Optical Conductivity Of Graphene Research Articles

Optical conductivity of disordered graphene beyond the Dirac cone approximation

In this paper we systemically study the optical conductivity and density of states of disordered graphene beyond the Dirac cone approximation. The optical conductivity of graphene is computed by using the Kubo formula, within the framework of a full $\ensuremath{\pi}$-band tight-binding model. Different types of noncorrelated and correlated disorder are considered, such as random or Gaussian potentials, random or Gaussian nearest-neighbor hopping parameters, randomly distributed vacancies or their clusters, and randomly adsorbed hydrogen atoms or their clusters. For a large enough concentration of resonant impurities, an additional peak in the optical conductivity is found, associated with transitions between the midgap states and the Van Hove singularities of the main $\ensuremath{\pi}$ band. We further discuss the effect of doping on the spectrum, and find that small amounts of resonant impurities are enough to obtain a background contribution to the conductivity in the infrared part of the spectrum, in agreement with recent experiments.

Absence of interaction corrections in the optical conductivity of graphene

The exact vanishing of the interaction corrections to the zero temperature and zero frequency conductivity of graphene in the presence of weak short range interactions is rigorously established.

Optical conductivity of graphene in the presence of random lattice deformations

We study the influence of lattice deformations on the optical conductivity of a two-dimensional electron gas. Lattice deformations are taken into account by introducing a non-abelian gauge field into the Eucledian action of two-dimensional Dirac electrons. This is in analogy to the introduction of the gravitation in the four-dimensional quantum field theory. We examine the effect of these deformations on the averaged optical conductivity. Within the perturbative theory up to second order we show that corrections of the conductivity due to the deformations cancel each other exactly. We argue that these corrections vanish to any order in perturbative expansion.

Density of states and magneto-optical conductivity of graphene in a perpendicular magnetic field

The density of states (DOS) and the optical conductivity of graphene is calculated in the presence of a perpendicular magnetic field and where scattering on charged and short-range impurities is included. The standard Kubo formula is employed where the self-energy induced by impurity scattering and the Green's function are calculated self-consistently including inter-Landau level (LL) coupling and screening effects. It is found that the scattering from those two types of impurities results in a symmetric LL broadening and asymmetric inter-LL coupling renormalizes the LL positions to lower energy. The peak position and intensity of the magneto-optical conductivity depends on the filling factor and the broadened DOS. Good agreement is found with recent cyclotron resonance measurements.

Excitonic Effects in the Optical Conductivity of Gated Graphene

We study the effect of electron-electron interactions in the optical conductivity of graphene under an applied gate and derive a generalization of Elliott's formula, commonly used for semiconductors, for the optical intensity. We show that excitonic resonances are responsible for several features of the experimentally measured midinfrared response of graphene such as the increase of the conductivity beyond the universal value above the Fermi blocked regime, the broadening of the absorption at the threshold, and the decrease of the optical conductivity at higher frequencies.

Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties, and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\ensuremath{\tau}$ sets the energy scale for the rise of the optical conductivity from its universal dc value $4{e}^{2}/\ensuremath{\pi}h$ (expected in the simplest theory when chemical potential and temperature are both $⪡1/2\ensuremath{\tau}$) to its universal ac background value $({\ensuremath{\sigma}}_{0}=\ensuremath{\pi}{e}^{2}/2h)$. As in ordinary metals the dc conductivity remains unrenormalized while its ac value is changed. The optical spectral weight under the intraband Drude is reduced by a mass-renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below ${\ensuremath{\sigma}}_{0}$ at large energies.

Optical conductivity and electron–hole pair creation in graphene

The optical conductivity of graphene is studied in detail. It is shown how crossover fromnonlinear to linear behaviour of the current density occurs when the frequency of theexternal electric field is increased. We also study electron–hole pair creation in bilayergraphene and show that its rate in a static electric field is determined by a power law as forsingle-layer graphene but with a different exponent. Subsequently, transport in carbonnanotubes is studied.

High-energy optical conductivity of graphene determined by reflection contrast spectroscopy

Optical conductivity $G(\ensuremath{\omega})$ of graphene, which is famous for its universality close to the Dirac point, is determined from the visible to near-ultraviolet region by using reflection contrast spectroscopy. We find that the universality does not survive beyond the visible region. Instead, $G(\ensuremath{\omega})$ increases rapidly with the energy, which is originated from the flat dispersion relation at the $M$ point corresponding to an extraordinarily large density of states (DOS). The first-principles-calculated band structure and DOS spectrum explain well the high-energy behaviors of $G(\ensuremath{\omega})$. Our work presents a more comprehensive map of graphene's optical conductivity and electronic structure.