Focus on Graphene Optics

Chiral symmetry, fundamental in the physics of graphene, guarantees the existence of topologically stable doubled Dirac cones and anomalous behaviors of the zero-energy Landau level in magnetic fields. Its crucial role, especially its manifestation in optical responses and many-body physics in graphene, is explained in this paper. We also give an overview of multilayer graphene from the viewpoint of the optical properties and their relation with chiral symmetry.

We study the infrared optical absorption properties of ABA- and ABC-stacked graphene multilayers using the effective mass approximation. We calculate the optical absorption spectrum at various carrier densities, and find the characteristic features that identify the stacking types and the number of layers. We fully include the band parameters and discuss detailed features such as trigonal warping and electron–hole asymmetry.

The transient optical conductivity of freely suspended graphene was examined by femtosecond time-resolved spectroscopy using pump excitation at 400 nm and probe radiation at 800 nm. The optical conductivity (or, equivalently, absorption) changes abruptly upon excitation and subsequently relaxes to its initial value on the time scale of 1 ps. The form of the induced change in the optical conductivity varies strongly with excitation conditions, exhibiting a crossover from enhanced to decreased optical conductivity with increasing pump fluence. We describe the graphene response in terms of transient heating of the electrons, with the characteristic relaxation time of the transient conductivity reflecting the cooling of the electron system and the strongly coupled optical phonons through emission of lower energy phonons. The change in the optical conductivity is attributed to a combination of induced absorption from intra-band transitions of the photo-generated carriers and bleaching of the inter-band transitions by Pauli blocking. The former effect, which corresponds to the high-frequency wing of the Drude response, dominates at low pump fluence. In this regime of a limited rise in the electron temperature, an increase in the optical conductivity is observed. At high pump fluence, elevated electron temperatures are achieved. The decrease in the inter-band bleaching then dominates the transient response, the intra-band contribution being overwhelmed despite an increase in the Drude scattering rate with temperature. The temporal evolution of the optical conductivity in all the regimes can be described within a model including the intra- and inter-band contributions with a time-varying electronic temperature. An increased Drude scattering rate is inferred for high electron temperature and mechanisms for this enhancement are considered. The calculated scattering rate for interactions of the carriers with zone-center and zone-edge optical phonons agrees well with the rates obtained from experiment.

The interest in graphene stems from its unique band structure that photoemission spectroscopy can directly probe. However, the preparation method can significantly alter graphene's pristine atomic structure and in turn the photoemission spectroscopy spectra. After a short review of the observed band structure for graphene prepared by various methods, we focus on graphene grown on silicon carbide. The semiconducting single crystalline hexagonal SiC provides a substrate of various dopings, where bulk bands do not interfere with that of graphene. Large sheets of high structural quality flat graphene grow on SiC, which allows the exact same material to be used for fundamental studies and as a platform for scalable electronics. Moreover, a new graphene allotrope (multilayer epitaxial graphene) was discovered to grow on the 4H-SiC C-face by the confinement controlled sublimation method. We will focus on the electronic structure of this new graphene allotrope and its connection to its atomic structure.

The optical response of graphene micro-structures, such as micro-ribbons and discs, is dominated by the localized plasmon resonance in the far infrared spectral range. An ensemble of such structures is usually involved and the effect of the coupling between the individual structures is expected to play an important role. In this paper, plasmonic coupling of graphene micro-structures in different configurations is investigated. Whereas a relatively weak coupling between graphene discs on the same plane is observed, the coupling between vertically stacked graphene discs is strong and a drastic increase of the resonance frequency is demonstrated. The plasmons in a more complex structure can be treated as the hybridization of plasmons from more elementary structures. As an example, the plasmon resonances of graphene micro-rings are presented, in conjunction with their response in a magnetic field. Finally, the coupling of the plasmon and the surface polar phonons of SiO ₂ substrate is demonstrated by the observation of a new hybrid resonance peak around 500 cm ⁻¹.

In contrast to semiconductor structures, the experimentally observed plasma resonances in graphene show an asymmetrical and rather broad linewidth. We show that this can be explained by the linear electron energy dispersion in this material and is related to the violation of the generalized Kohn theorem in graphene.

We investigate the optical properties of layered structures with graphene at the interface for arbitrary linear polarization at finite temperature including full retardation by working in the Weyl gauge. As a special case, we obtain the full response and the related dielectric function of a layered structure with two interfaces. We apply our results to discuss the longitudinal plasmon spectrum of several single- and double-layer devices such as systems with finite and zero electronic densities. We further show that a nonhomogeneous dielectric background can shift the relative weight of the in-phase and out-of-phase modes, and discuss how the plasmonic mode of the upper layer can be tuned into an acoustic mode with a specific sound velocity.

We investigate the signature of the low-energy electronic excitations in the Raman spectrum of monolayer and bilayer graphenes. The dominant contribution to the Raman spectra is due to the interband electron–hole (e–h) pairs, which belong to the irreducible representation A ₂ of the point group C _6v of the graphene lattice, and are characterized by crossed polarization of incoming and outgoing photons. At high magnetic fields, this is manifested by the excitation of e–h inter-Landau-level (LL) transitions with selection rule n ⁻ →  n ⁺. Weaker Raman-active inter-LL modes also exist. One of those has a selection rule similar to the infrared absorption process, n ⁻ → ( n ± 1) ⁺, but the created e–h excitation belongs to the irreducible representation E ₂ (rather than E ₁) and couples to the optical phonon mode, thus undergoing an anticrossing with the optical phonon G-line in Raman in a strong magnetic field. The fine structure acquired by the G-line due to such anticrossing depends on the carrier density, inhomogeneity of doping and presence of inhomogeneous strain in the sample.

In this paper, we present direct time-domain investigations of the relaxation of electric currents in graphene due to hot carrier scattering. We use coherent control with ultrashort optical pulses to photoinject a current and detect the terahertz (THz) radiation emitted by the resulting current surge. We pre-inject a background of hot carriers using a separate pump pulse, with a variable delay between the pump and current-injection pulses. We find the effect of the hot carrier background is to reduce the current and hence the emitted THz radiation. The current damping is determined simply by the density (or temperature) of the thermal carriers. The experimental behavior is accurately reproduced in a microscopic theory, which correctly incorporates the nonconservation of velocity in scattering between Dirac fermions. The results indicate that hot carriers are effective in damping the current, and are expected to be important for understanding the operation of high-speed graphene electronic devices.

We report on absolute magneto-transmission experiments on highly doped quasi-free-standing epitaxial graphene targeting the classical-to-quantum crossover of the cyclotron resonance. This study allows us to directly extract the carrier density and also other relevant quantities such as the quasiparticle velocity and the Drude weight, which is precisely measured from the strength of the cyclotron resonance. We find that the Drude weight is renormalized with respect to its non-interacting (or random phase approximation) value and that the renormalization is tied to the quasiparticle velocity enhancement. This finding is in agreement with recent theoretical predictions, which attribute the renormalization of the Drude weight in graphene to the interplay between broken Galilean invariance and electron–electron interactions.

We show how the magneto-phonon resonance, particularly pronounced in sp ² carbon allotropes, can be used as a tool to probe the band structure of multilayer graphene specimens. Even when electronic excitations cannot be directly observed, their coupling to the E _2g phonon leads to pronounced oscillations of the phonon feature observed through Raman scattering experiments with multiple periods and amplitudes determined by the electronic excitation spectrum. Such experiment and analysis has been performed up to 28 T on an exfoliated four-layer graphene specimen deposited on SiO ₂, and the observed oscillations correspond to the specific AB stacked four-layer graphene electronic excitation spectrum.

Photoemission studies of graphene have resulted in a long-standing controversy concerning the strength of the experimental electron–phonon (el–ph) interaction in comparison with theoretical calculations. Using high-resolution angle-resolved photoemission spectroscopy we study graphene grown on a copper substrate, where the metallic screening of the substrate substantially reduces the electron–electron interaction, simplifying the comparison of the el–ph interaction between theory and experiment. By taking the nonlinear bare bandstructure into account, we are able to show that the strength of the el–ph interaction shows better agreement with theoretical calculations. In addition, we observe a significant bandgap at the Dirac point of graphene.

We show that the opacity of a clean multilayer graphene flake depends on the helicity of the circular polarized electromagnetic radiation. The effect can be understood in terms of the pseudospin selection rules for the interband optical transitions in the presence of exchange electron–electron interactions which alter the pseudospin texture in momentum space. The interactions described within a semi-analytical Hartree–Fock approach lead to the formation of topologically different broken symmetry states characterized by Chern numbers and zero-field anomalous Hall conductivities.