Low-Dimensional Functional Materials pp 77-87 | Cite as
On the Electron-Phonon Interactions in Graphene
Abstract
Chiral polaron formation arising from the electron-E2g phonon coupling and the mini band gap formation due to electron-A1g phonon coupling are investigated in pristine graphene. We present an analytical method to calculate the ground-state of the electron-phonon system within the framework of the Lee-Low-Pines theory. We show that the degenerate band structure of the graphene promotes the chiral polaron formation. Within our theoretical analysis, we also show that the interaction of charge carriers with the highest frequency zone-boundary phonon mode with A1g -symmetry induces a mini band gap at the corners of the two-dimensional Brillouin zone of the graphene.
Keywords
Optical Phonon Unitary Transformation Phonon Mode Pristine Graphene Optical Phonon ModeReferences
- 1.Ajiki H, Ando T (1995) Lattice distortion of metallic carbon nanotubes induced by magnetic fields. J Phys Soc Jpn 64:260–267ADSCrossRefGoogle Scholar
- 2.Ajiki H, Ando T (1996) Lattice distortion with spatial variation of carbon nanotubes in magnetic fields. J Phys Soc Jpn 65:2976–2986ADSCrossRefGoogle Scholar
- 3.Araki Y (2011) Chiral symmetry restoration in monolayer graphene induced by Kekule distortion. Phys Rev B 84:113402ADSCrossRefGoogle Scholar
- 4.Araujo PT, Mafra DL, Sato K, Saito R, Kong J, Dresselhaus MS (2012) Phonon self-energy corrections to nonzero wave-vector phonon modes in single-layer graphene. Phys Rev Lett 109:046801ADSCrossRefGoogle Scholar
- 5.Badalyan SM, Peeters FM (2012) Electron-phonon bound state in graphene. Phys Rev B 85:205453ADSCrossRefGoogle Scholar
- 6.Basko DM (2007) Effect of inelastic collisions on multiphonon Raman scattering in graphene. Phys Rev B 76:081405(R)Google Scholar
- 7.Basko DM (2008) Theory of resonant multiphonon Raman scattering in graphene. Phys Rev B 78:125418ADSCrossRefGoogle Scholar
- 8.Basko DM, Aleiner IL (2008) Interplay of Coulomb and electron-phonon interactions in graphene. Phys Rev B 77:041409(R)Google Scholar
- 9.Calandra M, Mauri F (2007) Electron-phonon coupling and electron self-energy in electron-doped graphene: calculation of angular-resolved photoemission spectra. Phys Rev B 76:205411ADSCrossRefGoogle Scholar
- 10.Carbotte JP, Nicol EJ, Sharapov SG (2010) Effect of electron-phonon interaction on spectroscopies in graphene. Phys Rev B 81:045419ADSCrossRefGoogle Scholar
- 11.Dubay O, Kresse G (2003) Accurate density functional calculations for the phonon dispersion relations of graphite layer and carbon nanotubes. Phys Rev B 67:0354012003CrossRefGoogle Scholar
- 12.Farjam M, Rafii-Tabar H (2010) Uniaxial strain on gapped graphene. Physica E 42:2109–2114ADSCrossRefGoogle Scholar
- 13.Faugeras C, Amado M, Kossacki P, Orlita M, Sprinkle M, Berger C, de Heer WA, Potemski M (2009) Tuning the electron-phonon coupling in multilayer graphene with magnetic fields. Phys Rev Lett 103:186803ADSCrossRefGoogle Scholar
- 14.Giuliani A, Mastropietro V, Porta M (2010) Lattice gauge theory model for graphene. Phys Rev B 82:121418(R)Google Scholar
- 15.Goerbig MO, Fuchs J-N, Kechedzhi K, Fal’ko VI (2007) Filling-factor-dependent magnetophonon resonance in graphene. Phys Rev Lett 99:087402ADSCrossRefGoogle Scholar
- 16.Griffiths D (1987) Introduction to elementary particles. Wiley, Singapore, p 249CrossRefGoogle Scholar
- 17.Harigaya K (1992) From C60 to a fullerene tube: Systematic analysis of lattice and electronic structures by the extended Su-Schrieffer-Heeger model. Phys Rev B 45:12071ADSCrossRefGoogle Scholar
- 18.Harigaya K, Fujita M (1993) Dimerization structures of metallic and semiconducting fullerene tubules. Phys Rev B 47:16563ADSCrossRefGoogle Scholar
- 19.Hwang EH, Sensarma R, Das Sarma S (2010) Plasmon-phonon coupling in graphene. Phys Rev B 82:195406ADSCrossRefGoogle Scholar
- 20.Ishikawa K, Ando T (2006) Optical phonon interacting with electrons in carbon nanotubes. J Phys Soc Jpn 75:084713ADSCrossRefGoogle Scholar
- 21.Jishi RA, Dresselhaus MS, Dresselhaus G (1993) Electron-phonon coupling and the electrical conductivity of fullerene nanotubules. Phys Rev B 48:11385ADSCrossRefGoogle Scholar
- 22.Kandemir BS (2013) Possible formation of chiral polarons in graphene. J Phys Condens Matter 25:025302ADSCrossRefGoogle Scholar
- 23.Kandemir BS, Mogulkoc A (2012) Zone-boundary phonon induced mini band gap formation in graphene. arXiv:1211.3528Google Scholar
- 24.Krstajić PM, Peeters FM (2012) Energy-momentum dispersion relation of plasmarons in graphene. Phys Rev B 85:205454ADSCrossRefGoogle Scholar
- 25.Lazzeri M, Piscanec S, Mauri F, Ferrari AC, Robertson J (2005) Electron transport and hot phonons in carbon nanotubes. Phys Rev Lett 95:236802ADSCrossRefGoogle Scholar
- 26.Lazzeri M, Piscanec S, Mauri F, Ferrari AC, Robertson J (2006) Phonon linewidths and electron-phonon coupling in graphite and nanotubes. Phys Rev B 73:155426ADSCrossRefGoogle Scholar
- 27.Lazzeri M, Attaccalite C, Wirtz L, Mauri F (2008) Impact of the electron-electron correlation on phonon dispersion: failure of LDA and GGA DFT functionals in graphene and graphite. Phys Rev B 78:081406(R)Google Scholar
- 28.Lee S-H, Chung H-J, Heo J, Yang H, Shin J, Chung U-I, Seo S (2011) Band gap opening by two-dimensional manifestation of Peierls instability in graphene. ACS Nano 5:2964–2969CrossRefGoogle Scholar
- 29.Lee TD, Low FE, Pines D (1953) The motion of slow electrons in a polar crystal. Phys Rev 90:297–302MathSciNetADSMATHCrossRefGoogle Scholar
- 30.Li WP, Wang ZW, Yin JW, Yu YF (2012) The effects of the magnetopolaron on the energy gap opening in graphene. J Phys Condens Matter 24:135301ADSCrossRefGoogle Scholar
- 31.Mariani E, von Oppen F (2008) Flexural phonons in free-standing graphene. Phys Rev Lett 100:076801ADSCrossRefGoogle Scholar
- 32.Mariani E, von Oppen F (2010) Temperature-dependent resistivity of suspended graphene. Phys Rev B 82:195403ADSCrossRefGoogle Scholar
- 33.Ni ZH, Yu T, Lu YH, Wang YY, Feng YP, Shen ZX (2008) Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2:2301–2305CrossRefGoogle Scholar
- 34.Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK (2005) Two-dimensional atomic crystals. Proc Nat Acad Sci USA 102:10451ADSCrossRefGoogle Scholar
- 35.Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306:666ADSCrossRefGoogle Scholar
- 36.Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov A (2005) Two-dimensional gas of massless Dirac fermions in graphene. Nature 438:197–200ADSCrossRefGoogle Scholar
- 37.Park CH, Giustino F, Cohen ML, Louie SG (2007) velocity renormalization and carrier lifetime in graphene from the electron–phonon interaction. Phys Rev Lett 99:086804Google Scholar
- 38.Pietronero L, Strässler S, Zeller HR, Rice MJ (1980) Electrical conductivity of a graphite layer. Phys Rev B 22:904ADSCrossRefGoogle Scholar
- 39.Pisana S, Lazzeri M, Casiraghi C, Novoselov KS, Geim AK, Ferrari AC, Mauri F (2007) Breakdown of the adiabatic Born-Oppenheimer approximation in graphene. Nat Mater 3:198ADSCrossRefGoogle Scholar
- 40.Piscanec S, Lazzeri M, Mauri F, Ferrari AC, Robertson J (2004) Kohn anomalies and electron-phonon interactions in graphite. Phys Rev Lett 93:185503ADSCrossRefGoogle Scholar
- 41.Rana F, George PA, Strait JH, Dawlaty J, Shivaraman S, Chandrashekhar M, Spencer MG (2009) Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene. Phys Rev B 79:115447ADSCrossRefGoogle Scholar
- 42.Samsonidze GG, Barros EB, Saito R, Jiang J, Dresselhaus G, Dresselhaus MS (2007) Electron-phonon coupling mechanism in two-dimensional graphite and single-wall carbon nanotubes. Phys Rev B 75:155420ADSCrossRefGoogle Scholar
- 43.Semenoff GW (1984) Condensed-matter simulation of a three-dimensional anomaly. Phys Rev Lett 53:2449MathSciNetADSCrossRefGoogle Scholar
- 44.Stauber T, Peres NMR (2008) Effect of Holstein phonons on the electronic properties of graphene. J Phys Condens Matter 20:055002ADSCrossRefGoogle Scholar
- 45.Stauber T, Peres NMR, Castro Neto AH (2008) Conductivity of suspended and non-suspended graphene at finite gate voltage. Phys Rev B 78:085418ADSCrossRefGoogle Scholar
- 46.Stojanović VM, Vukmirovic N, Bruder C (2010) Polaronic signatures and spectral properties of graphene antidot lattices. Phys Rev B 82:165410ADSCrossRefGoogle Scholar
- 47.Suzuura H, Ando T (2008) Zone-boundary phonon in graphene and nanotube. J Phys Soc Jpn 77:044703ADSCrossRefGoogle Scholar
- 48.Viet NA, Ajiki H, Ando T (1994) Lattice instability in metallic carbon nanotubes. J Phys Soc Jpn 63:3036–3047ADSCrossRefGoogle Scholar
- 49.Wallace PR (1947) The band theory of graphite. Phys Rev 71:622ADSMATHCrossRefGoogle Scholar
- 50.Yan J, Zhang Y, Kim P, Pinczuk A (2007) Electric field effect tuning of electron-phonon coupling in graphene. Phys Rev Lett 98:166802ADSCrossRefGoogle Scholar
- 51.Zhou SY, Gweon GH, Federov AV, First PN, De Heer WA, Lee D-H, Guinea F, Castro Neto AH, Lanzara A (2007) Substrate-induced bandgap opening in epitaxial graphene. Nature 6:770CrossRefGoogle Scholar
- 52.Zhou SY, Siegel DA, Fedorov AV, Lanzara A (2008) Kohn anomaly and interplay of electron-electron and electron-phonon interactions in epitaxial graphene. Phys Rev B 78:193404ADSCrossRefGoogle Scholar