An analytical theory of the nonlinear electromagnetic response of a two-dimensional (2D) electron system in the second order in the electric field amplitude is developed. The second-order polarizability and the intensity of the second harmonic signal are calculated within the self-consistent-field approach both for semiconductor 2D electron systems and for graphene. The second harmonic generation in graphene is shown to be about two orders of magnitude stronger than in GaAs quantum wells at typical experimental parameters. Under the conditions of the 2D plasmon resonance the second harmonic radiation intensity is further increased by several orders of magnitude.
Graphene plasmonics is a rapidly growing field with multiple potential applications. One of the standard ways to study plasmons in graphene is by fabricating an array of graphene nanoribbons where nanoribbon edges provide the efficient photon-plasmon coupling. We systematically analyze the problem of optical plasmonic response in such systems and demonstrate the purely geometric nature of the size quantization condition for graphene plasmons. Accurate numerical calculations allowed us to tabulate the universal geometric parameters of plasmon size quantization, which is expected to become usefu…
Plasmon in graphene possesses many unique properties. It originates from the collective motion of massless Dirac fermions and the carrier density dependence is distinctively different from conventional plasmons. In addition, graphene plasmon is highly tunable and shows strong energy confinement capability. Most intriguing, as an atom-thin layer, graphene and its plasmon are very sensitive to the immediate environment. Graphene plasmons strongly couple to polar phonons of the substrate, molecular vibrations of the adsorbates, and lattice vibrations of other atomically thin layers. In this revie…
Using the ultrafast pump-probe transient absorption spectroscopy, the femtosecond-resolved plasmon-exciton interaction of graphene-Ag nanowire hybrids is experimentally investigated, in the VIS-NIR region. The plasmonic lifetime of Ag nanowire is about 150 femtosecond (fs). For a single layer of graphene, the fast dynamic process at 275 fs is due to the excitation of graphene excitons, and the slow process at 1.4 picosecond (ps) is due to the plasmonic hot electron interaction with phonons of graphene. For the graphene-Ag nanowire hybrids, the time scale of the plasmon-induced hot electron tra…
The short wavelength of graphene plasmons relative to the light wavelength makes them attractive for applications in optoelectronics and sensing. However, this property limits their coupling to external light and our ability to create and detect them. More efficient ways of generating plasmons are therefore desirable. Here we demonstrate through realistic theoretical simulations that graphene plasmons can be efficiently excited via electron tunneling in a sandwich structure formed by two graphene monolayers separated by a few atomic layers of hBN. We obtain plasmon generation rates of $\sim10^…
We theoretically demonstrate that a system formed by a drift-current biased graphene sheet on a silicon carbide substrate enables loss compensation and plasmon amplification. The active response of the graphene sheet is rooted in the optical pumping of the graphene plasmons with the gain provided by the streaming current carriers. The proposed system behaves as an optical amplifier for the plasmons co-propagating with the drifting electrons and as a strong attenuator for the counter-propagating plasmons. Furthermore, we show that the feedback obtained by connecting the input and output of the …
Graphene supports strongly confined transverse-magnetic sheet plasmons whose spectral characteristics depend on the energetic distribution of Dirac particles. The question arises whether plasmons can become amplified when graphene is pumped into a state of inversion. In establishing a theory for the dynamic non-equilibrium polarizability, we are able to determine the exact complex-frequency plasmon dispersion of photo-inverted graphene and study the impact of doping, collision loss, and temperature on the plasmon gain. We calculate the spontaneous emission spectra and carrier recombination rat…
We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At sub-nanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nano-imaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tu…
Numerical and closed-form analytic expressions for plasmon dispersion relations and rates of dissipation are first obtained at finite-temperatures for free-standing gapped graphene. These closed-system results are generalized to an open system with Coulomb coupling of graphene electrons to an external electron reservoir. New plasmon modes, as well as new plasmon dissipation channels, are found in this open system, including significant modifications arising from the combined effect of thermal excitation of electrons and an energy bandgap in gapped graphene. Moreover, the characteristics of the…
We present a simple device architecture that allows all-electrical detection of plasmons in a graphene waveguide. The key principle of our electrical plasmon detection scheme is the non-linear nature of the hydrodynamic equations of motion that describe transport in graphene at room temperature and in a wide range of carrier densities. These non-linearities yield a dc voltage in response to the oscillating field of a propagating plasmon. For illustrative purposes, we calculate the dc voltage arising from the propagation of the lowest-energy modes in a fully analytical fashion. Our device archi…
Plasmon collective excitations are studied in a planar graphene superlattice formed by periodically alternating regions of gapless graphene and of its gapped modification. The plasmon dispersion law is determined both for the quasi-one-dimensional case (the Fermi level is located within the minigap) and for the quasi-two-dimensional case (the Fermi level is located within the miniband). The problem concerning the absorption of modulated electromagnetic radiation at the excitation of plasmons is also considered.
Quantum confinement of graphene carriers is an effective way to engineer its properties. It is commonly realized through physical edges that are associated with the deterioration of mobility and strong suppression of plasmon resonances. Here, we demonstrate a simple, large-area, edge-free nanostructuring technique, based on amplifying random nanoscale structural corrugations to a level where they efficiently confine carriers, without inducing significant inter-valley scattering. This soft confinement, allows the low-loss lateral ultra-confinement of graphene plasmons, scaling up their resonanc…
Here, we investigate the nonreciprocal propagation and amplification of surface plasmons in drift-current biased graphene, using both Galilean and relativistic-type Doppler shift transformations of the graphene's conductivity. Consistent with previous studies, both conductivity models predict strongly nonreciprocal propagation of surface plasmons due to the drag effect caused by the drifting electrons. In particular, the Galilean Doppler shift model leads to stronger spectral asymmetries in the plasmon dispersion with regimes of unidirectional propagation. Remarkably, it is shown that both con…
We calculate the plasmon dispersion relation for Coulomb coupled metallic armchair graphene nanoribbons and doped monolayer graphene. The crossing of the plasmon curves, which occurs for uncoupled 1D and 2D systems, is split by the interlayer Coulomb coupling into a lower and an upper plasmon branch. The upper branch exhibits a highly unusual behavior with endpoints at finite $q$. Accordingly, the structure factor shows either a single or a double peak behavior, depending on the plasmon wavelength. The new plasmon structure is relevant to recent experiments, its properties can be controlled by…
Graphene plasmons have recently attracted a great deal of attention because of their tunability, long lifetime, and high degree of field confinement in the vertical direction. Nearby metal gates have been shown to modify the graphene plasmon dispersion and further confine their electric field. We study the plasmons of a graphene sheet deposited on a metal, in the regime in which metal bands do not hybridize with massless Dirac fermion bands. We derive exact results for the dispersion and lifetime of the plasmons of such hybrid system, taking into account metal nonlocalities. The graphene plasm…
Plasmons in van der Waals heterostructures comprised of graphene and related layered materials demonstrate deep subwavelength confinement and large propagation length. In this letter, we show that graphene-insulator-graphene tunnel structures can serve as plasmonic gain media. The gain stems from the stimulated electron tunneling accompanied by the emission of coherent plasmons under interlayer population inversion. The probability of tunneling with plasmon emission appears to be resonantly large at certain values of frequency and interlayer voltage corresponding to the transitions between ele…
In this comment we show that some equations and results of the paper titled "Dielectric screening and plasmons in AA-stacked bilayer graphene" are not correct. Furthermore, we present our results which seems to be more correct.
Electrically tunable graphene plasmons are anticipated to enable strong light-matter interactions with resonant quantum emitters. However, plasmon resonances in graphene are typically limited to infrared frequencies, below those of optical excitations in robust quantum light sources and many biologically interesting molecules. Here we propose to utilize near fields generated by the plasmon-assisted nonlinear optical response of nanostructured graphene to resonantly couple with proximal quantum emitters operating in the near-infrared. We show that the nonlinear near-field produced by a graphene…
In this study we report our numerical results on finite temperature non-interacting dynamical polarization function, plasmon modes and electron energy loss function of doped single layer gapped graphene within the random phase approximation. We find that the interplay of linear energy band dispersion, chirality, bandgap and temperature endow single layer gapped graphene with strange polarizability behaviour which is a mixture of 2DEG, single layer and bilayer graphene and as a result the plasmon spectrum also manifests strikingly peculiar behaviour. The plasmon dispersion is observed to be sup…
In this paper we show that graphene surface plasmons can be excited when an electromagnetic wave packet impinges on a single metal slit covered with graphene. The excitation of the plasmons localized over the slit is revealed by characteristic peaks in the absorption spectrum. It is shown that the position of the peaks can be tuned either by the graphene doping level or by the dielectric function of the material filling the slit. The whole system forms the basis for a plasmonic sensor when the slit is filled with an analyte.
Surface and volume plasmons in metallic nanospheres in semiclassical RPA-type approach; near-field coupling of surface plasmons with semiconductor substrate
Non-reciprocal plasmons in current-driven, isotropic, and homogenous graphene with proximal metallic gates is theoretically explored. Nearby metallic gates screen the Coulomb interactions, leading to linearly dispersive acoustic plasmons residing close to its particle-hole continuum counterpart. We show that the applied bias leads to spectral broadband focused plasmons whose resonance linewidth is dependent on the angular direction relative to the current flow due to Landau damping. We predict that forward focused non-reciprocal plasmons are possible with accessible experimental parameters and…
Plasmons in graphene nanostructures show great promise for mid-infrared applications ranging from a few to tens of microns. However, mid-infrared plasmonic resonances in graphene nanostructures are usually weak and narrow-banded, limiting their potential in light manipulation and detection. Here we investigate the coupling among graphene plasmonic nanostructures and further show that by engineering the coupling, enhancement of light-graphene interaction strength and broadening of spectral width can be achieved simultaneously. Leveraging the concept of coupling, we demonstrate a hybrid 2-layer …
The generation of highly-confined plasmons through far-field optical illumination appears to be impractical for technological applications due to their large energy-momentum mismatch with external light. Electrical generation of plasmons offers a possible solution to this problem, although its performance depends on a careful choice of material and geometrical parameters. Here we theoretically investigate graphene-based structures and show in particular the very different performance between (i) two layers of graphene separated by a dielectric and (ii) metal$|$insulator$|$graphene sandwiches a…
We develop a theory of electron tunneling accompanied by carrier-carrier scattering in graphene - insulator - graphene heterostructures. Due to the dynamic screening of Coulomb interaction, the scattering-aided tunneling is resonantly enhanced if the transferred energy and momentum correspond to those of surface plasmons. We reveal the possible experimental manifestations of such plasmon-assisted tunneling in current-voltage curves and plasmon emission spectra of graphene-based tunnel junctions. We find that inelastic current and plasmon emission rates have sharp peaks at voltages providing eq…
We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change…
Interactions between localized plasmons in proximal nanostructures is a well-studied phenomenon. Here we explore plasmon plasmon interactions in connected extended systems. Such systems can now be easily produced using graphene. Specifically we employ the finite element method to study such interactions in graphene nanoribbon arrays with a periodically modulated electrochemical potential or number of layers. We find a rich variation in the resulting plasmonic resonances depending on the dimensions and the electrochemical potentials (doping) of the nanoribbon segments and the involvement of tra…
The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a…
Within linear-response theory we derive a response function that thoroughly takes into account the influence of elastic scattering and is valid beyond the long-wavelength limit. We apply the theo-ry to plasmons in graphene and the two-dimensional electron gas (2DEG), in the random-phase ap-proximation, and for the former take into account intraband and interband excitations. The scatte-ring-modified dispersion relation shows that below a critical scattering strength $γ_c$, simply related to the plasmon frequency $ω$, no plasmons are allowed. The critical strengths $γ_c$ and the allowed $(ω, q)…
AB-stacked bilayer graphene with a tunable electronic bandgap in excess of the optical phonon energy presents an interesting active medium, and we consider such theoretical possibility in this work. We argue the possibility of a highly resonant optical gain in the vicinity of the asymmetry gap. Associated with this resonant gain are strongly amplified plasmons, plasmons with negative group velocity and superluminal effects, as well as directional leaky modes.
Large photon drag effect of the massless Dirac Fermions in intrinsic graphene is predicted for a graphene-on-plasmonic-layer system. The surface plasmons in the plasmonic layer enlarge the wave number of photon for hundreds of time of that in vacuum. The evanescent field of the surface plasmons generates directional motion of carriers in the intrinsic graphene, because of the large momentum transfer from the surface plasmon to the excited carriers. A model Hamiltonian is developed on the assumption that the in-plane wavelength of the surface plasmons is much smaller than the mean free path of …
It is by now well established that high-quality graphene enables a gate-tunable low-loss plasmonic platform for the efficient confinement, enhancement, and manipulation of optical fields spanning a broad range of frequencies, from the mid infrared to the Terahertz domain. While all-electrical detection of graphene plasmons has been demonstrated, electrical plasmon injection (EPI), which is crucial to operate nanoplasmonic devices without the encumbrance of a far-field optical apparatus, remains elusive. In this work, we present a theory of EPI in double-layer graphene, where a vertical tunnel …
Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron …
We have developed an analytical formulation to calculate the plasmon dispersion relation for a two-dimensional layer which is encapsulated within a narrow spatial gap between two bulk half-space plasmas. This is based on a solution of the inverse dielectric function integral equation within the random-phase approximation (RPA). We take into account the nonlocality of the plasmon dispersion relation for both gapped and gapless graphene as the sandwiched two-dimensional (2D) semiconductor plasma. The associated nonlocal graphene plasmon spectrum coupled to the "sandwich" system is exhibited in d…
We investigate the plasmon dispersion relation and damping rate of collective excitations in a double-layer system consisting of bilayer graphene and GaAs quantum well, separated by a distance, at zero temperature with no interlayer tunneling. We use the random-phase-approximation dielectric function and take into account the nonhomogeneity of the dielectric background of the system. We show that the plasmon frequencies and damping rates depend considerably on interlayer correlation parameters, electron densities and dielectric constants of the contacting media.
