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Multiple Satellites in Materials with Complex Plasmon Spectra: from Graphite to Graphene Matteo Guzzo, Joshua J

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Multiple Satellites in Materials with Complex Plasmon Spectra: from Graphite to Graphene Matteo Guzzo, Joshua J Multiple satellites in materials with complex plasmon spectra: From graphite to graphene Matteo Guzzo, Joshua J. Kas, Lorenzo Sponza, Christine Giorgetti, Francesco Sottile, Debora Pierucci, Mathieu G. Silly, Fausto Sirotti, John J. Rehr, Lucia Reining To cite this version: Matteo Guzzo, Joshua J. Kas, Lorenzo Sponza, Christine Giorgetti, Francesco Sottile, et al.. Multiple satellites in materials with complex plasmon spectra: From graphite to graphene. Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2014, 89, pp.085425. 10.1103/PhysRevB.89.085425. hal-01011562 HAL Id: hal-01011562 https://hal-polytechnique.archives-ouvertes.fr/hal-01011562 Submitted on 24 Jun 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICAL REVIEW B 89, 085425 (2014) Multiple satellites in materials with complex plasmon spectra: From graphite to graphene Matteo Guzzo,1,2,* Joshua J. Kas,3 Lorenzo Sponza,1,2 Christine Giorgetti,1,2 Francesco Sottile,1,2 Debora Pierucci,4 Mathieu G. Silly,4 Fausto Sirotti,4 John J. Rehr,2,3 and Lucia Reining1,2,† 1Laboratoire des Solides Irradies,´ Ecole´ Polytechnique, CNRS, CEA-DSM, F-91128 Palaiseau, France 2European Theoretical Spectroscopy Facility (ETSF) 3Department of Physics, University of Washington, Seattle, Washington 98195, USA 4Synchrotron-SOLEIL, BP 48, Saint-Aubin, F91192 Gif sur Yvette CEDEX, France (Received 15 February 2013; revised manuscript received 23 January 2014; published 27 February 2014) The photoemission spectrum of graphite is still debated. To help resolve this issue, we present photoemission measurements at high photon energy and analyze the results using a Green’s function approach that takes into account the full complexity of the loss spectrum. Our measured data show multiple satellite replicas. We demonstrate that these satellites are of intrinsic origin, enhanced by extrinsic losses. The dominating satellite is due to the π + σ plasmon of graphite, whereas the π plasmon creates a tail on the high-binding energy side of the quasiparticle peak. The interplay between the two plasmons leads to energy shifts, broadening, and additional peaks in the satellite spectrum. We also predict the spectral changes in the transition from graphite towards graphene. DOI: 10.1103/PhysRevB.89.085425 PACS number(s): 73.22.Pr, 71.45.Gm, 71.10.−w, 71.15.Qe I. INTRODUCTION the one-body Green’s function G contains plasmon excitations that may lead to satellites. However, GW is believed to fail in Photoemission is a prominent experimental tool to access predicting the satellite spectra [4], although it performs well the electronic structure of materials. Angular-resolved photo- for QP energies. Satellites are rarely computed, so that much electron spectroscopy (ARPES) is frequently used to extract of the information obtained from experiment is wasted. Our the band structure and quasiparticle (QP) lifetimes of a large aim is to push this limit. variety of systems [1]. However, in a photoemission spectrum, In the present work we focus on plasmon satellites, which besides the QP peaks and incoherent background, satellite occur in most materials, from metals to insulators. Plasmons peaks often appear. In the intrinsic spectral function, within the lead to multiple satellites, forming a decaying series of peaks three-step model [2], these satellites can be understood in terms below the QP.These structures can be explained with a spectral of coupling of a QP to additional excitations of the system. function derived from an exponential (also referred to as Their nature is often debated. In simple metals plasmon cumulant) form of the one-particle Green’s function, itself a satellite replicas are observed [3], but it is difficult to discern solution of an electron-boson coupling model [4,12,13]. In the experimentally to which extent these are intrinsic features present case the plasmon plays the role of the boson, though the [4], or due to losses of the outgoing photoelectron (called cumulant form is more general. The plasmon contribution has extrinsic). In nickel, the satellite at 6 eV below the QP peak been derived in several ways, e.g., starting from GW [4,13,14], cannot be explained with the plasmon spectrum, but is due or as a linear response contribution of the Hartree potential to a bound hole-hole state [5,6]. Recently a satellite in doped [15]. The combination of the cumulant solution with the GW graphene was interpreted as a plasmaron, a strongly coupled calculation (GW + C) and the same method with additional electron-plasmon excitation [7]. In 3d and 4f systems, satel- ∗ extrinsic and interference contributions (GW + C ) yielded lites have been ascribed to strong electron-electron interaction excellent agreement with experiment for bulk silicon [15,16]. within a Mott-Hubbard picture [8]. In other materials, e.g., The GW approximation alone, instead, gave rise to a spurious graphite, the very existence of intrinsic satellite features plasmaron solution in silicon, similarly to the homogeneous has been questioned. In this system observed valence-band ∗ electron gas [17–19]. Hence, GW + C appears to be the satellite structures have been attributed to extrinsic losses method of choice for plasmon satellites. and subtracted from the measured spectrum [9,10]. These In this article we address the layered material graphite debates, even for supposedly simple materials, are in part due and its building block graphene. We generalize the approach to the lack of a widely applicable theoretical approach for used in Refs. [15,16] that was based on the use of a single the description of satellites. Ab initio calculations typically plasmon pole approximation for W, to materials with an ignore satellites and concentrate on QP properties, often using arbitrarily complex excitation spectrum. Our computational the GW approximation for the self-energy in the framework results are compared to new bulk sensitive photoemission of many-body perturbation theory [11]. In this approach the data for graphite. The excellent agreement between theory and dynamically screened Coulomb interaction W that multiplies experiment allows us to address several important questions: (i) does graphite have intrinsic satellites? (ii) Does the GW ap- proximation create a spurious plasmaron also in this material? *[email protected]; present address: Physics De- (iii) Are there any new effects in the XPS spectrum caused by partment, Humboldt-Universitat¨ zu Berlin, Zum Großen Windkanal the more complex plasmon spectrum, and in particular by the 6, D-12489 Berlin, Germany. existence of two main plasmon peaks? Finally, it allows us to †[email protected] make predictions for the satellite structure in graphene. 1098-0121/2014/89(8)/085425(6) 085425-1 ©2014 American Physical Society MATTEO GUZZO et al. PHYSICAL REVIEW B 89, 085425 (2014) We start describing the experimental setup for the 1 XPS measurements and the computational details of the XPS 800 eV calculations in Sec. II. Results are discussed in Sec. III. 0.8 Total We analyze the shortcomings of the GW approximation in Intrinsic GW graphite and discuss the absence of a plasmaron in this Int. 1-pole particular case in Sec. III B. We give the interpretation of 0.6 the XPS spectrum of graphite on the basis of our GW + C∗ + ∗ calculations in Sec. III C. Then we calculate the GW C ) (arb. units) 0.4 spectral function of undoped graphene showing how and ω J( why this differs from its graphite counterpart in Sec. III D. Conclusions are drawn in Sec. IV. 0.2 0 II. TECHNICAL DETAILS -100 -80 -60 -40 -20 0 A. Experimental setup E - EF (eV) ARPES measurements were performed at the UHV photoe- FIG. 1. (Color online) XPS spectrum of HOPG at 800 eV photon mission station of the TEMPO beamline [20] at the SOLEIL energy. The experimental data collected at normal emission (blue synchrotron radiation source. Linearly polarized photons from dots) are compared to the spectral function A(ω) calculated from GW the Apple II type Insertion Device (HU44) were selected in (magenta dashed line) and from a multipole version of Eq. (1) (green energy using a high resolution plane grating monochromator dot-dashed line). On top of the latter the black solid line also includes with a resolving power E/E = 5000. The end-station extrinsic and interference effects. The result for A(ω) in the single −10 chamber (base pressure 10 mbar) is equipped with a plasmon pole approximation (Np = 1) for Eq. (1) (red dotted line) is modified SCIENTA-2002 electron analyzer with a delay-line shown for comparison. All curves are scaled to match the intensity 2D detector which optimizes the detection linearity and of the main QP peak at −20 eV. All theoretical spectra contain signal/background ratio [21]. The overall energy resolution photoabsorption cross sections, the calculated secondary electron was better than 200 meV. The photon beam impinged on the background, and 0.4 eV Gaussian broadening to account for finite sample at an angle of 43◦, and photoelectrons were detected BZ sampling and experimental resolution. on an angular range of 12◦. Highly oriented pyrolytic graphite (HOPG) was cleaved in the introduction stage of the UHV The GW0 spectral function of graphene was calculated system exposing a new surface immediately before the transfer using equivalent parameters on a slightly different k-point grid × × to UHV. At 800 eV kinetic energy the Brillouin zone (BZ) is (12 12 1).
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