The van de Waals interaction between two graphene sheets is studied at finite temperatures. Graphene's thermal length ͑ T = បv / k B T͒ controls the force versus distance ͑z͒ as a crossover from the zero temperature results for z Ӷ T , to a linear-in-temperature, universal regime for z ӷ 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.

We present an effective (minimal) theory for chiral two-dimensional materials. These materials possess an electromagnetic coupling without exhibiting a topological gap. As an example, we study the response of doped twisted bilayers, unveiling unusual phenomena in the zero frequency limit. An in-plane magnetic field induces a huge paramagnetic response at the neutrality point and, upon doping, also gives rise to a substantial longitudinal Hall response. The system also accommodates nontrivial longitudinal plasmonic modes that are associated with a longitudinal magnetic moment, thus endowing them with a chiral character. Finally, we note that the optical activity can be considerably enhanced upon doping and our general approach would enable systematic exploration of 2D material heterostructures with optical activity.

We introduce a Heisenberg Hamiltonian for describing the magnetic properties of GaMnAs. Electronic degrees of freedom are integrated out leading to a pairwise interaction between Mn spins. Monte Carlo simulations in large systems are then possible, and reliable values for the Curie temperatures of diluted magnetic semiconductors can be obtained. Comparison of mean field and Monte Carlo Curie temperatures shows that fluctuation effects are important for systems with a large hole density and/or increasing locality in the carriers-Mn coupling. We have also compared the results obtained by using a realistic k · p model with those of a simplified parabolic two band model. In the two band model, the existence of a spherical Fermi surface produces the expected sign oscillations in the coupling between Mn spins, magnifying the effect of fluctuations and leading to the eventual disappearance of ferromagnetism . In the more realistic k · p model, warping of the Fermi surface diminishes the sign oscillations in the effective coupling and, therefore, the effect of fluctuations on the critical temperature is severely reduced. Finally, by studying the collective magnetic excitations of the this model at zero temperature, we analyze the stability of the fully polarized ferromagnetic ground state.

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 anisotropy.

Graphene's fluorescence quenching is studied as a function of distance. Transverse decay channels, full retardation, and graphene-field coupling to all orders are included, extending previous instantaneous results. For neutral graphene, a virtually exact analytical expression for the fluorescence yield is derived, valid for arbitrary distances and only based on the fine structure constant α, the fluorescent wavelength λ, and distance z. Thus graphene's fluorescence quenching measurements provide a fundamental distance ruler. For doped graphene and at appropriate energies, the fluorescence yield at large distances is dominated by transverse plasmons, providing a platform for their detection.

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, and for inhomogeneous dielectric media. We find an 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 ≈ 500 μm 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 the out-of-phase plasmon mode depending on the order of the low-and high-density layers. This opens up the possibility of a tunable near-field amplifier or switch.

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 subwavelength resolution exhibits universal features, independent of model details. This is due to the unavoidable near degeneracy of surface electromagnetic modes in the deep subwavelength 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 cutoff length emerges, removing the problem of divergences claimed to invalidate Pendry's proposal.

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.