Ab InitioGWMany-Body Effects in Graphene

Abstract

We present an ab initio numerical many-body GW calculation of the band plot in free-standing graphene. We consider the full ionic and electronic structure introducing e-e interaction and correlation effects via a self-energy containing non-hermitian and dynamical terms. With respect to the density-functional theory local-density approximation, the Fermi velocity is renormalized with an increase of 17%, in better agreement with the experiment. Close to the Dirac point the linear dispersion is modified by the presence of a kink, as observed in angle-resolved photoemission spectroscopy. We demonstrate that the kink is due to low-energy π → π * single-particle excitations and to the π plasmon. The GW self-energy does not open the band gap.PACS numbers: 71.45.Gm, 79.20.Uv, The discovery of graphene by micromechanical cleavage [1, 2] and epitaxial grow [3] has attracted tremendous interest in consideration of its unusual electronic properties. In the tight-binding (TB) formalism, the graphene 2D honeycomb lattice structure gives rise to a semiconductor with zero band gap occurring at the K point in the Brillouin zone and a cone-like linear band-dispersion at low energy. This part is usually described by a massless Dirac (Weyl) dispersion [4]. Ab initio density-functional theory (DFT) calculations [5] confirm the TB linear dispersion picture and give an estimate of the Fermi velocity v F lower by 15∼20% than the experimental value. Recently, two angle-resolved photoemission spectroscopy (ARPES) experiments on graphene epitaxially grown on SiC [6,7,8,9, 10] raised the general interest. The first one [6,9] observed at low energy a nearly linear band dispersion with slight deviations in the form of small kinks interpreted as due to many-body electron-electron (e-e) and electron-phonon (e-ph) self-energy effects. The second one [7,8,10] provided a different picture, with the opening of a band gap occurring at the Dirac K point and attributed either to substrate (SiC) or to many-body selfenergy effects. A DFT calculation [11] seemed to confirm a substrate induced symmetry breaking, but recent STM measures [12] provided some evidence to exclude it. This situation calls for clarification about the role of e-e selfenergy effects on the quasiparticle (QP) band plot, the Fermi velocity and the band gap opening. Previous ab initio works have dealt with e-ph effects [5,13] and with e-e GW effects in graphene nanoribbons [14]. There are also several non ab initio works [15,16,17,18] which studied e-e self-energy effects in a 2D massless Dirac model.In this work we calculate the band plot of free-standing undoped graphene introducing e-e interaction and correlation effects by an ab initio many-body GW selfenergy [19,20]. We numerically simulate the full ionic and electronic structure of real graphene. We take into account the full dynamical dependence and nonhermiticity of the self-energy by an accurate contourdeformation (CD) integration. From the self-energy we then obtain the QP energies and the spectral function which can be di...

Local electronic properties of the graphene-protected giant Rashba-split BiAg2 surface

“…3(d) is for the graphene π states around the K point of the graphene-derived BZ. Analysis of the graphene dispersion relation shows that graphene on BiAg 2 is n doped with a position of the Dirac point of E D = −400 ± 30 meV and a Fermi velocity of (1.17 ± 0.06)×10 6 m/s, which is in good agreement with a value for nearly free-standing graphene on a metallic substrate [34,35].…”

Many‐body effects in optical response of graphene‐based structures

“…This experimental finding is well reproduced within the RPA. [34,38] The calculated energy loss function of graphene shows the total p1r plasmon at $15 eV, the p plasmon at $5 eV and a shoulder around $2.5 eV corresponding to the p ! pà single-particle excitations.…”

Fully self-consistent GW calculations for molecules

“…The fact that the screening is determined by the system itself instead of being fixed a priori as in the screened hybrid schemes, suggests that the GW method should be applicable to a broad class of systems ranging from metals with strong screening to molecules with weak screening. With the entry of nanoscience the use of GW has been extended to low-dimensional systems and nanostructures [21][22][23][24][25][26][27][28][29][30][31] and more recently even nonequilibrium phenomena such as quantum transport. [32][33][34][35][36] In view of this trend it is important to establish the performance of the GW approximation for other systems than the crystalline solids.…”