Universal Features of the Time Evolution of Evanescent Modes in a Left-Handed Perfect Lens

The time evolution of evanescent modes in Pendry's perfect lens proposal for ideally lossless and homogeneous, left-handed materials is analyzed. We show that time development of sub-wavelength resolution exhibits universal features, independent of model details. This is due to the unavoidable near-degeneracy of surface electromagnetic modes in the deep sub-wavelength region. By means of a mechanical analog, it is shown that an intrinsic time scale (missed in stationary studies) has to be associated with any desired lateral resolution. A time-dependent cut-off length emerges, removing the problem of divergences claimed to invalidate Pendry's proposal.Comment: 4 pages, 3 figures, title slightly changed, reference added, minor correction

Plasmons and near-field amplification in double-layer graphene

We study the optical properties of double-layer graphene for linearly polarized evanescent modes and discuss the in-phase and out-of-phase plasmon modes for both, longitudinal and transverse polarization. We find a energy for which reflection is zero, leading to exponentially amplified transmitted modes similar to what happens in left-handed materials. For layers with equal densities $n=10^{12}$cm$^{-2}$, we find a typical layer separation of $d\approx500\mu$m to detect this amplification for transverse polarization which may serve as an indirect observation of transverse plasmons. When the two graphene layers lie on different chemical potentials, the exponential amplification either follows the in-phase or out-of-phase plasmon mode depending on the order of the low- and high-density layer. This opens up the possibility of a tunable near-field amplifier or switch.Comment: 9 pages, 8 figure

Plasmonics in topological insulators: Spin-charge separation, the influence of the inversion layer, and phonon-plasmon coupling

We demonstrate via three examples that topological insulators (TI) offer a new platform for plasmonics. First, we show that the collective excitations of a thin slab of a TI display spin-charge separation. This gives rise to purely charge-like optical and purely spin-like acoustic plasmons, respectively. Second, we argue that the depletion layer mixes Dirac and Schr\"odinger electrons which can lead to novel features such as high modulation depths and interband plasmons. The analysis is based on an extension of the usual formula for optical plasmons that depends on the slab width and on the dielectric constant of the TI. Third, we discuss the coupling of the TI surface phonons to the plasmons and find strong hybridisation especially for samples with large slab widths.Comment: 37 pages, 7 figure

Spin-charge separation of plasmonic excitations in thin topological insulators

We discuss plasmonic excitations in a thin slab of a topological insulators. In the limit of no hybridization of the surface states and same electronic density of the two layers, the electrostatic coupling between the top and bottom layers leads to optical and acoustic plasmons which are purely charge and spin collective oscillations. We then argue that a recent experiment on the plasmonic excitations of Bi2Se3 [Di Pietro et al, Nat. Nanotechnol. 8, 556 (2013)] must be explained by including the charge response of the two-dimensional electron gas of the depletion layer underneath the two surfaces. We also present an analytic formula to fit their data.Comment: 7 pages, 5 figure

Extraordinary absorption of decorated undoped graphene

We theoretically study absorption by an undoped graphene layer decorated with arrays of small particles. We discuss periodic and random arrays within a common formalism, which predicts a maximum absorption of $50\%$ for suspended graphene in both cases. The limits of weak and strong scatterers are investigated and an unusual dependence on particle-graphene separation is found and explained in terms of the effective number of contributing evanescent diffraction orders of the array. Our results can be important to boost absorption by single layer graphene due to its simple setup with potential applications to light harvesting and photodetection based on energy (F\"orster) rather than charge transfer.Comment: 5 pages, 3 figure

Measurable lattice effects on the charge and magnetic response in graphene

The simplest tight-binding model is used to study lattice effects on two properties of doped graphene: (i) magnetic orbital susceptibility and (ii) regular Friedel oscillations, both suppressed in the usual Dirac cone approximation. (i) An exact expression for the tight-binding magnetic susceptibility is obtained, leading to orbital paramagnetism in graphene for a wide range of doping levels which is relevant when compared with other contributions. (ii) Friedel oscillations in the coarse-grained charge response are considered numerically and analytically and an explicit expression for the response to lowest order in lattice effects is presented, showing the restoration of regular 2d behavior, but with strong sixfold anisotropyThis work has been supported by FCT under Grant No. PTDC/ FIS/101434/2008 and MIC under Grant No. FIS2010- 21883-C02-0

Thermal van der Waals Interaction between Graphene Layers

The van de Waals interaction between two graphene sheets is studied at finite temperatures. Graphene's thermal length $(\xi_T = \hbar v / k_B T)$ controls the force versus distance $(z)$ as a crossover from the zero temperature results for $z\ll \xi_T$, to a linear-in-temperature, universal regime for $z\gg \xi_T$. The large separation regime is shown to be a consequence of the classical behavior of graphene's plasmons at finite temperature. Retardation effects are largely irrelevant, both in the zero and finite temperature regimes. Thermal effects should be noticeable in the van de Waals interaction already for distances of tens of nanometers at room temperature.Comment: enlarged version, 9 pages, 4 figures, updated reference