The physics of electrons, photons, and their plasmonic interactions changes greatly when one or more dimensions are reduced down to the nanometer scale 1 . For example, graphene shows unique electrical, optical, and plasmonic properties, which are tunable through gating or chemical doping 2-5 . Similarly, ultrathin metal films (UTMFs) down to atomic thickness can possess new quantum optical effects 6,7 , peculiar dielectric properties 8 , and predicted strong plasmons 9,10 . However, truly two-dimensional plasmonics in metals has so far elusive because of the difficulty in producing large areas of sufficiently thin continuous films. Thanks to a deposition technique that allows percolation even at 1 nm thickness, we demonstrate plasmons in few-nanometer gold UTMFs, with clear evidence of new dispersion regimes and large electrical tunability. Resonance peaks at 1.5-5 m wavelengths are shifted by hundreds of nanometers and amplitude-modulated by tens of per cent through gating using relatively low voltages. The results suggest ways to use metals in plasmonic applications, such as electrooptic modulation, bio-sensing, and smart windows. Main text:Since ancient times, plasmons in nanoparticles of noble metals such as silver and gold have been used to color glass, culminating during the last two decades with a remarkable broadening of the use of plasmon excitations triggered by an improved understanding of their origin and behaviour, as well as by the availability of more sophisticated means to synthesize and pattern the metals [11][12][13] . New applications promise to have an impact on the optical industry: for example, super lenses allowing unprecedented sub-diffraction-limited optical imaging 14 , metasurfaces providing on-chip functionality in ultrathin form factor 15 , light modulation 16 , compact biosensors 17 and electrochemical effects that can be used in smart windows 18 . All

Control over the optical response of metal nanoparticles and their associated plasmons is currently enabling many promising applications in areas as diverse as biosensing and photocatalysis. In this context, experiments based upon colloid synthesis and nanofabricated structures are assisted by numerical electromagnetic modeling, which supplies predictive simulations, but not the kind of physical intuition needed for exploration of new ideas, such as one finds when simple mathematical expressions can describe a problem. This tutorial review presents and extends a simple analytical simulation method that allows us to accurately describe the optical response of metal nanoparticles, including retardation effects, without the requirement of large computational resources. More precisely, plasmonic extinction spectra and near-field enhancement are described through a small set of real numbers for each nanoparticle shape, which we tabulate for a wide selection of common morphologies. Remarkably, these numbers are independent of size, composition and environment. We further present a compilation of nanoplasmonic experimental data that are excellently described by the simple mathematical expressions here introduced.

The ultrafast response of metals to light is governed by intriguing nonequilibrium dynamics involving the interplay of excited electrons and phonons. The coupling between them leads to nonlinear diffusion behavior on ultrashort time scales. Here, we use scanning ultrafast thermomodulation microscopy to image the spatiotemporal hot-electron diffusion in thin gold films. By tracking local transient reflectivity with 20-nm spatial precision and 0.25-ps temporal resolution, we reveal two distinct diffusion regimes: an initial rapid diffusion during the first few picoseconds, followed by about 100-fold slower diffusion at longer times. We find a slower initial diffusion than previously predicted for purely electronic diffusion. We develop a comprehensive three-dimensional model based on a two-temperature model and evaluation of the thermo-optical response, taking into account the delaying effect of electron-phonon coupling. Our simulations describe well the observed diffusion dynamics and let us identify the two diffusion regimes as hot-electron and phonon-limited thermal diffusion, respectively.

Optical excitation and subsequent decay of graphene plasmons can produce a significant increase in charge-carrier temperature. An efficient method to convert this temperature elevation into electrical signals can enable important mid-infrared applications. However, the modest thermoelectric coefficient and weak temperature dependence of carrier transport in graphene hinder this goal. Here, we demonstrate mid-infrared graphene detectors consisting of arrays of plasmonic resonators interconnected by quasi-one-dimensional nanoribbons. Localized barriers associated with disorder in the nanoribbons produce a dramatic temperature dependence of carrier transport, thus enabling the electrical detection of plasmon decay in the nearby graphene resonators. Our device has a subwavelength footprint of 5 × 5 μm and operates at 12.2 μm with an external responsivity of 16 mA W and a low noise-equivalent power of 1.3 nW Hz at room temperature. It is fabricated using large-scale graphene and possesses a simple two-terminal geometry, representing an essential step towards the realization of an on-chip graphene mid-infrared detector array.

Light absorption in conducting materials produces heating of their conduction electrons, followed by relaxation into phonons within picoseconds, and subsequent diffusion into the surrounding media over longer timescales. This conventional picture of optical heating is supplemented by radiative cooling, which typically takes place at an even lower pace, only becoming relevant for structures held in vacuum or under extreme thermal isolation. Here, we reveal an ultrafast radiative cooling regime between neighboring plasmon-supporting graphene nanostructures in which noncontact heat transfer becomes a dominant channel. We predict that more than 50% of the electronic heat energy deposited on a graphene disk can be transferred to a neighboring nanoisland within a femtosecond timescale. This phenomenon is facilitated by the combination of low electronic heat capacity and large plasmonic field concentration in doped graphene. Similar effects should occur in other van der Waals materials, thus opening an unexplored avenue toward efficient heat management.

Plasmons provide excellent sensitivity to detect analyte molecules through their strong interaction with the dielectric environment. Plasmonic sensors based on noble metals are, however, limited by the spectral broadening of these excitations. Here we identify a new mechanism that reveals the presence of individual molecules through the radical changes that they produce in the plasmons of graphene nanoislands. An elementary charge or a weak permanent dipole carried by the molecule are shown to be sufficient to trigger observable modifications in the linear absorption spectra and the nonlinear response of the nanoislands. In particular, a strong second-harmonic signal, forbidden by symmetry in the unexposed graphene nanostructure, emerges due to a redistribution of conduction electrons produced by interaction with the molecule. These results pave the way toward ultrasensitive nonlinear detection of dipolar molecules and molecular radicals that is made possible by the extraordinary optoelectronic properties of graphene. DOI: 10.1103/PhysRevLett.117.123904 Localized surface plasmons (LSPs) have attracted considerable attention in the nanophotonics community due to their pivotal role in optical sensing applications such as antibody-antigen [1-3], gas [4,5], and pH [6,7] sensors. These excitations also enable the detection and chemical identification of single molecules through their enhancement of molecule-specific Raman scattering intensities [8][9][10][11][12][13]. LSPs are routinely observed in noble metal nanostructures, appearing as pronounced spectral features in their optical absorption and scattering spectra. Plasmonbased sensing heavily relies on the ability of these collective modes to confine and strongly amplify the optical near field. These properties are equally responsible for the large nonlinear optical response observed in metal nanoparticles [14][15][16][17][18][19], which has inspired alternative mechanisms for nonlinear plasmonic sensing. For instance, the aggregation of gold nanoparticles caused by targeted heavy metal ions [20], Escherichia coli bacteria [21], or Alzheimer's disease biomarkers [22] can be detected through an increase in second-harmonic generation (SHG). Additionally, third-harmonic generation has been recently claimed to offer large sensitivity to the dielectric environment compared to the linear response [23].Doped graphene is widely recognized as a promising material platform for plasmonics, capable of supporting electrically tunable plasmons with higher quality factors and spatial confinement than those of metal nanoparticles [24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Moreover, tunable graphene plasmons, so far observed at midinfrared (IR) and THz frequencies, provide the strong near-electric-field confinement needed for sensing [38][39][40][41]. In particular, graphene plasmons have been demonstrated to reveal vibrational fingerprints of biomolecules [38]. Additionally, the anharmonic electron motion associated with the Dirac cones of this material [42,43]...

The two-dimensionality of graphene and other layered materials can be exploited to simplify the theoretical description of their plasmonic and polaritonic modes. We present an analytical theory that allows us to simulate these excitations in terms of plasmon wave functions (PWFs). Closed-form expressions are offered for their associated extinction spectra, involving only two real parameters for each plasmon mode and graphene morphology, which we calculate and tabulate once and for all. Classical and quantum-mechanical formulations of this PWF formalism are introduced, in excellent mutual agreement for armchaired islands with > 10 nm characteristic size. Examples of application are presented to predict both plasmon-induced transparency in interacting nanoribbons and excellent sensing capabilities through the response to the dielectric environment. We argue that the PWF formalism has general applicability and allows us to analytically describe a wide range of 2D polaritonic behavior, thus facilitating their use for the design of actual devices. Plasmons are collective oscillations of conduction electrons found in different materials, where they interact strongly with light and can confine it down to nanoscale spatial regions to generate enormous optical field intensity enhancement [1]. These extraordinary properties are of paramount importance for a wide range of applications, such as optical sensing and modulation [2][3][4][5][6], the enhancement of nonlinear optical processes [7,8], photocatalysis [9][10][11][12][13][14], and photothermal therapies [15,16]. In these applications, precise spectral positioning of plasmon resonances is needed to achieve optimal performance. This is commonly achieved by fabricating noble metal nanostructures with specific sizes and morphologies. However, despite being the workhorse of plasmonics research, noble metals unfortunately present relatively large inelastic losses, thus limiting plasmon lifetimes in metallic nanostructures [17] and leading to a severe reduction in optical confinement. Additionally, the large number of electrons involved in the plasmons of metallic nanostructures limits the ways in which we can influence them in a dynamical fashion.Recently, highly-doped graphene has emerged as an outstanding plasmonic material [18][19][20][21][22][23][24][25][26][27][28][29][30][31] that simultaneously provides strong field confinement with relatively lower loss [32]. More importantly, plasmons in graphene are sustained by a small number of charge carriers compared to those of traditional noble metals, a property that makes them amenable to display new phenomena, including an unprecedented electro-optical response. Indeed, active tunability of the plasmon resonance frequency has been achieved via electrical gating [21][22][23][24][25][26][28][29][30]. Additionally, many of the aforementioned applications that were first realized using noble metal plasmons have now been realized using a tunable graphene platform [31][32][33][34]. However, the design of graphene-based plasmoni...

Control over charge carrier density provides an efficient way to trigger phase transitions and modulate the optoelectronic properties of materials. This approach can also be used to induce topological transitions in the optical response of photonic systems. Here we report a topological transition in the isofrequency dispersion contours of hybrid polaritons supported by a two-dimensional heterostructure consisting of graphene and α-phase molybdenum trioxide. By chemically changing the doping level of graphene, we observed that the topology of polariton isofrequency surfaces transforms from open to closed shapes as a result of doping-dependent polariton hybridization. Moreover, when the substrate was changed, the dispersion contour became dominated by flat profiles at the topological transition, thus supporting tunable diffractionless polariton propagation and providing local control over the optical contour topology. We achieved subwavelength focusing of polaritons down to 4.8% of the free-space light wavelength by using a 1.5-μm-wide silica substrate as an in-plane lens. Our findings could lead to on-chip applications in nanoimaging, optical sensing and manipulation of energy transfer at the nanoscale.