Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene

Abstract

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long wavelength optical phonons of graphene. The EFE in this two dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and line-width demonstrate optically the particle-hole symmetry about the charge-neutral Dirac-point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of mass-less Dirac fermions.The interaction between electrons and quantized lattice vibrations in a solid is one of the most fundamental realms of study in condensed matter physics. In particular, the electron-phonon interaction in graphene and its derivatives plays an important role in understanding anomalies of photoemission spectra observed in graphite [1] and graphene [2], the non-linear high energy electron transport in carbon nanotubes [3,4,5,6,7], as well as phonon structures in graphite [8,9] and carbon nanotubes [9,10,11].Traditionally, electron-phonon interactions are investigated through chemical doping, in which the charge carrier density is varied by introduction of impurities. The electric field effect (EFE) is an alternative method for changing the charge carrier density effectively in lowdimensional systems. The EFE has proven very successful in graphene, a single atomic sheet of graphite, where unconventional integer quantum Hall effect [12,13] has revealed physics linked to the uniqueness of the electronic band structure near the charge neutral Dirac points ( Fig. 1(a)).We measured Raman spectra of optical phonons in graphene where large densities of free electrons or free holes are modulated by the EFE. We discovered that the even parity long wavelength optical phonon (the graphene G band) has marked dependence on gate voltage and the induced charge density. The dependence of phonon frequency and line-width on the EFE induced charge density demonstrates that the intriguing physics of mass-less Dirac fermions with particle-hole symmetry is encoded in the electron-phonon interaction.Raman studies of graphite [14] are at the forefront of research on carbon based materials. The recent availability of few-layer and single-layer graphene [15,16], has stimulated great interest in Raman scattering in such novel and exciting systems. For example, dimensional crossover was observed in Raman spectra of thin graphitic films as a function of multilayer thickness [17,18,19]. In the work reported here, Raman spectroscopy emerges as an insightful method to probe the EFE in a single atomic layer and the phonon dynamics that are associated with the two dimensional (2D) Dirac fermions.We focus on the doubly degenerate optical phonon of E 2g symmetry at ∼1580 cm −1 , known as the G band. We also report on the s...

Calculation of the RamanGpeak intensity in monolayer graphene: role of Ward identities

“…We take λ = 0.03, as obtained from the doping dependence of the G peak frequency [7,8], and we take λ K /λ = 3, as extracted from the ratio of the intensities of the 2D peak at 2700 cm −1 and the 2D peak at 3250 cm −1 [18]. Let us assume the inelastic scattering rate to be dominated by electron-phonon scattering (which is a lower bound), then it can be estimated as γ = (λ + λ K )ω in /8 [19].…”

Raman spectroscopy and imaging of graphene

“…For comparison, the Raman bands of bulk graphite do not shift after deposition and annealing, which supports the above explanation, as bulk graphite is too thick and is not easily compressed by SiO 2 . Recently, Yan et al [22] and Pisana et al [23] found that the frequency of the G and 2D Raman bands can also be adjusted by charge doping through electron-phonon coupling changes. In addition to the blueshift of the G band, a bandwidth narrowing of ~10 cm 1 was also observed in the case of charge doping.…”

Weak localization scattering lengths in epitaxial, and CVD graphene

“…Because of the very large optical phonon energies in graphene, 24 the dominant cooling mechanism for carriers at low temperatures comes from acoustic phonons. 13 The acoustic phonon cooling in graphene is a fairly weak mechanism which allows carriers to attain temperatures far in excess of that of the lattice, 13,14 and at low temperatures in the Bloch-Grüneisen limit this process is strongly temperature dependent.…”