Electron-phonon Coupling In Graphene Research Articles

Probing Enhanced Electron-Phonon Coupling in Graphene by Infrared Resonance Raman Spectroscopy.

We report on resonance Raman spectroscopy measurements with excitation photon energy down to 1.16eV on graphene, to study how low-energy carriers interact with lattice vibrations. Thanks to the excitation energy close to the Dirac point at K, we unveil a giant increase of the intensity ratio between the double-resonant 2D and 2D^{'} peaks with respect to that measured in graphite. Comparing with fully abinitio theoretical calculations, we conclude that the observation is explained by an enhanced, momentum-dependent coupling between electrons and Brillouin zone-boundary optical phonons. This finding applies to two-dimensional Dirac systems and has important consequences for the modeling of transport in graphene devices operating at room temperature.

Dichotomy of Electron-Phonon Coupling in Graphene Moiré Flat Bands.

Graphene moiré superlattices are outstanding platforms to study correlated electron physics and superconductivity with exceptional tunability. However, robust superconductivity has been measured only in magic-angle twisted bilayer graphene (MA-TBG) and magic-angle twisted trilayer graphene (MA-TTG). The absence of a superconducting phase in certain moiré flat bands raises a question on the superconducting mechanism. In this work, we investigate electronic structure and electron-phonon coupling in graphene moiré superlattices based on atomistic calculations. We show that electron-phonon coupling strength λ is dramatically different among graphene moiré flat bands. The total strength λ is very large (λ>1) for MA-TBG and MA-TTG, both of which display robust superconductivity in experiments. However, λ is an order of magnitude smaller in twisted double bilayer graphene (TDBG) and twisted monolayer-bilayer graphene (TMBG) where superconductivity is reportedly rather weak or absent. We find that the Bernal-stacked layers in TDBG and TMBG induce sublattice polarization in the flat-band states, suppressing intersublattice electron-phonon matrix elements. We also obtain the nonadiabatic superconducting transition temperature T_{c} that matches well with the experimental results. Our results clearly show a correlation between strong electron-phonon coupling and experimental observations of robust superconductivity.

Detection of electron-phonon coupling in two-dimensional materials by light scattering

Electron-phonon coupling affects the properties of two-dimensional (2D) materials significantly, leading to a series of novel phenomena. Inelastic light scattering provides a powerful experimental tool to explore electron-phonon interaction in 2D materials. This review gives an overview of the basic theory and experimental advances of electron-phonon coupling in 2D materials detected by Raman and Brillouin scattering, respectively. In the Raman scattering part, we review Raman spectroscopy studies of electron-phonon coupling in graphene, transition metal disulfide compounds, van der Waals heterostructures, strongly correlated systems, and 2D magnetic materials. In the Brillouin scattering part, we extensively introduce Brillouin spectroscopy in non-van der Waals 2D structures, including temperature sensors for phonons and magnons, interfacial Dzyaloshinsky-Moriya interaction and spin torque in multilayer magnetic structures, as well as exciton-polariton in semiconductor quantum well.

Numerical study of the rippling instability driven by electron-phonon coupling in graphene

Suspended graphene exhibits ripples of size ranging from 50 to 100 {\AA} and height $\sim$10{\AA}, however, their origin remains undetermined. Previous theoretical works have proposed that rippling in graphene might be generated by the coupling between the bending modes and the density of electrons. These studies theoretically proposed that in the thermodynamic limit a membrane of single layer graphene displays a lattice instability for large enough electron-phonon coupling, undergoing a phase transition from a flat phase to a rippled one. In this work we solve the elasticity equations for a finite membrane of graphene coupled to the charge distribution, modeled in the tight-binding approximation, we find that the electron-phonon coupling controls a transition from a stable flat configuration to a stable rippled phase.

Phonon-induced linewidths of graphene electronic states

The linewidths of the electronic bands originating from the electron-phonon coupling in graphene are analyzed based on model tight-binding calculations and experimental angle-resolved photoemission spectroscopy (ARPES) data. Our calculations confirm the prediction that the high-energy optical phonons provide the most essential contribution to the phonon-induced linewidth of the two upper occupied $\sigma$ bands near the $\bar{\Gamma}$-point. For larger binding energies of these bands, as well as for the $\pi$ band, we find evidence for a substantial lifetime broadening from interband scattering $\pi \rightarrow \sigma$ and $\sigma \rightarrow \pi$, respectively, driven by the out-of-plane ZA acoustic phonons. The essential features of the calculated $\sigma$ band linewidths are in agreement with recent published ARPES data [F. Mazzola et al., Phys.~Rev.~B. 95, 075430 (2017)] and of the $\pi$ band linewidth with ARPES data presented here.

Concomitant enhancement of electron-phonon coupling and electron-electron interaction in graphene decorated with ytterbium

The interplay between electron-electron interaction and electron-phonon coupling has been one of the key issues in graphene as it can provide information on the origin of enhanced electron-phonon coupling in graphene by foreign atoms. In ytterbium-decorated graphene on SiC substrate, electron-phonon coupling exhibits strong enhancement compared to that of as-grown graphene. Based on angle-resolved photoemission study, the presence of ytterbium is also found to result in the decrease of Fermi velocity, revealing the enhancement of electron-electron interaction within the Fermi liquid theory. Our finding on the concomitant enhancement of electron-electron interaction and electron-phonon coupling suggests a possibility of the interplay between the two representative many-body interactions in graphene decorated with foreign atoms.

Electron-phonon coupling in graphene placed between magnetic Li and Si layers on cobalt

Superconductivity in two-dimensional materials remains largely unexplored and attracts much attention. Although graphene is not a superconductor, adsorption of alkali metals on its surface may enhance electron-phonon coupling (EPC) sufficiently to induce superconductivity. Here, using photoemission spectroscopy, the authors study the electronic structure and EPC in a Li-doped graphene monolayer weakly bonded to a cobalt substrate. It is shown that EPC is high enough to create superconductivity in graphene, however the nonmagnetic graphene layer is clamped between two oppositely magnetized atomic layers. This condition makes the studied system a promising platform for understanding the influence of magnetic environment on superconductivity at low dimensions.

Strong electron-phonon coupling in the σ band of graphene

First-principles studies of the electron-phonon coupling in graphene predict a high coupling strength for the $\sigma$ band with $\lambda$ values of up to 0.9. Near the top of the $\sigma$ band, $\lambda$ is found to be $\approx 0.7$. This value is consistent with the recently observed kinks in the $\sigma$ band dispersion by angle-resolved photoemission. While the photoemission intensity from the $\sigma$ band is strongly influenced by matrix elements due to sub-lattice interference, these effects differ significantly for data taken in the first and neighboring Brillouin zones. This can be exploited to disentangle the influence of matrix elements and electron-phonon coupling. A rigorous analysis of the experimentally determined complex self-energy using Kramers-Kronig transformations further supports the assignment of the observed kinks to strong electron-phonon coupling and yields a coupling constant of $0.6(1)$, in excellent agreement with the calculations.

Enhanced electron-phonon coupling in graphene with periodically distorted lattice

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically-active in-plane bond stretching vibrations with femtosecond mid-infrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. Firstly, TeraHertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Secondly, the relaxation rate of hot quasi-particles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient three-fold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

Model study of the electron-phonon coupling in graphene; relative importance of intraband and interband scattering

The aim of this model study of the electron-phonon coupling in graphene was to find out about the relative importance of the inter- and intraband scattering and which phonon modes are the most active. This was achieved by analyzing the electron-phonon matrix element of the carbon dimer in the unit cell. We found that for the intra molecular orbital matrix elements the longitudinal optical phonon mode is the active phonon mode. The matrix element corresponding to σ→σ is greater than the matrix element for π→π. The inter molecular orbital scattering π→σ is driven by the out-of-plane acoustic phonon mode, while the out-of-plane optical mode does not contribute for symmetry reasons. We found the unexpected result that the magnitude of matrix element of the inter molecular orbital scattering π→σ exceeds the intra molecular orbital scattering π→π. These results indicate that the in general not considered inter-band scattering has to be taken into account when analyzing e.g. photo-hole lifetimes and the electron-phonon coupling constant λ from photoemission data of graphene.

Room-temperature quantum Hall effect in graphene: the role of the two-dimensional nature of phonons

We consider two-dimensional nature of the electron-phonon coupling in graphene as a source for the room-temperature quantum Hall effect discovered in 2007. It is shown that magnetic field introduces strong cut-off for coupling with the two-dimensional acoustic phonons, viz. the processes with energy tranfer exceeding ℏslB−1 are exponentially suppressed, while for three-dimensional phonons the cut-off is set by a temperature T (here s is the sound velocity and lB ∝ B−1/2 is the magnetic length). Consequently, at sufficiently high temperatures and magnetic fields only a small part (~ ℏslB−1/T) of the electron states is involved in coupling with a given electron state in comparison with the case of three-dimensional phonons. Hence, the percolation threshold is postponed, and the quantum Hall effect survives up to T = 300 K.

Raman spectroscopy of graphite intercalation compounds: Charge transfer, strain, and electron–phonon coupling in graphene layers (Phys. Status Solidi B 12/2014)

Graphite intercalation compounds, a three-dimensional molecular system, has renascence as a powerful tool to study the effects of charge transfer, strain, and electron phonon coupling in graphene. Since 1980's, the use of alkali metals intercalated in between graphitic layers has been of high interest to the scientific community. In 2007 the discovery of superconductivity in Ca intercalated graphite attracted the attention to further investigate graphite intercalation compounds and develop high temperature superconductors. More recently, in 2010 the Nobel prize in physics was awarded for the discovery of graphene by mechanical exfoliation of graphite. Since then, a breakthrough in the study of graphene has exploded and different approaches have emerged to resolve the properties of this novel material. Graphite intercalation compounds are one of these approaches shown to be a highly efficient top-bottom method to analyze the electronic and mechanical properties of graphene. Additionally, they have brought information about doping levels, lattice parameters, and structural properties of mono-, bi-, tri- and few-layer graphene which will serve as an outstanding mechanism for future research in graphene based-materials and their composites. For further details see the Feature Article by Chacón-Torres et al. (pp. 2337–2355.)

Ytterbium-driven strong enhancement of electron-phonon coupling in graphene

We present high-resolution angle-resolved photoemission spectroscopy study in conjunction with first principles calculations to investigate how the interaction of electrons with phonons in graphene is modified by the presence of Yb. We find that the transferred charges from Yb to the graphene layer hybridize with the graphene $\pi$ bands, leading to a strong enhancement of the electron-phonon interaction. Specifically, the electron-phonon coupling constant is increased by as much as a factor of 10 upon the introduction of Yb with respect to as grown graphene ($\leq$0.05). The observed coupling constant constitutes the highest value ever measured for graphene and suggests that the hybridization between graphene and the adatoms might be a critical parameter in realizing superconducting graphene.

Electron energy and temperature relaxation in graphene on a piezoelectric substrate

We study the energy and temperature relaxation of electrons in graphene on a piezoelectric substrate. Scattering from the combined potential of extrinsic piezoelectric surface acoustical (PA) phonons of the substrate and intrinsic deformation acoustical (DA) phonons of graphene is considered in a (non-)degenerate gas of Dirac fermions. It is shown that in the regime of low energies or temperatures the PA phonons dominate the relaxation and change qualitatively its character. This prediction is relevant for quantum metrology and electronic applications using graphene devices and suggests a new experimental setup for probing electron-phonon coupling in graphene.

First-Principles Calculations on the Effect of Doping and Biaxial Tensile Strain on Electron-Phonon Coupling in Graphene

Graphene has exhibited a wealth of fascinating properties, but is also known not to be a superconductor. Remarkably, we show that graphene can be made a conventional Bardeen-Cooper-Schrieffer superconductor by the combined effect of charge doping and tensile strain. While the effect of doping obviously enlarges the Fermi surface, the effect of strain profoundly increases the electron-phonon coupling. At the experimental accessible doping (~4×10(14) cm(-2)) and strain (~16%) levels, the superconducting critical temperature T(c) is estimated to be as high as ~30 K, the highest for a single-element material above the liquid hydrogen temperature.

Screening of electron-phonon coupling in graphene on Ir(111)

The phonon dispersion of graphene on Ir(111) has been determined by means of angle-resolved inelastic electron scattering and density functional calculations. Kohn anomalies of the highest optical-phonon branches are observed at the $\Gamma$ and K point of the surface Brillouin zone. At K the Kohn anomaly is weaker than observed from pristine graphene and graphite. This observation is rationalized in terms of a decrease of the electron-phonon coupling due to screening of graphene electron correlations by the metal substrate.

Symmetry based analysis of the Kohn anomaly and electron-phonon interaction in graphene and carbon nanotubes

Symmetry based analysis of the electron-phonon coupling in graphene and carbon nanotubes is performed and Kohn anomalies, their Brillouin-zone positions together with the complete set of good quantum numbers are predicted. Interestingly, graphene dynamical representation is found to contain only a small portion of quite a large set of inequivalent irreducible representations of the relevant full symmetry group. Besides, vanishing of the electron-phonon interaction for majority of the normal displacements is also shown to be a consequence of the symmetry. The results are further numerically confirmed within full and tight-binding density-functional calculations and force constants model and enhanced coupling to the Fermi level electrons of the Dirac point ${A}_{1g}$ mode with respect to the $\ensuremath{\Gamma}$ point ${E}_{2g}$ mode is confirmed. Finally, energy dispersion of the kink phonon spectrum is analytically evaluated and compared to the classical phonon spectrum.

ELECTRON-PHONON COUPLING IN GRAPHENE

Numerical and symmetry based analysis of the electron-phonon coupling in graphene have been performed. Symmetry alone predicts the Kohn anomalies, their positions in the Brillouin zone and all quantum numbers of the Kohn modes and the vectors of the Kohn displacements. Dispersion of kink phonons is calculated and found to be similar to the classical phonon spectrum. Interestingly, most of the Γ (including all the acoustic phonons as well) and K modes are shown to be uncoupled to electrons.

Electric Field Effect Tuning of Electron-Phonon Coupling in Graphene

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 linewidth 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 massless Dirac fermions.

Electron-phonon coupling and Raman spectroscopy in graphene

We show that the electron-phonon coupling in graphene, in contrast with the non-relativistic two-dimensional electron gas, leads to shifts in the phonon frequencies that are non-trivial functions of the electronic density. These shifts can be measured directly in Raman spectroscopy. We show that depending whether the chemical potential is smaller (larger) than half of the phonon frequency, the frequency shift can negative (positive) relative to the neutral case (when the chemical potential is at the Dirac point), respectively. We show that the use of the static response function to calculate these shifts is incorrect and leads always to phonon softening. In samples with many layers, we find a shift proportional to the carrier concentration, and a splitting of the phonon frequencies if the charge is not homogeneously distributed. We also discuss the effects of edges in the problem.