Session Z22: Graphene Optical Properties and Imaging

Photon interactions with graphene electrons: consequences for the optical conductivity

We calculate the lowest-order amplitude for interaction between 3D photons and 2D graphene electrons. Using Fermi's Golden Rule, we find the thermal corrections to the graphene's zero-temperature opacity of $\pi\alpha$. Equating the power absorbed to the Joule heating rate gives an expression for the optical conductivity. We find an optical conductivity that agrees with previous results in the limit of zero temperature, but gives a finite value at zero frequency and finite temperature.   

Photoresponse in reduced graphene oxide thin films

We examine photo-response and positional dependent photocurrent generation in chemically reduced graphene oxide (RGO) thin film under near infrared illumination. We have observed that the photocurrent depends strongly on the position of laser spot with maximum photocurrent occurring at the metal-film interface. A slow time constant ($\sim $2.8 seconds) was observed and the photocurrent exhibits a linear dependence on the incident laser intensity. In light of our observations, the positional sensitive photocurrent generation is explained as originating from the diffusion of photo-excited carriers around the Schottky barriers at the RGO thin film electrode junctions.   

Why is the optical transparency of graphene determined by the fine structure constant?

The observed $97.7\%$ optical transparency of graphene [R.R. Nair, et al, Science {\bf 320}, 1308 (2008)] has been linked to the value $1/137$ of the fine structure constant, by using results for noninteracting Dirac fermions. The agreement in three significant figures requires an explanation for the apparent unimportance of the Coulomb interaction. Using arguments based on Ward identities, the leading corrections to the optical conductivity due to the Coulomb interactions are correctly computed (resolving a theoretical dispute) and shown to amount to only $1$-$2\%$, corresponding to $0.03$-$0.04\%$ in the transparency.   

Far infrared spectroscopy of graphene

The electronic properties of graphene are described by massless Dirac electrons, and their DC conductivity and Hall conductivity have attracted great attention. However, the high frequency conductivity (AC conductivity) of graphene is little known. Here we perform far-infrared spectroscopy on large area graphene sample to probe its AC conductivity response. The response can be largely described by the Drude model, which yields direct information on the electron density and scattering rate in the graphene samples. We will discuss the comparison of our experimental results to theoretical predictions.   

GW-Bethe-Salpeter study of the optical properties of graphane

Recently, hydrogenated graphene (i.e., graphane) has been synthesized experimentally. Interesting properties such as reversible hydrogenation and transforming from a metal into an insulator have been observed. According to a recent study [Lebegue et. al., Phys. Rev. B 79, 245117 (2009)], the band gap of graphene is open up from 0 to $\sim $5 eV through the hydrogenation of graphene to graphane. In this talk, we will present results of a first-principles study of the optical properties of graphane using the GW-Bethe-Salpeter equation approach.   

Optical study of electron-phonon coupling in multilayer graphene with different stacking order

The optical conductivity spectra of mechanically exfoliated multi-layer graphene samples were explored in the infrared range. In samples from three to six layers in thickness, two distinct types of spectra were observed for different samples with precisely the same number of layers, which can be attributed to the optical absorption of multi-layer graphene samples with Bernal stacking (ABAB series) and rhombohedral stacking (ABC series). Furthermore, the G-mode phonon exhibits a lineshape characteristic of a Fano resonance due to strong electron-phonon coupling. The width and lineshape of the phonons are strongly modified by the interband electronic transition as the layer number increases. The intensity of the phonons in samples with rhombohedral stacking is much higher than those in samples with Bernal stacking. We will discuss the new aspects of electron-phonon coupling in multi-layer graphene revealed by this work.   

Infrared imaging of power dissipation in graphene field effect transistors

We have employed thermal infrared microscopy to image temperature distributions in monolayer and bilayer graphene transistors under high bias. The hot spot position is sensitive to device electrostatics, corresponding to the location of minimum charge density in unipolar transport, and to that of charge neutrality in ambipolar operation. The hot spot shape carries information of spatial variations in charge density of devices. By comparison with a self-consistent electrical-thermal model, the imaged temperature profiles are correlated with power dissipation, carrier distributions, and electric fields within such devices, providing rich insight into their operation and energy relaxation physics. For instance, the combined approach reveals that low-field mobility is limited by impurity scattering, while velocity saturation is set by substrate phonon scattering in our samples. These results also open up the possibility of thermal imaging as a more general non-invasive tool for examining transport and energy dissipation in novel devices.   

Light Emission from Graphene Induced by Femtosecond Laser Pulses

Since graphene has no band gap, light emission is not expected from relaxed carriers. On the other hand, the strong optical absorption in graphene over a wide spectral range suggests the possibility of hot luminescence from non-equilibrium carriers. Here we report the observation of light emission from monolayer graphene induced by excitation with ultrashort (30-fs) laser pulses. We observe emission throughout the visible spectrum, extending to a photon energy of 3.5 eV in the near UV. In contrast to conventional hot luminescence processes, however, we find strong light emission at photon energies \textit{exceeding }that of the pump laser at 1.5 eV. In addition to detailed measurements of the emission spectra and their dependence on pump fluence, we have performed ultrafast time-domain correlation technique in which light emission is measured as a function of the temporal separation between a pair of femtosecond excitation pulses. A dominant relaxation time of a few 10's of fs is observed. The origin of this unusual light emission process and its relation to the underlying carrier dynamics in graphene will be discussed.   

Anomalous Dirac charge dynamics in multilayer graphene at high optical transition energies

Almost all discussion of the optical absorption, the interlayer interaction and relationship between them in multilayer graphene is almost conclusively decided~ taking into account only the charge dynamic in states at K point in the hexagonal Brillouin zone while other states are relatively ignored. The lack of charge dynamic information at states beyond the Dirac cone may give us inadequate knowledge of their interaction with the lower states. Here, we present an optical conductivity study on graphene as function of layers using a combination of the dc-conductivity, optical ellipsometry, and vacuum ultraviolet (VUV) reflectance to reveal the electronic band structure and the novel interlayer interaction of graphene in pi and sigma bands over a broad energy range from 0 to 35 eV.   

Observation of coherent excitation of the interlayer shearing mode in graphite and multilayer graphene

Raman spectroscopy is one of the key methods for the characterization of single and multilayer graphene. In the bulk limit, the lateral motion of adjacent graphene planes gives rise to a Raman active low-frequency mode, the so-called interlayer shearing mode. Coherent excitation of this mode has been observed by femtosecond time-resolved reflectivity [1]. For the case of few-layer graphene, related modes are predicted to be present and to exhibit different properties as a function of layer thickness [2]. Here we report the observation of coherent oscillation of such shearing mode phonons in multilayer graphene. The experiments are performed on mechanically exfoliated graphene samples using femtosecond laser excitation pulses and time-delayed femtosecond probe pulses in a transient reflectivity measurement. The coherent shearing-mode phonons exhibit a period of 800 fs, with a lifetime exceeding 10 ps. We will discuss the characteristics of shearing mode phonons as a function of the thickness of multilayer graphene. [1] T. Mishina et al., Phys. Rev. B 62, 2908 (2000) [2] S. K. Saha et al., Phys Rev. B 78, 165421 (2008)   

Nonlinear photoluminescence from graphene

Upon femtosecond laser irradiation, a bright, broadband nonlinear photoluminescence (PL) is observed from graphene at frequencies well above the excitation frequency. Analyses show that it arises from radiative recombination of a broad distribution of non-equilibrium electrons and holes, generated by rapid scattering between photo-excited carriers within tens of femtoseconds after the optical excitation. Its highly unusual characteristics come from the unique electronic and structural properties of graphene.   

Infrared Transmission of Chemically Reduced Graphene Oxide from 0.2-200THz

Single-layer graphene oxide can be chemically reduced and deposited from solution to form conducting films of graphene flakes in an inexpensive, versatile and scalable process. However, chemically reduced graphene oxide (CRGO) films produced to date have low DC conductivities (10$^{2 }$ -- 10$^{4}$S/m) compared to pristine graphite, likely due to poor electrical transport between flakes and from structural disorder. We prepared thin, free-standing CRGO films by reduction of graphene oxide in hydrazine, solution deposition and substrate removal. Film properties are similar to previous reports[1], with DC conductivity $\sim $1700 S/m, and ordered domain sizes of $\sim $15nm determined from Raman spectroscopy. THz and IR measurements of 400nm thick films show $T\sim $0.8 for $f<$1THz smoothly decreasing to $T\sim $0.05 at $f$=100THz, consistent with a $\sim $70-fold increase in conductivity over this frequency range. We will compare our results to a model of the films as a network of weakly linked conductive particles. Future work will investigate carrier scattering rates and lifetimes in this material.\\[4pt][1] Sungjin Park, Rodney S. Ruoff. Nature Nanotechnology 2009; \textbf{4}: 217.   

Ultrafast Spectroscopy of Hot Carriers in Graphite

We studied the ultrafast dynamics of photogenerated hot carriers in graphite single crystal by using transient pump-probe photoreflectivity (PR) spectroscopy with $\sim $100 fs resolution. Using two different laser systems;visible/near-IR {\&} mid IR range with pump excitation photon energies at 1.55 {\&} 3.1 eV, our transient PR spectrum covers a broad spectral range from 0.2 -- 2.4 eV. Surprisingly, we found that the transient PR spectrum resembles the cw thermo-modulation spectrum that was measured and explained previously by the well-known band structure of graphite; and contains several zero-crossings modulated reflectivity that are determined by the van-Hove singularities in the band structure at the K point of the Brillouin zone. We interpret the transient PR spectrum as due to hot carriers in the various valence and conduction bands of graphite. The decay dynamics can be fit with a bi-exponential decay with two processes that are interpreted as: sub-picosecond Auger recombination following hot plasma with well defined electronic temperature; and a longer process of hot plasma cooling to the lattice temperature by emitting strongly coupled phonons.   

THz Time Domain Spectroscopy Studies of a Graphite Film and Perforated Graphite Hole Arrays

We studied the optical properties of highly ordered pyrolytic graphite (HOPG) films in the 0.1 to 0.5 THz spectral range using the technique of time domain THz spectroscopy. HOPG has a low free carrier density, and highly anisotropic conductivity tensor, having much higher in-plane conductivity compared to that of the out-of-plane. First we studied a thin graphite film for obtaining the spectra of both real and imaginary components of the dielectric constant, from which we obtained the free carrier relaxation time. Subsequently we fabricated and investigated hole arrays in an otherwise opaque graphite film, which consist of \textit{periodic} hole array (``plasmonic lattice''), and corresponding \textit{random} hole array. For the periodic hole array we found that the transmission spectrum is modulated with several resonance/anti-resonances that correspond with the reciprocal vectors in the Fourier space; whereas a broad transmission band of which peak depends on the hole diameter characterizes the random hole arrays.   

Optical Properties of Suspended and Substrate Graphene

Graphene, a two-dimensional material made purely of carbon atoms arranged in a hexagonal lattice has attracted the attention of scientific community since it was first produced in 2004. Due to the peculiarity in its band structure and various striking characteristics (eg. high electrical conductivity, mechanical robustness, large thermal conductivity, tunable carrier type and mobility etc.) this has become significant both technologically as well as for fundamental research. Both experimental and theoretical investigations have been taking place to study its various properties viz. transport, electronic, thermal and optical properties. In this work, optical properties of suspended monolayer-graphene and monolayer-graphene deposited on dielectric substrates are studied by calculating the optical quantities such as coefficient of reflection and reflected polarization analytically with the help of Maxwell's equations for the respective systems. Behavior of above mentioned optical quantities with respect to various parameters are studied to compare the two systems. This study can be used to obtain the conductivity tensor of graphene with its anisotropic behavior obtained from the azimuthal angle dependence of the optical quantities. The substrate-graphene is also interesting due to the observation of Brewster's phenomena with Brewster's angle varying with respect to the azimuthal angle (an oscillation with a period of 180 degrees).