Session V12: Graphene: Optical Properties and Responses

Temperature dependence of hot carrier-assisted photoresponse in graphene

We report on temperature dependent photocurrent measurements of high-quality dual-gated monolayer graphene p-n junction devices. Over temperatures ranging from 5 K to 300 K, we find that the photocurrent at the p-n interface peaks at an intermediate temperature, and decreases at higher and lower temperatures. Spatial photocurrent microscopy (at wavelength 850 nanometers) shows that the photocurrent measured as a function of distance away from the p-n interface also varies with temperature. We consider various electronic cooling processes in graphene to explain the photocurrent temperature dependence. Our measurements may reveal novel energy loss processes that reduce the electronic temperature of photoexcited charge carriers in graphene, and give additional insight into hot carrier photoresponse.   

Hot-Carrier cooling at Graphene-Metal Contact Interface

There has been a recent surge of interest in using graphene as broadband and ultrafast optoelectronics, however the mechanisms of photodetection are not yet fully understood. Our previous measurements at a top gated graphene pn junction and at a monolayer-bilayer interface have found the dominating mechanism to be photothermoelectric (PTE) in nature, whereas most graphene-metal contact (GM) studies attribute photocurrent to the photovoltaic effect. By performing comprehensive ultrafast optical pump-probe measurements of photocurrent as a function of temperature, Fermi level, and laser power at various GM interfaces, the current work differentiates the contributions of PTE and photovoltaic effects to the photocurrent and identifies a hot-carrier relaxation time of $\sim $2 ps at room temperature and $\sim $7 ps at cryogenic temperatures. This work provides valuable insight to the design of new graphene based optoelectronic devices for sensing and communication.   

Time Resolved Carrier Distributions in Graphene

Graphene, a recently discovered two-dimensional form of carbon, is a strong candidate for many future electronic devices. A question of central importance in optoelectronics, particularly high-speed applications, is how photoexcited carriers behave on ultrashort time scales. Even though time-resolved studies have provided a wealth of information, fundamental questions concerning the quantum descriptions of the transient electron-hole plasma remain. On one hand, conflicting views on the relaxation dynamics go as far as precluding the possibility of observing some predicted phenomena, such as THz lasing or tunable lasers while the observation of phenomena such as ultrafast photoluminescence and carrier multiplication are already established. Here, by employing the technique of time-resolved photoemission, we directly obtain the evolving Fermi-Dirac distributions of the electrons and holes: on an ultrashort 500 fs time scale the electron and hole populations can be described by two separate Fermi-Dirac distributions, while on longer time scales the populations coalesce to form a single Fermi-Dirac distribution at an elevated temperature. This unusual behavior is a consequence of graphene's unique band structure and has important implications for possible applications.   

Gate-tunable nanoplasmonic effects in single- and bi-layer graphene

We employed near-field infrared (IR) nanoscopy and nanoimaging to study mid-IR nanoplasmonic effects of both single-layer graphene (SLG) and bilayer graphene (BLG) on SiO2/Si substrate. In our previous study, we found that SLG enhanced and blueshifted the surface phonon resonance of SiO2 due to plasmon-phonon coupling [Z. Fei et al. Nano. Lett. 2011]. Here we report that both these effects are also observed in BLG. Using back-gate we were able to systematically change the carrier density in both SLG and BLG while monitoring the evolution of the hybrid plasmon-phonon resonance. New data are in accord with our point-dipole modeling results. IR imaging with nanoscale resolution revealed fringe patterns extending along the edges of both SLG and BLG. We ascribe these patterns to the interference of plasmon waves launched by the near-field probe with those reflected from the edges. Detailed analysis allowed us to observe gate-induced changes in the plasmon dispersion of both SLG and BLG, which are consistent with the notion of massless Dirac fermions in SLG and massive carriers in BLG.   

Atomically Localized Plasmon Enhancement in Monolayer Graphene

Graphene has attracted significant attention due to its exceptional properties and very promising applications, including optoelectronics and nanoplasmonics. All localized plasmon resonances observed so far in materials have been limited to the sub-10 nanometer scale, with a reported record of $\lambda/40$, where $\lambda$ is the wavelength of the related plasmon excitation. In this talk, using aberration-corrected scanning trasmission electron microscopy and total energy first-principles calculations, we show that single point defects can enhance the $\pi$ and $\pi + \sigma$ plasmons of monolayer graphene at the atomic level. Our study shows that point defects in monolayer graphene represent a length scale smaller than $\lambda$/200, and suggest that the physical limit for the size of plasmonic and optoelectronic devices can be down to the single atom level. This research was supported by NSF grant No. DMR-0938330 (WZ, J-CI), DOE grant DE- F002-09ER46554 (STP), by the Shared Research Equipment (SHaRE) User Facility, Oak Ridge National Laboratory, which is sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences (J-CI), and by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, U.S. Department of Energy (JL, JN, SJP).   

Effect of nonhomogenous dielectric background on the plasmon modes in graphene double-layer structures

We have calculated the plasmon modes in graphene double layer structures, taking into account the non-homogeneity of the system dielectric background. The effective dielectric function is obtained from the solution of the Poisson equation in three-layer dielectric medium with the graphene sheets located at the interfaces, separating different materials. Due to the momentum dispersion of the effective dielectric function, the intra- and inter-layer bare Coulomb interactions in graphene double layer systems acquire additional momentum dependence--an effect of the order of inter-layer interaction itself. It has been shown that in the long wavelength limit the energies of optical and acoustical plasmons, respectively, with the square root and linear dispersions are determined by different dielectric permittivities.   

Measurement of plasmon dispersion in graphene: tunable graphene plasmonics

Graphene is an intriguing material for plasmonics. We have measured the transmission spectrum of large area graphene, grown using chemical vapor deposition, using Fourier transform infrared spectroscopy. By varying the Fermi level of graphene, we are able to explore the energy dispersion of plasmons in graphene. Our result lays the foundation for tunable plasmonic devices based on graphene.   

Scattering theory for graphene plasmons near edges and interfaces

Motivated by recent infrared nano-imaging experiments, we study eigenmodes of graphene plasmons near sample boundaries, corners, and interfaces. Such modes can be understood as standing-wave patters formed by multiple scattering of elementary waves. We derive the rules of the corresponding scattering theory by analyzing the integro-differential equation for the plasmon dynamics. Our analytical results include the solution for the edge reflection problem in uniform graphene and a quasiclassical formalism for graphene of slowly varying density. Numerical simulations are employed for more complicated boundary geometries (wedge, constriction, etc.) and for singular density distributions that exist near the edge of a gated graphene.   

Edge Functionalization and Optical Excitations in Graphene Nanoflakes

We investigate the effects of edge covalent functionalization on the opto-electronic properties of finite elongated graphene nano-flakes (GNFs). Following our previous work on nanojunctions[1], we compute mean-field ground state electronic properties and configuration-interaction UV-vis optical excitations at varying size and functionalization by means of semi-empirical methods. The character of the lowest energy excitations and the influence exerted on them both by length/width modulation and by the specific chemical properties of the terminating groups are analyzed in details. The role of local distortions spontaneously arising upon geometrical optimization is inspected. Nanoplasmonic-like features related to the spectrum of these elongated finite graphene nanostructures are also discussed. [1] C. Cocchi et al. J. Phys. Chem. Lett. 2, 1315 (2011)   

Theory of double-resonant Raman spectra in graphene: intensity and line shape of defect-induced and two-phonon bands

We calculate the double resonant Raman spectrum of graphene associated to both phonon-defect processes (such as the $D$ and $D'$ lines), and two-phonons ones (such as the $2D$, $2D'$ and $D+D''$ lines). For an excitation energy of $2.4$~eV, the agreement with measurements is very good and calculations reproduce the relative intensities among phonon-defect or among two-phonon lines and the measured small widths of the $D$, $D'$, $2D$ and $2D'$ lines. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could be used to identify actual defects. The present analysis reveals that, for both $D$ and $2D$ lines, the dominant DR processes are those in which electrons and holes are both involved in the scattering. The most important phonons belong to the {\bf K}$\rightarrow{\mathbf{\Gamma}}$ direction ($inner$ phonons) and not to the {\bf K}$\rightarrow${\bf M} one ($outer$ phonons), as usually assumed. The small $2D$ line width at $\epsilon_L=2.4$~eV is a consequence of the interplay between the opposite trigonal warpings of the electron and phonon dispersions.   

A TD-DFT study on the Optical and dielectric properties of graphene nanoflakes

Optical and dielectric properties of graphene nanostructures are of current interest because the potential applications in electronic and photonics devices. Recently, it has been reported important progress in the synthesis of graphene nanoflakes and their applications as quantum dots. In this work, the size and geometric shape effects on the optical spectrum and dielectric constant of graphene nanoflakes are studied by using an ab-initio approach. The calculations were performed using the Time-Dependent Density Functional Theory (TD-DFT) as implemented in the plane wave method and the results provide insights about controlling the optical properties of graphene using the size and shape of the nanostructure. This research was supported by Conacyt-M\'{e}xico under Grant No. 83604.   

Two-photon absorption measurements in graphene fragments: Role of electron-electron interactions

Many-body interactions in graphene are an active field of research. There is a clear evidence of strong electron correlation effects in other carbon based materials which have the same sp$^2$ hybridization as graphene. For example, in linear-polyenes, the electron-electron interactions are considered responsible for the occurrence of lowest two-photon state below the optical one-photon state. The electronic correlation in these linear systems is a strong function of the chain length. Thus, it is pertinent to question if the two-dimensional graphene fragments also exhibit strong correlation effects and how these effects scale with fragment size. Using a white light super-continuum source, we perform z-scan measurements to extract frequency-dependent two-photon absorption coefficients in symmetric molecular fragments of graphene, e.g. coronene and hexabenzocoronene. A comparison of one-photon and two-photon absorption coefficients is then used to uncover the extent of correlation effects. In the smallest fragment, coronene, our results indicate a strong signature of the Coulomb interactions. We will discuss how the importance of electron-electron interaction varies with system size and its implication for the correlation effects in graphene.   

Pump-probe study of electron dynamics in bilayer graphene

Bilayer graphene exhibit many unusual physical properties, including a gate tunable electronic bandgap, and there is great interest in using it for novel electronic and optical devices. Understanding ultrafast dynamics in bilayer graphene is a prerequisite for many of its potential applications. We use ultrafsat pump-probe spectroscopy to investigate such ultrafast electron relaxation behavior in bilayer graphene. In this talk, I will discuss the observed dynamic relaxations taking place in femto- and pico-second time scales..   

Theory of Two-Photon Absorptions in Graphene Fragments

Electron-electron correlations in graphene is currently an active field of research [1-3]. The carbon atoms in graphene have the same sp$^2$ hybridization as in strongly correlated $\pi$-conjugated polymer systems. The low energy behavior in graphene however appears to be reasonably described within the one-electron Dirac massless fermions model. Historically, the occurrence of the lowest two-photon state {\it below} the optical one-photon state provided the strongest proof for strong electron correlations in linear polyenes [4]. We systematically study the Coulomb interaction effects on the ground state and nonlinear absorptions in graphene fragments as a function of system size, beginning from the smallest stable fragment coronene. We report high order calculations of one- vs two-photon spin singlet and triplet states, in coronene, hexabenzocoronene and other molecular fragments that clearly indicate the strong role of electron-electron interactions. We will discuss the implications of our work on molecular systems for the thermodynamic limit of graphene. \\[4pt] [1] Siegel David A.; et al., PNAS, v108, 28, 11365-11369 (2011)\\[0pt] [2] Gr\"onqvist J. H.; et al., arXiv: 1107.5653v1\\[0pt] [3] Uchoa B.; et al., arXiv: 1109.1577v1\\[0pt] [4] Ramasesha S.; et al., J. Chem. Phys. 80, 3278 (1984)   

Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon

Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.