Graphene transparency in weak magnetic fields

International Journal of Modern Physics B, 2016

We model the low energy dynamics of graphene in the continuum in terms of a version of reduced quantum electrodynamics (QED) restricting fermions to a [Formula: see text]-dimensional brane, while photons remain within the [Formula: see text]-dimensional bulk. For charge carriers, besides the Dirac mass gap, we consider a Haldane mass term which is induced by parametrizing an effective parity [Formula: see text] and time-reversal [Formula: see text] symmetry breaking that occurs on the brane when distortions of the honeycomb array are such that the equivalence between sublattices is lost. We make use of the relativistic Kubo formula and carry out an explicit calculation of the transverse conductivity. As expected, the filling factor is a half (in natural units) for each fermion species. Furthermore, assuming that a sample of this material is radiated perpendicularly with polarized monochromatic light of frequency [Formula: see text], from the modified Maxwell’s equations we address t...

Optics Express, 2013

Graphene has shown intriguing optical properties as a new class of plasmonic material in the terahertz regime. In particular, plasmonic modes in graphene nanostructures can be confined to a spatial size that is hundreds of times smaller than their corresponding wavelengths in vacuum. Here, we show numerically that by designing graphene nanostructures in such deep-subwavelength scales, one can obtain plasmonic modes with the desired radiative properties such as radiative and dark modes. By placing the radiative and dark modes in the vicinity of each other, we further demonstrate electromagnetically induced transparency (EIT), analogous to the atomic EIT. At the transparent window, there exist very large group delays, one order of magnitude larger than those offered by metal structures. The EIT spectrum can be further tuned electrically by applying a gate voltage. Our results suggest that the demonstrated EIT based on graphene plasmonics may offer new possibilities for applications in photonics.

Physical Review Letters, 2007

The intensity as well as position in energy of the absorption lines in the infrared conductivity of graphene, both exhibit features that are directly related to the Dirac nature of its quasiparticles. We show that the evolution of the pattern of absorption lines as the chemical potential is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to this level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.

Physical Review B, 2016

Graphene and other two-dimensional materials display remarkable optical properties, including a simple transparency of T ≈ 1 − πα for visible light. Most theoretical rationalizations of this "universal" opacity employ a model coupling light to the electron's crystal momentum and put emphasis on the linear dispersion of the graphene bands. However, such a formulation of interband absorption is not allowable within band structure theory, because it conflates the crystal momentum label with the canonical momentum operator. We show that the physical origin of the optical behavior of graphene can be explained within a straightforward picture with the correct use of canonical momentum coupling. Its essence lies in the two-dimensional character of the density of states rather than in the precise dispersion relation, and therefore the discussion is applicable to other systems such as semiconductor membranes. At higher energies the calculation predicts a peak corresponding to a van Hove singularity as well as a specific asymmetry in the absorption spectrum of graphene, in agreement with previous results.

We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum mechanics, and leads to an exactly solvable model. We study in detail the bound spectra. For a narrow barrier the spectra is characterized by a few bands, except for the zero energy level that remains degenerated. As, the width of the barrier increases we can track the bands evolution into the degenerated Landau levels. In the scattering regime a simple analytical formula is obtained for the transmission coefficient, this result allow us to identify the resonant conditions at which the barrier becomes transparent.

The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields.

2016

Graphene and other two-dimensional materials display remarkable optical properties, including a simple light transparency of T ≈ 1 - πα for light in the visible region. Most theoretical rationalizations of this "universal" opacity employ a model coupling light to the electron's crystal momentum and put emphasis on the linear dispersion of the graphene bands. However, such a formulation of interband absorption is not allowable within band structure theory, because it conflates the crystal momentum label with the canonical momentum operator. We show that the physical origin of the optical behavior of graphene can be explained within a straightforward picture with the correct use of canonical momentum coupling. Its essence lies in the two-dimensional character of the density of states rather than in the precise dispersion relation, and therefore the discussion is applicable to other systems such as semiconductor membranes. At higher energies the calculation predicts a pea...

New Journal of Physics, 2009

The latest experiments have confirmed the theoretically expected universal value πe 2 /2h of the ac conductivity of graphene and have revealed departures of the quasiparticle dynamics from predictions for the Dirac fermions in idealized graphene. We present analytical expressions for the ac conductivity in graphene which allow one to study how it is affected by interactions, temperature, external magnetic field and the opening of a gap in the quasiparticle spectrum. We show that the ac conductivity of graphene does not necessarily give a metrologically accurate value of the von Klitzing constant h/e 2 , because it is depleted by the electron-phonon interaction. In a weak magnetic field the ac conductivity oscillates around the universal value and the Drude peak evolves into a peak at the cyclotron frequency. (Some figures in this article are in colour only in the electronic version)

Physical Review B, 2009

Computer Physics Communications, 2013

The generalized tight-binding model is developed to largely reduce the numerical computation time in calculating optical properties. Modulated electric potentials can control the low-frequency magnetooptical absorption spectra of monolayer graphene. They induce the oscillatory energy dispersions of Landau subbands and the spatial symmetry breaking of the wave function; therefore, the original peaks and extra peaks of different selection rules come into existence simultaneously. Such peaks mainly arise from the band-edge states and/or the middle states. Their number, intensities, frequencies and structures are dominated by the modulation strength and period. More absorption peaks appear with an increase in potential. The extra peaks can relatively easily be observed for higher frequencies and stronger potentials. However, the absorption spectra remain unchanged for a fixed ratio of strength over period. (M.F. Lin). selection rules, the absorption peaks are investigated in detail in terms of how they are tuned by the potential strength and period.