The success of metal-based plasmonics for manipulating light at the nanoscale has been empowered by imaginative designs and advanced nano-fabrication. However, the fundamental optical and electronic properties of elemental metals, the prevailing plasmonic media, are difficult to alter using external stimuli. This limitation is particularly restrictive in applications that require modification of the plasmonic response at sub-picosecond timescales. This handicap has prompted the search for alternative plasmonic media1,2,3, with graphene emerging as one of the most capable candidates for infrared wavelengths. Here we visualize and elucidate the properties of non-equilibrium photo-induced plasmons in a high-mobility graphene monolayer4. We activate plasmons with femtosecond optical pulses in a specimen of graphene that otherwise lacks infrared plasmonic response at equilibrium. In combination with static nano-imaging results on plasmon propagation, our infrared pump–probe nano-spectroscopy investigation reveals new aspects of carrier relaxation in heterostructures based on high-purity graphene.
Graphene plasmonics5,6,7 has progressed rapidly, propelled by the electrical tunability, high field confinement8,9, potentially long lifetimes10,11 of plasmons and the strong light–matter interactions12,13,14,15 in graphene. An earlier spectroscopic study has reported photo-induced alteration of the plasmonic response of graphene on optical pumping16. In this work, we harnessed ultrafast optical pulses to generate mid-infrared (mid-IR) plasmons in a sample that lacks a plasmonic response at equilibrium. We examined the real-space aspects of non-equilibrium plasmon–polariton generation and propagation under femtosecond (fs) photo-excitation using a new ultrafast nano-infrared (IR) technique that fuses real-space plasmon imaging with spectroscopy. We applied this method to investigate high-quality graphene specimens encapsulated in hexagonal boron nitride: hBN/G/hBN4.
We performed time-resolved broadband nano-IR experiments using antenna-based near-field nanoscopy (see Methods). This set-up (Fig. 1a,b) combines exceptional spatial, spectral and temporal resolution16,17,18, allowing an experimental probe of the dispersion of graphene plasmons under photo-excitation—a feat previously considered technologically infeasible. In our measurements, the metalized tip of an atomic force microscope (AFM) was illuminated by a focused IR probe beam, generating strong evanescent electric fields beneath the tip. These fields possess a wide range of in-plane momenta q and therefore facilitate efficient coupling to graphene plasmons19. Such evanescent fields extend ∼20 nm beneath the top surface of our structures, which is sufficient to launch and detect surface plasmons in a graphene microcrystal protected by a thin (10 nm) encapsulating layer of hBN10. The tip of the nanoscope acts as a launcher for surface plasmons of wavelength (λp) that propagate radially outwards from the tip. On reflection from the sample edge, these plasmons form standing waves between the tip and the reflector. While scanning the tip towards a graphene edge, one can collect the near-field signal, which displays oscillations with a period of λp/2. Recent nano-IR imaging experiments with encapsulated high-mobility graphene have registered oscillations with both λp/2 and λp periodicity; the latter were assigned to plasmons launched directly from the sample edge by incident light10.
We begin with the principal result of this work: the ultrafast dynamics of plasmons in encapsulated graphene revealed by means of nano-IR pump–probe spectroscopy (Fig. 1c,d). The broadband mid-IR probe allows for visualization of the frequency–momentum dispersion of graphene plasmons in the course of a single line-scan across the sample surface20. We investigated the photo-induced changes in near-field scattering amplitude s(ω,x) collected from sequential 20 × 20 nm2 spatial pixels that together constitute a hyperspectral line-scan. Acquired at varying pump–probe delay times, hyperspectral scans reveal a rich spatiotemporal plasmonic response, which arises and then decays according to the dynamics of photo-excited carriers. It is instructive to present hyperspectral line-scans in the form of two-dimensional frequency-position maps s(ω,x) plotted in Fig. 1c,d (and see Supplementary Information (SI)). This representation highlights the novelty of our experimental approach, which combines non-equilibrium spectroscopy with imaging of plasmonic standing waves.
The strongest photo-induced signal is recorded at zero time delay between pump and probe pulses (Fig. 1c): we observe a set of three dispersing peaks in the s(ω,x) hyperspectral map. The dashed lines shown in Fig. 1c trace peaks of the signal determined from the spatial derivative of the raw data, ds(ω,x)/dx = 0 (Fig. 1e). The spatial period of oscillations, as well as the relative separation between peaks and troughs, systematically increases with decreasing ω. These findings are consistent with expectations for plasmonic modes dispersing with positive group velocity.
The photo-induced plasmonic signal decays as the probe pulse is temporally delayed with respect to the pump pulse (Fig. 1d,f). After t = 2 ps pump–probe delay, we observe only a single peak in close proximity to the sample edge. Plasmonic features completely vanish after 5 ps (Supplementary Section 6): a timescale consistent with earlier diffraction-limited measurements21,22,23. Figure 1c,d depicts the first direct observation of plasmon interference patterns produced by photo-excited Dirac quasiparticles.
We will now examine the physical mechanism underlying the ultrafast plasmonic effects in Fig. 1. By way of a photo-induced increase in the Drude weight (D), this transient plasmonic response originates from a strongly enhanced electronic temperature (Tel) in photo-excited graphene16,23. Specifically, at timescales longer than ∼30 fs, it is expected that the optical excitation of graphene preserves the electron density, but results in an elevated Tel (ref. 24, for details see Supplementary Section 5). At t = 0, Tel, D(Tel), and λp(ω) are the largest. The reduction in λp(ω) shown in Fig. 1d at 2 ps following the pump pulse can be explained by a decrease of D(Tel) as electrons begin to cool. Thus, the plasmonic response observed experimentally within the first several ps following photo-excitation is consistent with the expected dynamical evolution in D(Tel).
We now proceed to survey nano-imaging data acquired for the same device using a continuous-wave (cw) laser at ω = 890 cm−1 (Fig. 2b–d). With zero applied back-gate voltage Vg = 0, the near-field signal from the entire structure is nearly uniform with no optical contrast from graphene (Fig. 2b). This is because our encapsulated graphene remains nearly charge neutral even at ambient conditions (Vg = VCN = 0 V, where VCN is the charge neutrality voltage)4. As Vg increases, plasmon fringes start to develop, with the most prominent plasmon fringe observed closest to the sample edges. Figure 2c shows the near-field image obtained at Vg = 60 V. Compared with the Vg = 0 case, the triangular graphene shape can be clearly discerned. Moreover, multiple plasmonic fringes along the graphene edges can be detected. Increasing Vg to 115 V improves the visibility of the graphene plasmon fringes, yielding at least 12 fringes within a micrometre of the sample edge (Fig. 2d). The round-trip distance travelled by plasmons in Fig. 2 is therefore approaching 2 μm, similar to ref. 10, and attests to a reduction of plasmonic losses in high-mobility samples.
Alternating bright and dark fringes in Fig. 2 encode information about λp and the dimensionless damping constant γp8,9,10,11. We recall that γp = (σ1/σ2) + (κ2/κ1) is related to the ratios of the real and imaginary parts of the conductivity σ(ω) = σ1(ω)+iσ2(ω), and the effective permittivity κ(ω) = κ1(ω)+iκ2(ω) of the graphene environment25,26 (see Supplementary Section 4). For a quantitative analysis, we plot imaging data in the form of line-profiles (Fig. 2e,f) acquired along the lines marked in Fig. 2c,d. Multiple plasmon fringes are clearly resolved in the graphene interior. These fringes appear in pairs, indicating the coexistence of two types of oscillations: one with period λp/2 and the other with period λp (Supplementary Section 3). The plasmonic line-profiles can be simulated numerically by approximating the tip as an elongated spheroid (Supplementary Section 4). The best fit, shown by the green curve in Fig. 2f, yields an estimate of γp = 0.02 and λp = 150 nm.
Our analysis of plasmonic images acquired under near-equilibrium conditions confirms the relevance of both λp- and λp/2-periodic plasmonic interference patterns to the infrared response of the high-mobility device. Nevertheless, these two distinct periodicities are not apparent in our dynamic data. This is not unexpected. Pump–probe traces show substantially broadened plasmonic fringes: an anticipated outcome of increased damping in the regime of elevated Tel. In Fig. 3a we display an attempt to model the influence of scattering associated with an increase in Tel. We start with parameters that most accurately describe our equilibrium nano-IR data (red trace), and then examine the effect of increasing γp. Enhanced scattering rapidly washes out weaker fringes with period λp/2 whereas stronger oscillations of period λp persist over a broader range of γp. Based on this analysis, we assume that separations between the dashed lines in Fig. 1c,e are equal to λp (Supplementary Section 3).
The dispersion of non-equilibrium photo-induced plasmons is presented in Fig. 3b. The dots were obtained from the fringe separations extracted from derivative plots in Fig. 1c,e. To model the plasmonic response we followed a standard procedure as detailed in the Supplementary Sections 2 and 5. The plasmon dispersion in Fig. 3b is visualized via a false colour map of the imaginary part of the reflectivity rp = rp(q,ω)16. By varying Tel, we obtain a best match to the experimental data for Tel = 3,200 K. The corresponding D versus Tel relationship is plotted in Fig. 3c, which is similar to previous results16. With all parameters determined, we are at the position to plot the output of the model in the form of hyperspectral maps (Supplementary Section 5) that reproduce the gross features of the raw data in Fig. 1c. This overall agreement establishes the plasmonic origin for the real-space features observed in pump-probe data.
An important unresolved issue is the origin of the tenfold increase in the linewidth of the non-equilibrium plasmon dispersion compared with the equilibrium one. One possible candidate for the enhanced plasmon decay is the emission of acoustic phonons10,27. Another possibility is electron–hole scattering, for which recent relativistic hydrodynamics theories28,29 predict that γee = (2ωτ)−1 ∼ α2Tel/ω. For α ∼ 1 and Tel = 3,200 K the estimate yields γee ∼ 2.5, which is more than an order of magnitude higher than the measured γp. Two possible reasons for this discrepancy are that the theory assumes undoped graphene, whereas in our case the doping is non-negligible, and the assumption of weak interactions (α << 1) that may not describe the realistic case of α ∼ 1. On the other hand, the lower than expected intrinsic damping is good news for the implementation of practical ultrafast plasmonic devices using graphene.
Our hBN/G/hBN high-quality devices were fabricated using a polymer-free multilevel stacking dry-transfer process to form the encapsulated graphene structure (Supplementary Section 1). This technique is essential for maintaining graphene flakes free of contamination, bubbles and wrinkles. Consequently, the charge neutrality point of graphene in these samples is very close to the zero gate voltage Vg at ambient conditions, as confirmed from our near-field gating experiments. After multi-stacking transfer, the metal contacts were fabricated at the exposed graphene edge4. Note that graphene is entirely encapsulated within the hBN flakes.
At ambient conditions, the carrier mobility near the Dirac point exceeds 140,000 cm2 V–1 s–1. For the carrier densities relevant to the plasmonic regime n > 3 × 1012 cm−2, the mobility is reduced considerably. However, it still exceeds by more than an order of magnitude that of the first-generation graphene devices and approaches the room-temperature limit set by the acoustic phonon scattering4.
Figures 1b and 2a show optical microscope and AFM images of the hBN/G/hBN device. The region of a tapered graphene microcrystal encapsulated between the two hBN layers can be clearly seen in the AFM topography. The graphene edges in our devices were preserved in their pristine state without any exposure to oxygen plasma etching, a process that is likely to introduce extrinsic edge doping and/or scattering. The underlying Si/SiO2 (285 nm) substrate serves as the back gate to which we apply voltage Vg (up to 120 V at ambient conditions) to tune the carrier density in graphene30. Equation (S4) is based on the assumption19 that the sheet optical conductivity σ(ω) of graphene is dominated by the intraband component σintra(ω) = D(Tel)/[π(Γ−iω)].
Infrared nano-imaging experiments
The infrared nano-imaging experiments were performed using a scattering-type scanning near-field optical microscope (s-SNOM). Our s-SNOM (http://www.neaspec.com) is equipped with continuous wave mid-IR quantum cascade lasers (http://www.daylightsolutions.com) and CO2 lasers (http://www.accesslaser.com). The s-SNOM is based on an AFM with a tip apex radius of 25 nm operating in a tapping frequency around 270 kHz. A pseudo-heterodyne interferometric detection module is implemented in our s-SNOM to extract both scattering amplitude s and phase of the near-field signal. In the current work, we discuss only the former. To subtract the background signal, we demodulated the near-field signal at the third harmonic of the tapping frequency. All of the infrared nano-imaging experiments were performed under ambient conditions.
Nano-Fourier transform infrared (nano-FTIR) experiments
The ultrafast nano-FTIR set-up is based on s-SNOM. The s-SNOM is integrated with a mid-IR source (Lasnix) that emits ultrashort (<40 fs) pulses produced via an 80 MHz near-IR Er-doped fibre laser (Toptica Photonics). Pulses of mid-IR probe light are generated by difference-frequency mixing of near-IR pulses in a 2 mm thick, z-cut GaSe crystal. Ultrafast temporal resolution (∼ 200 fs) is achieved by operating the s-SNOM in a pump–probe mode whereby the synchronized 40 fs near-IR pulses of the fibre laser (λ = 1.56 µm) serve as a pump with a variable pump–probe time delay.
An important technical detail of our pump–probe study is that application of 30 V back-gate voltages was necessary to achieve the plasmonic features shown in Fig. 1c,d. The static Drude weight produced by this gate voltage alone is insufficient to support steady-state plasmonic oscillations within our mid-IR probing window without photo-excitation (Fig. 3b). Previously, we carried out an analogous spatio-temporal imaging protocol on lower mobility graphene/SiO2 structures16. Although time-resolved nano-spectroscopy revealed a pump-induced modification of the plasmonic response16, we were unable to observe real-space plasmonic oscillations, with or without an applied gate voltage. We also wish to point out that the probe pulse in our apparatus is insufficient to launch plasmons or trigger plasmon interference patterns (Supplementary Section 6).
We thank P. Kim, Z. Sun, A. Sternbach, S. Dai and J.-S. Wu for helpful discussions. Research on static plasmon interferometry of high-mobility graphene is supported by DOE-BES DE-FG02-00ER45799. Work on ultrafast imaging of non-equilibrium plasmons is supported by ONR N00014-15-1-2671. The development of ultrafast pump–probe spectroscopy is supported by DOE-BES DE-SC0012592 and DE-SC0012376. The development of nano-imaging is supported by AFOSR and ARO. D.N.B is supported by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant GBMF4533. J.H. acknowledges support from ONR N00014-13-1-0662. G.X.N., B.O., and A.H.C.N. acknowledge the National Research Foundation, Prime Minister Office, Singapore, under its Medium Sized Centre Program and CRP award ‘Novel 2D materials with tailored properties: beyond graphene’ (R-144-000-295-281). B.O. acknowledge NRF-Competitive Research Programme (CRP award no. NRF-CRP9-2011-3).