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

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Handbook of Materials Modeling

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.

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References

  • Allen PB, Heine V (1976) Theory of the temperature dependence of electronic band structures. J Phys C 9:2305

    Article  ADS  Google Scholar 

  • 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 92:085137

    Article  ADS  Google Scholar 

  • Aryasetiawan F, Hedin L, Karlsson K (1996) Multiple plasmon satellites in Na and Al spectral functions from ab initio cumulant expansion. Phys Rev Lett 77:2268–2271

    Article  ADS  Google Scholar 

  • Aryasetiawan F, Gunnarson O (1998) The GW method. Rep Prog Phys 61:237–312

    Article  ADS  Google Scholar 

  • 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 1–218

    Google Scholar 

  • Baer Y, Busch G (1973) X-ray photoemission from aluminum. Phys Rev Lett 30:280–282

    Article  ADS  Google Scholar 

  • 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 328:999–1002

    Article  ADS  Google Scholar 

  • 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 7:10386

    Article  ADS  Google Scholar 

  • Caruso F, Giustino F (2015) Spectral fingerprints of electron-plasmon coupling. Phys Rev B 92:045123

    Article  ADS  Google Scholar 

  • Caruso F, Giustino F (2016) Theory of electron-plasmon coupling in semiconductors. Phys Rev B 94:115208

    Article  ADS  Google Scholar 

  • Caruso F, Rinke P, Ren X, Rubio A, Scheffler M (2013) Self-consistent GW: all-electron implementation with localized basis functions. Phys Rev B 88:075105

    Article  ADS  Google Scholar 

  • Caruso F, Lambert H, Giustino F (2015) Band structures of plasmonic polarons. Phys Rev Lett 114:146404

    Article  ADS  Google Scholar 

  • Caruso F, Dauth M, van Setten MJ, Rinke P (2016) Benchmark of GW approaches for the GW100 test set. J Chem Theory Comput 12:5076–5087

    Article  Google Scholar 

  • 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 97:165113

    Article  ADS  Google Scholar 

  • Chang YJ, Bostwick A, Kim YS, Horn K, Rotenberg E (2010) Structure and correlation effects in semiconducting SrTiO3. Phys Rev B 81:235109

    Article  ADS  Google Scholar 

  • 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 6:8585

    Article  ADS  Google Scholar 

  • Damascelli A, Hussain Z, Shen ZX (2003) Angle-resolved photoemission studies of the cuprate superconductors. Rev Mod Phys 75:473

    Article  ADS  Google Scholar 

  • 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 88:066805

    Article  ADS  Google Scholar 

  • Fröhlich H (1954) Electrons in lattice fields. Adv Phys 3:325

    Article  ADS  Google Scholar 

  • Giustino F (2017) Electron-phonon interactions from first principles. Rev Mod Phys 89:015003

    Article  ADS  MathSciNet  Google Scholar 

  • Giustino F, Cohen ML, Louie SG (2007) Electron-phonon interaction using Wannier functions. Phys Rev B 76:165108

    Article  ADS  Google Scholar 

  • Giustino F, Louie SG, Cohen ML (2010) Electron-phonon renormalization of the direct band gap of diamond. Phys Rev Lett 105:265501

    Article  ADS  Google Scholar 

  • 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 94:035103

    Article  ADS  Google Scholar 

  • 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 107:166401

    Article  ADS  Google Scholar 

  • 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 85:324

    Article  ADS  Google Scholar 

  • Hedin L (1965) New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys Rev 139:A796

    Article  ADS  Google Scholar 

  • Hedin L (1980) Effects of recoil on shake-up spectra in metals. Phys Scr 21:477

    Article  ADS  Google Scholar 

  • Hedin L, Lundqvist S (1970) Effects of electron-electron and electron-phonon interactions on the one-electron states of solids. Solid State Phys 23:1–181

    Article  Google Scholar 

  • Holm B, Aryasetiawan F (1997) Self-consistent cumulant expansion for the electron gas. Phys Rev B 56:12825–12831

    Article  ADS  Google Scholar 

  • Holm B, von Barth U (1998) Fully self-consistent GW self-energy of the electron gas. Phys Rev B 57:2108

    Article  ADS  Google Scholar 

  • Hüfner S (2003) Photoelectron spectroscopy, 3rd edn. Springer, Berlin

    Book  Google Scholar 

  • Kas JJ, Rehr JJ, Reining L (2014) Cumulant expansion of the retarded one-electron Green function. Phys Rev B 90:085112

    Article  ADS  Google Scholar 

  • 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 5:3414

    Article  Google Scholar 

  • Kittel C (1976) Introduction to solid state physics, 5th edn. Wiley, New York

    MATH  Google Scholar 

  • 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

    Article  ADS  MathSciNet  Google Scholar 

  • 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 85:155129

    Article  ADS  Google Scholar 

  • Langreth DC (1970) Singularities in the X-ray spectra of metals. Phys Rev B 1:471–477

    Article  ADS  Google Scholar 

  • 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 412:510

    Article  ADS  Google Scholar 

  • 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 Tc in FeSe films on SrTiO3. Nature 515:245–248

    Article  ADS  Google Scholar 

  • 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 91:205113

    Article  ADS  Google Scholar 

  • Logothetidis S, Petalas J, Polatoglou HM, Fuchs D (1992) Origin and temperature dependence of the first direct gap of diamond. Phys Rev B 46:4483–4494

    Article  ADS  Google Scholar 

  • Lundqvist BI (1967) Single-particle spectrum of the degenerate electron gas. Phys Kondens Mater 6:193–205

    ADS  Google Scholar 

  • Mahan G (2000) Many-particle physics. Springer, New York

    Book  Google Scholar 

  • Marini A, Hogan C, Grning M, Varsano D (2009) Yambo: an ab initio tool for excited state calculations. Comput Phys Commun 180:1392–1403

    Article  ADS  Google Scholar 

  • 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 91:224310

    Article  ADS  Google Scholar 

  • 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 110:196403

    Article  ADS  Google Scholar 

  • 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 97:115145

    Article  ADS  Google Scholar 

  • Park CH, Giustino F, Cohen ML, Louie SG (2007) Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction. Phys Rev Lett 99:086804

    Article  ADS  Google Scholar 

  • 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 143:102813

    Article  ADS  Google Scholar 

  • 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 209:116–133

    Article  ADS  MathSciNet  Google Scholar 

  • 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 18:022001

    Article  Google Scholar 

  • 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 9:2305

    Article  ADS  Google Scholar 

  • 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):2908–2915

    Article  Google Scholar 

  • 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 92:054307

    Article  ADS  Google Scholar 

  • Steiner P, Höchst H, Hüfner S (1979) Photoemission in solids II. In: Ley L, Cardona M (eds) Topics in applied physics, vol 27. Springer, Heidelberg

    Google Scholar 

  • Story SM, Kas JJ, Vila FD, Verstraete MJ, Rehr JJ (2014) Cumulant expansion for phonon contributions to the electron spectral function. Phys Rev B 90:195135

    Article  ADS  Google Scholar 

  • Varga BB (1965) Coupling of plasmons to polar phonons in degenerate semiconductors. Phys Rev 137:A1896

    Article  ADS  Google Scholar 

  • Verdi C, Giustino F (2015) Fröhlich electron-phonon vertex from first principles. Phys Rev Lett 115:176401

    Article  ADS  Google Scholar 

  • Verdi C, Caruso F, Giustino F (2017) Origin of the crossover from polarons to Fermi liquids in transition metal oxides. Nat Commun 8:15769

    Article  ADS  Google Scholar 

  • 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 15:835–839

    Article  ADS  Google Scholar 

  • 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 94:165313

    Article  ADS  Google Scholar 

  • 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 143:184109

    Article  ADS  Google Scholar 

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Correspondence to Feliciano Giustino .

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Caruso, F., Verdi, C., Giustino, F. (2018). Many-Body Calculations of Plasmon and Phonon Satellites in Angle-Resolved Photoelectron Spectra Using the Cumulant Expansion Approach. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_2-1

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  • DOI: https://doi.org/10.1007/978-3-319-42913-7_2-1

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