Electron-phonon interactions in graphene, bilayer graphene, and graphite

Ab initio real-time quantum dynamics of charge carriers in momentum space

Application of the non-adiabatic molecular dynamics (NAMD) approach is limited to studying carrier dynamics in the momentum space, as a supercell is required to sample the phonon excitation and electron-phonon (e-ph) interaction at different momenta in a molecular dynamics simulation. Here we develop an ab initio approach for the real-time charge carrier quantum dynamics in the momentum space (NAMD_k) by directly introducing e-ph coupling into the Hamiltonian based on the harmonic approximation. The NAMD_k approach maintains the zero-point energy and includes memory effects of carrier dynamics. The application of NAMD_k to the hot carrier dynamics in graphene reveals the phonon-specific relaxation mechanism. An energy threshold of 0.2 eV-defined by two optical phonon modes-separates the hot electron relaxation into fast and slow regions with lifetimes of pico- and nanoseconds, respectively. The NAMD_k approach provides an effective tool to understand real-time carrier dynamics in the momentum space for different materials.

Energy dispersive anti-anharmonic effect in a Fano intervened semiconductor: revealed through temperature and wavelength-dependent Raman scattering

It is always interesting to understand how the interplay between two perturbations, affects any physical process and gets manifested in a semiconductor. Temperature- and wavelength-dependent Raman Spectromicroscopy was performed on heavily-doped Si to reveal an unusual anti-anharmonic effect. Additionally, the energy dispersive behaviour of Fano coupling strength was also studied and its possible interrelation with the observed anti-anharmonic effect was explored. A systematic study revealed that at the different excitation wavelengths, the strength of the Fano interaction was different, where the involved electron-phonon (Fano-Fano-interferon) bound states were counted together with different energies. By understanding how the interplay manifests in terms of the Raman line shape, a method to calculate the Fano-interferon dissociation energy was developed. The slope of the Raman linewidth at different excitation wavelengths with temperature showed a negative temperature coefficient and sign reversal on decreasing the doping concentration. A wavelength-dependent empirical relation is proposed to calculate the required thermal energy, required to dissociate the electron-phonon bound state.

Electron-Phonon Coupling in a Magic-Angle Twisted-Bilayer Graphene Device from Gate-Dependent Raman Spectroscopy and Atomistic Modeling

The importance of phonons in the strong correlation phenomena observed in twisted-bilayer graphene (TBG) at the so-called magic-angle is under debate. Here we apply gate-dependent micro-Raman spectroscopy to monitor the G band line width in TBG devices of twist angles θ = 0° (Bernal), ∼1.1° (magic-angle), and ∼7° (large-angle). The results show a broad and p-/n-asymmetric doping behavior at the magic angle, in clear contrast to the behavior observed in twist angles above and below this point. Atomistic modeling reproduces the experimental observations in close connection with the joint density of electronic states in the electron-phonon scattering process, revealing how the unique electronic structure of magic-angle TBGs influences the electron-phonon coupling and, consequently, the G band line width. Overall, the value of the G band line width in magic-angle TBG is larger when compared to that of the other samples, in qualitative agreement with our calculations.

Insight into the role of reduced graphene oxide for enhancing photocatalytic hydrogen evolution in disordered carbon nitride

Compared to crystalline carbon nitride, the performance of disordered carbon nitride (d-CN) as a hydrogen production photocatalyst is extremely poor. Owing to disordered atomic orientation, it is prone to numerous...

The electron-phonon coupling constant for single-layer graphene on metal substrates determined from He atom scattering

Recent theory has demonstrated that the value of the electron-phonon coupling strength λ can be extracted directly from the thermal attenuation (Debye-Waller factor) of helium atom scattering reflectivity. This theory is here extended to multivalley semimetal systems and applied to the case of graphene on different metal substrates and graphite. It is shown that λ rapidly increases for decreasing graphene-substrate binding strength. Two different calculational models are considered which produce qualitatively similar results for the dependence of λ on binding strength. These models predict, respectively, values of λ_HAS = 0.89 and 0.32 for a hypothetical flat free-standing single-layer graphene with cyclic boundary conditions. The method is suitable for analysis and characterization of not only the graphene overlayers considered here, but also other layered systems such as twisted graphene bilayers.

Roles of sliding-induced defects and dissociated water molecules on low friction of graphene

Sliding contact experiments and first-principles calculations were performed to elucidate the roles of structural defects and water dissociative adsorption process on the tribo-chemical mechanisms responsible for low friction of graphene. Sliding friction tests conducted in ambient air and under a dry N2 atmosphere showed that in both cases a high running-in coefficient of friction (COF) occurred initially but a low steady-state COF was reached only when the sliding was continued in air with moisture. Density functional theory (DFT) calculations indicated that the energy barrier (E b ) for dissociative adsorption of H2O was significantly lower in case of reconstructed graphene with a monovacancy compared to pristine graphene. Cross-sectional transmission electron microscopy of graphene transferred to the counterface revealed a partly amorphous structure incorporating damaged graphene layers with d-spacings larger than that of the original layers. DFT calculations on the reconstructed bilayer AB graphene systems revealed an increase of d-spacing due to the chemisorption of H, O, and OH at the vacancy sites and a reduction in the interlayer binding energy (E B ) between the bilayer graphene interfaces compared to pristine graphene. Thus, sliding induced defects facilitated dissociative adsorption of water molecules and reduced COF of graphene for sliding tests under ambient and humid environments but not under an inert atmosphere.

Theoretical Discovery of a Superconducting Two-Dimensional Metal-Organic Framework

Superconductivity is a fascinating quantum phenomenon characterized by zero electrical resistance and the Meissner effect. To date, several distinct families of superconductors (SCs) have been discovered. These include three-dimensional (3D) bulk SCs in both inorganic and organic materials as well as two-dimensional (2D) thin film SCs but only in inorganic materials. Here we predict superconductivity in 2D and 3D organic metal-organic frameworks by using first-principles calculations. We show that the highly conductive and recently synthesized Cu-benzenehexathial (BHT) is a Bardeen-Cooper-Schrieffer SC. Remarkably, the monolayer Cu-BHT has a critical temperature (T_c) of 4.43 K, while T_c of bulk Cu-BHT is 1.58 K. Different from the enhanced T_c in 2D inorganic SCs which is induced by interfacial effects, the T_c enhancement in this 2D organic SC is revealed to be the out-of-plane soft-mode vibrations, analogous to surface mode enhancement originally proposed by Ginzburg. Our findings not only shed new light on better understanding 2D superconductivity but also open a new direction to search for SCs by interface engineering with organic materials.

Electronic-structural dynamics in graphene

We review our recent time- and angle-resolved photoemission spectroscopy experiments, which measure the transient electronic structure of optically driven graphene. For pump photon energies in the near infrared ([Formula: see text]), we have discovered the formation of a population-inverted state near the Dirac point, which may be of interest for the design of THz lasing devices and optical amplifiers. At lower pump photon energies ([Formula: see text]), for which interband absorption is not possible in doped samples, we find evidence for free carrier absorption. In addition, when mid-infrared pulses are made resonant with an infrared-active in-plane phonon of bilayer graphene ([Formula: see text]), a transient enhancement of the electron-phonon coupling constant is observed, providing interesting perspective for experiments that report light-enhanced superconductivity in doped fullerites in which a similar lattice mode was excited. All the studies reviewed here have important implications for applications of graphene in optoelectronic devices and for the dynamical engineering of electronic properties with light.

Sublattice Interference as the Origin of σ Band Kinks in Graphene

Kinks near the Fermi level observed in angle-resolved photoemission spectroscopy (ARPES) have been widely accepted to represent electronic coupling to collective excitations, but kinks at higher energies have eluded a unified description. We identify the mechanism leading to such kink features by means of ARPES and tight-binding band calculations on σ bands of graphene, where anomalous kinks at energies as high as ∼4  eV were reported recently [Phys. Rev. Lett. 111, 216806 (2013)]. We found that two σ bands show a strong intensity modulation with abruptly vanishing intensity near the kink features, which is due to sublattice interference. The interference induced local singularity in the matrix element is a critical factor that gives rise to apparent kink features, as confirmed by our spectral simulations without involving any coupling to collective excitations.

Electron-phonon interaction and pairing mechanism in superconducting Ca-intercalated bilayer graphene

Using the ab initio anisotropic Eliashberg theory including Coulomb interactions, we investigate the electron-phonon interaction and the pairing mechanism in the recently-reported superconducting Ca-intercalated bilayer graphene. We find that C6CaC6 can support phonon-mediated superconductivity with a critical temperature Tc = 6.8-8.1 K, in good agreement with experimental data. Our calculations indicate that the low-energy Caxy vibrations are critical to the pairing, and that it should be possible to resolve two distinct superconducting gaps on the electron and hole Fermi surface pockets.

Fröhlich Electron-Phonon Vertex from First Principles

We develop a method for calculating the electron-phonon vertex in polar semiconductors and insulators from first principles. The present formalism generalizes the Fröhlich vertex to the case of anisotropic materials and multiple phonon branches, and can be used either as a postprocessing correction to standard electron-phonon calculations, or in conjunction with ab initio interpolation based on maximally localized Wannier functions. We demonstrate this formalism by investigating the electron-phonon interactions in anatase TiO(2), and show that the polar vertex significantly reduces the electron lifetimes and enhances the anisotropy of the coupling. The present work enables ab initio calculations of carrier mobilities, lifetimes, mass enhancement, and pairing in polar materials.

Population inversion in monolayer and bilayer graphene

The recent demonstration of saturable absorption and negative optical conductivity in the Terahertz range in graphene has opened up new opportunities for optoelectronic applications based on this and other low dimensional materials. Recently, population inversion across the Dirac point has been observed directly by time- and angle-resolved photoemission spectroscopy (tr-ARPES), revealing a relaxation time of only ∼130 femtoseconds. This severely limits the applicability of single layer graphene to, for example, Terahertz light amplification. Here we use tr-ARPES to demonstrate long-lived population inversion in bilayer graphene. The effect is attributed to the small band gap found in this compound. We propose a microscopic model for these observations and speculate that an enhancement of both the pump photon energy and the pump fluence may further increase this lifetime.

Phonon-pump extreme-ultraviolet-photoemission probe in graphene: anomalous heating of Dirac carriers by lattice deformation

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane E_{1u} lattice vibration at 6.3  μm. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the K point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the E_{1u} vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Electron-phonon coupling and its implication for the superconducting topological insulators

The recent observation of superconductivity in doped topological insulators has sparked a flurry of interest due to the prospect of realizing the long-sought topological superconductors. Yet the understanding of underlying pairing mechanism in these systems is far from complete. Here we investigate this problem by providing robust first-principles calculations of the role of electron-phonon coupling for the superconducting pairing in the prime candidate Cu_xBi₂Se₃. Our results show that electron-phonon scattering process in this system is dominated by zone center and boundary optical modes, with coexistence of phonon stiffening and softening. While the calculated electron-phonon coupling constant λ suggests that T_c from electron-phonon coupling is 2 orders smaller than the ones reported on bulk inhomogeneous samples, suggesting that superconductivity may not come from pure electron-phonon coupling. We discuss the possible enhancement of superconducting transition temperature by local inhomogeneity introduced by doping.

Bias free gap creation in bilayer graphene

For graphene to be utilized in the digital electronics industry the challenge is to create bandgaps of order 1 eV as simply as possible. The most successful methods for the creation of gaps in graphene are (a) confining the electrons in nanoribbons, which is technically difficult or (b) placing a potential difference across bilayer graphene, which is limited to gaps of around 300 meV for reasonably sized electric fields. Here we propose that electronic band gaps can be created without applying an external electric field, by using the electron-phonon interaction formed when bilayer graphene is sandwiched between highly polarisable ionic materials. We derive and solve self-consistent equations, finding that a large gap can be formed for intermediate electron-phonon coupling. The gap originates from the amplification of an intrinsic Coulomb interaction due to the proximity of carbon atoms in neighbouring planes.

Resistive switching in iron-oxide-filled carbon nanotubes

Iron-oxide-filled carbon nanotubes exhibit an intriguing charge bipolarization behavior which allows the material to be applied in resistive memory devices. Raman analysis conducted with an electric field applied in situ shows the Kohn anomalies and a strong modification of the electronic properties related to the applied voltage intensity. In addition, the I(D)/I(G) ratio indicated the reversibility of this process. The electrical characterization indicated an electronic transport governed by two main kinds of charge hopping, one between the filling and the nanotube and the other between the nanotube shells.

Pseudopotential-based studies of electron transport in graphene and graphene nanoribbons

The theoretical understanding of electron transport in graphene and graphene nanoribbons is reviewed, emphasizing the help provided by atomic pseudopotentials (self-consistent and empirical) in determining not only the band structure but also other fundamental transport parameters such as electron-phonon matrix elements and line-edge roughness scattering. Electron-phonon scattering in suspended graphene sheets, impurity and remote-phonon scattering in supported and gated graphene, electron-phonon and line-edge roughness scattering in armchair-edge nanoribbons are reviewed, keeping in mind the potential use of graphene in devices of the future very large scale integration technology.

Conversion of multilayer graphene into continuous ultrathin sp³-bonded carbon films on metal surfaces

The conversion of multilayer graphenes into sp(3)-bonded carbon films on metal surfaces (through hydrogenation or fluorination of the outer surface of the top graphene layer) is indicated through first-principles computations. The main driving force for this conversion is the hybridization between sp(3) orbitals and metal surface dz(2) orbitals. The induced electronic gap states and spin moments in the carbon layers are confined in a region within 0.5 nm of the metal surface. Whether the conversion occurs depend on the fraction of hydrogenated (fluorinated) C atoms at the outer surface and on the number of stacked graphene layers. In the analysis of the Eliashberg spectral functions for the sp(3) carbon films on a metal surface that is diamagnetic, the strong covalent metal-sp(3) carbon bonds induce soft phonon modes that predominantly contribute to large electron-phonon couplings, suggesting the possibility of phonon-mediated superconductivity. Our computational results suggest a route to experimental realization of large-area ultrathin sp(3)-bonded carbon films on metal surfaces.

Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene

In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS₂, WSe₂, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications.

Phonon self-energy corrections to nonzero wave-vector phonon modes in single-layer graphene

Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q=0) wave vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene originating from a double-resonant Raman process with q≠0. The observed phonon renormalization effects are different from what is observed for the zone-center q=0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons with nonzero wave vectors (q≠0) in single-layer graphene in which the frequencies and decay widths are expected to behave oppositely to the behavior observed in the corresponding zone-center q=0 processes. Within this framework, we resolve the identification of the phonon modes contributing to the G(⋆) Raman feature at 2450 cm(-1) to include the iTO+LA combination modes with q≠0 and also the 2iTO overtone modes with q=0, showing both to be associated with wave vectors near the high symmetry point K in the Brillouin zone.

Optical self-energy in graphene due to correlations

In highly correlated systems one can define an optical self-energy in analogy to its quasiparticle (QP) self-energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self-energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta (k) of the charge carriers, the structure in the optical self-energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for k equal to or near the Fermi momentum k(F). Consequently, plasmaronic structures which are associated with momenta near the Dirac point at k = 0 are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. We introduce a method whereby detailed quantitative information on such excitation spectra can be extracted from optical data. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self-energies around k(F) of the lower Dirac cone associated with the occupied states.

Electronic properties of graphene: a perspective from scanning tunneling microscopy and magnetotransport

This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magnetotransport techniques.

Temperature effects on the Raman spectra of graphenes: dependence on the number of layers and doping

Temperature effects on the various features in the Raman spectra of several graphene samples and graphene nanoribbons have been investigated over the temperature range 77-573 K. The temperature coefficient of the G and 2D band frequencies are found to depend on the number of layers, the former decreasing with the increase in the number of layers. The number of layers also affects the temperature coefficients of the FWHMs of these bands. Doping of graphene affects these Raman features significantly. The defect-related bands D and D(') bands are not sensitive to the number of layers or doping. We can understand the observed temperature effects on the basis of electron-phonon coupling, thermal expansion and anharmonic phonon-phonon interactions.

First-principles prediction of doped graphane as a high-temperature electron-phonon superconductor

We predict by first-principles calculations that p-doped graphane is an electron-phonon superconductor with a critical temperature above the boiling point of liquid nitrogen. The unique strength of the chemical bonds between carbon atoms and the large density of electronic states at the Fermi energy arising from the reduced dimensionality give rise to a giant Kohn anomaly in the optical phonon dispersions and push the superconducting critical temperature above 90 K. As evidence of graphane was recently reported, and doping of related materials such as graphene, diamond, and carbon nanostructures is well established, superconducting graphane may be feasible.

Phonon-assisted electroluminescence from metallic carbon nanotubes and graphene

We report on light emission from biased metallic single-wall carbon nanotube (SWNT), multiwall carbon nanotube (MWNT) and few-layer graphene (FLG) devices. SWNT devices were assembled from tubes with different diameters in the range 0.7-1.5 nm. They emit light in the visible spectrum with peaks at 1.4 and 1.8 eV. Similar peaks are observed for MWNT and FLG devices. We propose that this light emission is due to phonon-assisted radiative decay from populated pi* band states at the M point to the Fermi level at the K point. Since for most carbon nanotubes as well as for graphene the energy of unoccupied states at the M point is close to 1.6 eV, the observation of two emission peaks at approximately 1.6 +/- approximately 0.2 eV could indicate radiative decay under emission or absorption of optical phonons, respectively.

Doped graphene as tunable electron-phonon coupling material

We present a new way to tune the electron-phonon coupling (EPC) in graphene by changing the deformation potential with electron/hole doping. We show the EPC for highest optical branch at the high symmetry point K acquires a strong dependency on the doping level due to electron-electron correlation not accounted in mean-field approaches. Such a dependency influences the dispersion (with respect to the laser energy) of the Raman D and 2D lines and the splitting of the 2D peak in multilayer graphene. Finally this doping dependence opens the possibility to construct tunable electronic devices through external control of the EPC.

Infrared and Raman spectra of AA-stacking bilayer graphene

The infrared (IR) absorption and resonant Raman spectra of the undoped AA-stacking bilayer graphene have been calculated using density-functional theory in the local density approximation. It is found that the undoped AA-stacking bilayer graphene exhibits a different characteristic jump and peak structure in its IR spectra, and a different G-band peak structure in its resonant Raman spectra, compared with those of the AB-stacking one, which are caused by the different interlayer coupling effects, due to different stacking types in both of them. Based upon the different IR and Raman spectra, a powerful experimental method can be proposed to identify accurately the stacking type and the layer number in future experiments.

Graphene: the new two-dimensional nanomaterial

Every few years, a new material with unique properties emerges and fascinates the scientific community, typical recent examples being high-temperature superconductors and carbon nanotubes. Graphene is the latest sensation with unusual properties, such as half-integer quantum Hall effect and ballistic electron transport. This two-dimensional material which is the parent of all graphitic carbon forms is strictly expected to comprise a single layer, but there is considerable interest in investigating two-layer and few-layer graphenes as well. Synthesis and characterization of graphenes pose challenges, but there has been considerable progress in the last year or so. Herein, we present the status of graphene research which includes aspects related to synthesis, characterization, structure, and properties.

Giant kink in electron dispersion of strongly coupled lead nanowires

Our photoelectron spectroscopy study shows a giant kink in the electron dispersion, a sign of high-energy manybody interactions of electrons, in a well-ordered Pb nanowire array self-assembled on a silicon substrate. We show that the unique electronic band structure due to the strong lateral coupling and the atomic structure of the nanowires drives an enhanced manybody interaction for kinked electron dispersion. The major giant kink mechanisms discussed previously, the magnetic and plasmonic excitations, are not relevant in the present system, supporting the recent kink theory based purely on electron-electron correlation. This suggests that tailored electronic band structures in nano array systems can provide unprecedented ways to study manybody interactions of electrons.

First-principles study of electron linewidths in graphene

We present first-principles calculations of the linewidths of low-energy quasiparticles in n-doped graphene arising from both the electron-electron and the electron-phonon interactions. The contribution to the electron linewidth arising from the electron-electron interactions varies significantly with wave vector at fixed energy; in contrast, the electron-phonon contribution is virtually wave vector independent. These two contributions are comparable in magnitude at a binding energy of approximately 0.2 eV, corresponding to the optical phonon energy. The calculated linewidths, with both electron-electron and electron-phonon interactions included, explain to a large extent the linewidths seen in recent photoemission experiments.