Electron-Electron Correlation in Graphite: A Combined Angle-Resolved Photoemission and First-Principles Study

Abstract

The full three-dimensional dispersion of the bands, Fermi velocities, and effective masses are measured with angle-resolved photoemission spectroscopy and compared to first-principles calculations. The band structure by density-functional theory underestimates the slope of the bands and the trigonal warping effect. Including electron-electron correlation on the level of the GW approximation, however, yields remarkable improvement in the vicinity of the Fermi level. This demonstrates the breakdown of the independent electron picture in semimetallic graphite and points toward a pronounced role of electron correlation for the interpretation of transport experiments and double-resonant Raman scattering for a wide range of carbon based materials. Recently graphene has been investigated as a prototype system to address basic questions of quantum mechanics [1-3] (relativistic Dirac fermions) as well as for high speed semimetal field effect transistors in emerging nanoelectronic devices [4]. Many of these results are based on its peculiar electronic properties, i.e., an isotropic and linear dispersion close to the Fermi level (E F ). In low dimensional and strongly anisotropic systems correlation effects play a crucial role in understanding and describing the electronic band structure. Kinks in the quasiparticle (QP) dispersions and lifetimes were observed and interpreted as band renormalization due to electron-phonon [5] and electron-plasmon [6] interactions and band-structure effects [7]. Its electronic properties are also very sensitive to stacking and the number of layers [8]. In bilayer graphene a gap that could be tuned by doping was observed [9]. For few-layer graphene, the parent compound, graphite, is the key to understanding these new phenomena. Interlayer coupling in an AB stacking sequence leads to the formation of electron and hole pockets responsible for the semimetallic character in graphite. The linear dispersion is broken and only if we have an AA stacking the linear dispersion remains. Nevertheless, at the H point of graphite [2] the band dispersion is close to linear and has been interpreted as Dirac-fermion-like. Much less is known about the quantitative description of electron-electron correlations in these graphitic systems. Angle-resolved photoemission (ARPES) studies indicated that local density approximation (LDA) gives a dispersion that is too flat and a scaling has to be applied in order to fit the experimental dispersion of few-layer graphene and graphite. [15] for Raman scattering in graphene and graphite. Furthermore, it is important to know the exact k z dispersion, because it is responsible for the conductivity perpendicular to the graphene layers.In this Letter we report on a combined ARPES and theoretical ab initio QP study of the three-dimensional band structure and the Fermi surface in graphite single crystals. ARPES is best for studying correlations since it probes the complex self-energy function which contains the electronic interactions. We elucidate the full electronic QP disper...

Raman spectroscopy of graphite intercalation compounds: Charge transfer, strain, and electron–phonon coupling in graphene layers

“…All of these properties directly relate to the low-energy electronic structure of graphene [88,89]. ARPES has been proven to be a key tool to determine the electronic structure of graphene [94] and graphite [95][96][97].…”

Ultrafast Multiphoton Thermionic Photoemission from Graphite

“…Moreover, strong modulation of the carrier density through ultrafast optical excitation and the ensuing hot carrier multiplication drives the electron and hole distributions to different chemical potentials, enabling applications in energy harvesting, ultrafast electronics, and coherent optics [1,3,[16][17][18][19][20]. These novel properties derive from graphene's Dirac fermion band structure, weak screening, and strong, moleculelike electron correlation [21][22][23][24][25][26][27][28][29][30][31], which distinguish it from conventional metals and semiconductors [22,32,33].…”

Tight-binding description of the quasiparticle dispersion of graphite and few-layer graphene

“…It was shown recently by ARPES that the electronic structure of graphene 12 and its three-dimensional ͑3D͒ parent material, graphite, [13][14][15] is strongly renormalized by correlation effects. To date the best agreement between ARPES and ab initio calculations is obtained for GW ͑Greens function G of the Coulomb interaction W͒ calculations of the quasiparticle ͑QP͒ dispersion.…”

“…The GW calculations are computationally expensive and, thus, only selected k points have been calculated. 13 Therefore a tight-binding ͑TB͒ Hamiltonian with a transferable set of TB parameters that reproduces the QP dispersion in sp 2 stacked graphene sheets is needed for analysis of ARPES, optical spectroscopies, and transport properties for pristine and doped graphite and FLGs. So far there are already several sets of TB parameters published for graphene, FLG, and graphite.…”

“…For graphite, a semimetal with a tiny Fermi surface, the number of free electrons to screen the Coulomb interaction is very low ͑ϳ10 19 carriers cm −3 ͒, and thus the electron-electron correlation is a major contribution to the self-energy correction. 13 Theoretically, the interacting QP dispersion is obtained by the GW approximation. The GW calculations are computationally expensive and, thus, only selected k points have been calculated.…”