannier functions. Phys Rev B 76:165108ADSCrossRefGoogle Scholar
  22. Giustino F, Louie SG, Cohen ML (2010) Electron-phonon renormalization of the direct band gap of diamond. Phys Rev Lett 105:265501ADSCrossRefGoogle Scholar
  23. Gumhalter B, Kovač V, Caruso F, Lambert H, Giustino F (2016) On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: the paradigm of Si valence bands. Phys Rev B 94:035103ADSCrossRefGoogle Scholar
  24. Guzzo M, Lani G, Sottile F, Romaniello P, Gatti M, Kas JJ, Rehr JJ, Silly MG, Sirotti F, Reining L (2011) Valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites. Phys Rev Lett 107:166401ADSCrossRefGoogle Scholar
  25. Guzzo M, Kas JJ, Sottile F, Silly MG, Sirotti F, Rehr JJ, Reining L (2012) Plasmon satellites in valence-band photoemission spectroscopy. Eur Phys J B 85:324ADSCrossRefGoogle Scholar
  26. Hedin L (1965) New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys Rev 139:A796ADSCrossRefGoogle Scholar
  27. Hedin L (1980) Effects of recoil on shake-up spectra in metals. Phys Scr 21:477ADSCrossRefGoogle Scholar
  28. Hedin L, Lundqvist S (1970) Effects of electron-electron and electron-phonon interactions on the one-electron states of solids. Solid State Phys 23:1–181CrossRefGoogle Scholar
  29. Holm B, Aryasetiawan F (1997) Self-consistent cumulant expansion for the electron gas. Phys Rev B 56:12825–12831ADSCrossRefGoogle Scholar
  30. Holm B, von Barth U (1998) Fully self-consistent GW self-energy of the electron gas. Phys Rev B 57:2108ADSCrossRefGoogle Scholar
  31. Hüfner S (2003) Photoelectron spectroscopy, 3rd edn. Springer, BerlinCrossRefGoogle Scholar
  32. Kas JJ, Rehr JJ, Reining L (2014) Cumulant expansion of the retarded one-electron Green function. Phys Rev B 90:085112ADSCrossRefGoogle Scholar
  33. King PDC, McKeown Walker S, Tamai A, de la Torre A, Eknapakul T, Buaphet P, Mo SK, Meevasana W, Bahramy MS, Baumberger F (2014) Quasiparticle dynamics and spin-orbital texture of the SrTiO3 two-dimensional electron gas. Nat Commun 5:3414ADSCrossRefGoogle Scholar
  34. Kittel C (1976) Introduction to solid state physics, 5th edn. Wiley, New YorkzbMATHGoogle Scholar
  35. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138. https://link.aps.org/doi/10.1103/PhysRev.140.A1133 ADSMathSciNetCrossRefGoogle Scholar
  36. Kutepov A, Haule K, Savrasov SY, Kotliar G (2012) Electronic structure of Pu and Am metals by self-consistent relativistic GW method. Phys Rev B 85:155129ADSCrossRefGoogle Scholar
  37. Langreth DC (1970) Singularities in the X-ray spectra of metals. Phys Rev B 1:471–477ADSCrossRefGoogle Scholar
  38. Lanzara A, Bogdanov PV, Zhou XJ, Kellar SA, Feng DL, Lu ED, Yoshida T, Eisaki H, Fujimori A, Kishio K, Shimoyama JI, Noda T, Uchida S, Hussain Z, Shen ZX (2001) Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors. Nature 412:510ADSCrossRefGoogle Scholar
  39. Lee JJ, Schmitt FT, Moore RG, Johnston S, Cui YT, Li W, Yi M, Liu ZK, Hashimoto M, Zhang Y, Lu DH, Devereaux TP, Lee DH, Shen ZX (2014) Interfacial mode coupling as the origin of the enhancement of T c in FeSe films on SrTiO3. Nature 515:245–248ADSCrossRefGoogle Scholar
  40. Lischner J, Pálsson GK, Vigil-Fowler D, Nemsak S, Avila J, Asensio MC, Fadley CS, Louie SG (2015) Satellite band structure in silicon caused by electron-plasmon coupling. Phys Rev B 91:205113ADSCrossRefGoogle Scholar
  41. Logothetidis S, Petalas J, Polatoglou HM, Fuchs D (1992) Origin and temperature dependence of the first direct gap of diamond. Phys Rev B 46:4483–4494ADSCrossRefGoogle Scholar
  42. Lundqvist BI (1967) Single-particle spectrum of the degenerate electron gas. Phys Kondens Mater 6:193–205ADSGoogle Scholar
  43. Mahan G (2000) Many-particle physics. Springer, New YorkCrossRefGoogle Scholar
  44. Marini A, Hogan C, Grning M, Varsano D (2009) Yambo: an ab initio tool for excited state calculations. Comput Phys Commun 180:1392–1403ADSCrossRefGoogle Scholar
  45. Marini A, Poncé S, Gonze X (2015) Many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point. Phys Rev B 91:224310ADSCrossRefGoogle Scholar
  46. Moser S, Moreschini L, Jaćimović J, Barišić OS, Berger H, Magrez A, Chang YJ, Kim KS, Bostwick A, Rotenberg E, Forró L, Grioni M (2013) Tunable polaronic conduction in anatase TiO2. Phys Rev Lett 110:196403ADSCrossRefGoogle Scholar
  47. Nery JP, Allen PB, Antonius G, Reining L, Miglio A, Gonze X (2018) Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: cumulants applied to the full first-principles theory and the Fröhlich polaron. Phys Rev B 97:115145ADSCrossRefGoogle Scholar
  48. Park CH, Giustino F, Cohen ML, Louie SG (2007) Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction. Phys Rev Lett 99:086804ADSCrossRefGoogle Scholar
  49. Poncé S, Gillet Y, Laflamme Janssen J, Marini A, Verstraete M, Gonze X (2015) Temperature dependence of the electronic structure of semiconductors and insulators. J Chem Phys 143:102813ADSCrossRefGoogle Scholar
  50. Poncé S, Margine ER, Verdi C, Giustino F (2016) EPW: electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions. Comput Phys Commun 209:116–133ADSMathSciNetCrossRefGoogle Scholar
  51. Rademaker L, Wang Y, Berlijn T, Johnston S (2016) Enhanced superconductivity due to forward scattering in fese thin films on SrTiO3 substrates. New J Phys 18:022001CrossRefGoogle Scholar
  52. Riley JM, Caruso F, Verdi C, Duffy LB, Watson MD, Bawden L, Volckaert K, van der Laan G, Hesjedal T, Hoesch M, Giustino F, King PDC (2018) Crossover from lattice to plasmonic polarons of a spin-polarised electron gas in ferromagnetic EuO. Nat Commun 9:2305ADSCrossRefGoogle Scholar
  53. Settnes M, Saavedra JRM, Thygesen KS, Jauho AP, Garca de Abajo FJ, Mortensen NA (2017) Strong plasmon-phonon splitting and hybridization in 2D materials revealed through a self-energy approach. ACS Photon 4(11):2908–2915CrossRefGoogle Scholar
  54. Sjakste J, Vast N, Calandra M, Mauri F (2015) Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: polar-optical coupling in GaAs. Phys Rev B 92:054307ADSCrossRefGoogle Scholar
  55. Steiner P, Höchst H, Hüfner S (1979) Photoemission in solids II. In: Ley L, Cardona M (eds) Topics in applied physics, vol 27. Springer, HeidelbergGoogle Scholar
  56. Story SM, Kas JJ, Vila FD, Verstraete MJ, Rehr JJ (2014) Cumulant expansion for phonon contributions to the electron spectral function. Phys Rev B 90:195135ADSCrossRefGoogle Scholar
  57. Varga BB (1965) Coupling of plasmons to polar phonons in degenerate semiconductors. Phys Rev 137:A1896ADSCrossRefGoogle Scholar
  58. Verdi C, Giustino F (2015) Fröhlich electron-phonon vertex from first principles. Phys Rev Lett 115:176401ADSCrossRefGoogle Scholar
  59. Verdi C, Caruso F, Giustino F (2017) Origin of the crossover from polarons to Fermi liquids in transition metal oxides. Nat Commun 8:15769ADSCrossRefGoogle Scholar
  60. Wang Z, McKeown Walker S, Tamai A, Wang Y, Ristic Z, Bruno FY, de la Torre A, Riccò S, Plumb NC, Shi M, Hlawenka P, Sánchez-Barriga J, Varykhalov A, Kim TK, Hoesch M, King PDC, Meevasana W, Diebold U, Mesot J, Moritz B, Devereaux TP, Radovic M, Baumberger F (2016) Tailoring the nature and strength of electron-phonon interactions in the SrTiO3(001) two-dimensional electron liquid. Nat Mater 15:835–839ADSCrossRefGoogle Scholar
  61. Yukawa R, Ozawa K, Yamamoto S, Iwasawa H, Shimada K, Schwier EF, Yoshimatsu K, Kumigashira H, Namatame H, Taniguchi M, Matsuda I (2016) Phonon-dressed two-dimensional carriers on the ZnO surface. Phys Rev B 94:165313ADSCrossRefGoogle Scholar
  62. Zhou JS, Kas JJ, Sponza L, Reshetnyak I, Guzzo M, Giorgetti C, Gatti M, Sottile F, Rehr JJ, Reining L (2015) Dynamical effects in electron spectroscopy. J Chem Phys 143:184109ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Fabio Caruso
    • 1
  • Carla Verdi
    • 2
  • Feliciano Giustino
    • 2
    • 3
    Email author
  1. 1.Institut für Physik and IRIS AdlershofHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of MaterialsUniversity of OxfordOxfordUK
  3. 3.Department of Materials Science and EngineeringCornell UniversityIthacaUSA

Personalised recommendations