Terahertz (THz) fields are widely used for sensing, communication and quality control1. In future applications, they could be efficiently confined, enhanced and manipulated well below the classical diffraction limit through the excitation of graphene plasmons (GPs)2,3. These possibilities emerge from the strongly reduced GP wavelength, λp, compared with the photon wavelength, λ0, which can be controlled by modulating the carrier density of graphene via electrical gating4,5,6,7,8. Recently, GPs in a graphene/insulator/metal configuration have been predicted to exhibit a linear dispersion (thus called acoustic plasmons) and a further reduced wavelength, implying an improved field confinement9,10,11, analogous to plasmons in two-dimensional electron gases (2DEGs) near conductive substrates12. Although infrared GPs have been visualized by scattering-type scanning near-field optical microscopy (s-SNOM)6,7, the real-space imaging of strongly confined THz plasmons in graphene and 2DEGs has been elusive so far—only GPs with nearly free-space wavelengths have been observed13. Here we demonstrate real-space imaging of acoustic THz plasmons in a graphene photodetector with split-gate architecture. To that end, we introduce nanoscale-resolved THz photocurrent near-field microscopy, where near-field excited GPs are detected thermoelectrically14 rather than optically6,7. This on-chip detection simplifies GP imaging as sophisticated s-SNOM detection schemes can be avoided. The photocurrent images reveal strongly reduced GP wavelengths (λp ≈ λ0/66), a linear dispersion resulting from the coupling of GPs with the metal gate below the graphene, and that plasmon damping at positive carrier densities is dominated by Coulomb impurity scattering.
The graphene photodetector is illustrated in Fig. 1a. A monolayer graphene sheet was encapsulated between two h-BN layers15. The h-BN(13 nm)/graphene/h-BN(42 nm) heterostructure is placed on top of a pair of 15-nm-thick AuPd gates, which are laterally separated by a gap of 50 nm. Applying individual voltages to the gates allows the carrier concentrations n1 and n2 to be independently controlled in the graphene sheet at the left and right sides of the gap.
In Fig. 1a we also introduce the concept of THz photocurrent nanoscopy, and its application for GP mapping. The set-up is based on s-SNOM (NeaSNOM from Neaspec), where the metal tip is illuminated with the THz beam of a gas laser (SIFIR-50 from Coherent, providing an output power in the range of a few tens of milliwatts). Owing to a lightning-rod effect the incident field is concentrated at the tip apex, yielding a THz nanofocus16. Once brought into close proximity to the sample, the near fields of the nanofocus induce a current in the graphene sheet, similar to infrared photocurrent nanoscopy14,17. Recording the current as a function of the tip position yields nanoscale-resolved THz photocurrent images. To measure the current the graphene is contacted electrically in a lateral geometry (that is, metal contacts were fabricated on both sides of the heterostructure, as shown in Fig. 1a). Analogously to s-SNOM18 and infrared photocurrent nanoscopy14,17, we isolate the near-field contribution to the total photocurrent, IPC, by (i) oscillating the tip vertically at frequency Ω and (ii) demodulating the detector signal at 2Ω. This technical procedure is required because of the background photocurrent generated by the diffraction limited illumination spot. We achieved a spatial resolution of about 50 nm (Supplementary Section 1), which is an improvement of more than three orders of magnitude compared with diffraction-limited THz imaging.
Figure 1b shows a photocurrent image of the photodetector recorded at 2.52 THz (λ0 = 118.8 μm). Choosing graphene charge carrier densities n1 = 0.77 × 1012 cm−2 and n2 = −0.71 × 1012 cm−2, we generate a sharp p–n junction in the graphene above the gap between the gates. We observe a strong photocurrent IPC that is localized to a region that is approximately 1 μm wide and centred above the gap (central part of Fig. 1b). It can be explained by a photothermoelectric effect: due to a variation of the local Seebeck coefficient S in graphene (generated by the carrier density gradient), a local temperature gradient (caused by the THz nanofocus at the tip apex) generates a net charge current14,17. Because the variation of the carrier concentration—and thus ΔS—is largest between the two gates, we expect a maximum in the photocurrent at this location. In Fig. 1b, however, we observe a slight decrease of the photocurrent between the gates. This can be explained by the near-field intensity being reduced when the tip is above the gap, owing to the weaker near-field coupling between the tip and the metal gates. To corroborate the photothermoelectric origin of the THz photocurrent, we carried out local near-field photocurrent measurements at the gap location as a function of n1 and n2. The obtained near-field photocurrent pattern, IPC (n1, n2), exhibits six regions of alternating sign (Supplementary Section 2), which is a characteristic signature of the thermoelectric effect19,20.
Intriguingly, near the p–n junction we observe photocurrent oscillations that are perpendicular to the graphene edge (indicated by the horizontal white line in the upper part of Fig. 1b), which decay with increasing distance from the edge (Supplementary Section 3). Resembling the s-SNOM images of infrared GPs6,7, we attribute them to THz GPs—collective excitations of 2D mass-less electrons coupled to THz fields. The mechanism of photocurrent generation has been studied in detail14.To summarize, the near fields at the tip apex launch radially propagating GPs, which interfere with their own reflections from the graphene edge, producing oscillations of the electric field intensity—and thus the local energy dissipation—when the tip is scanned perpendicular to the graphene edge. The dissipated energy heats the p–n junction, yielding a photothermally induced current that oscillates with a period of half of the plasmon wavelength λp/2. We corroborate the plasmonic origin of the photocurrent oscillations by recording line profiles along the dashed black line in Fig. 1b at different illumination frequencies but fixed carrier densities n1 = 0.11 × 1012 cm−2 and n2 = −1.11 × 1012 cm−2. We find that the oscillation period decreases with increasing illumination frequency f (Fig. 2a). By measuring the oscillation period as a function of f (see Supplementary Section 4), we obtain the dispersion relation (f versus Re(qp) = 2π/λp, where qp is the complex-valued GP wavevector), which is shown in Fig. 2b (red symbols). Interestingly, we find a nearly linear dispersion at low frequencies, in excellent agreement with the calculated GP dispersion (the blue contour plot in Fig. 2b). Note that the calculations (see Methods) take into account the different layers of the heterostructure as well as the metal gates (air/h-BN/G/h-BN/AuPd/SiO2). The linear dispersion is typical for acoustic plasmons9,10,11,21 but is in strong contrast to conventional GPs in free-standing graphene, where (the blue solid curve in Fig. 2b)2,3. We conclude that acoustic GPs rather than conventional GPs are observed.
Interestingly, the GP wavelengths in the heterostructure are reduced by a factor of 12 compared with GPs of free-standing graphene (that is, by a factor of about 70 compared with λ0). We further highlight the small slope of the GP dispersion. It corresponds to a group velocity vg ≈ 0.014c, which is about one order of magnitude smaller than that of GPs in free-standing graphene at f = 2.52 THz. For low frequencies, the group velocity can be approximated by the analytical expression in equation (1). It is derived within the random phase approximation approach, where for the effective electron–electron interaction in graphene we took into account the screening stemming from both the h-BN slabs and the metal gates11 (Supplementary Sections 5 and 6): ɛz is the out-of-plane h-BN permittivity, is the Fermi wave number, νF = 106 m s–1 is the Fermi velocity of graphene, and d is the bottom h-BN thickness. The result of equation (1) for our heterostructure is shown in Fig. 2b by the dashed black line. At low frequencies, we observe an excellent agreement with the experimental (symbols) and calculated (blue colour plot) dispersions. Equation (1) further predicts a decreasing group velocity with decreasing d between the metal and the graphene, which will be the subject of future studies.
The strongly reduced wavelength of the acoustic THz GPs implies an extreme plasmonic field confinement, which we study by numerical electromagnetic simulations (see Methods) of the real part of the vertical near-field distribution of the GPs, Re(Ez(x,z)) (Fig. 3a,b). To that end, we place a dipole source above the h-BN encapsulated graphene on gold (inset Fig. 3b). For comparison, we place a dipole source above a free-standing graphene sheet to excite conventional GPs (inset Fig. 3a). For the free-standing graphene (Fig. 3a) we observe propagating GPs with an antisymmetric near-field distribution22,23, where the out-of-plane field decay length is λp/2π. In strong contrast, for the GPs in the heterostructure (Fig. 3b) we observe an asymmetric near-field distribution, where the GP field is concentrated inside the 42-nm-thick h-BN layer between the metal and the graphene (see zoom-in of Fig. 3b). This deep-subwavelength-scale vertical (z-direction) confinement of about λ0/2,800 cannot be achieved by pure dielectric loading (see Supplementary Section 7). Inside the h-BN, the field Ez is constant across the layer owing to the antisymmetric distribution of charge carriers (illustrated in the zoom-in of Fig. 3b). We explain this finding by the hybridization of GPs in the graphene sheet with their mirror image in the AuPd layer (illustrated in Fig. 3d), yielding an antisymmetric (short-wavelength) GP mode, analogous to out-of-phase plasmon modes in double-layer graphene24,25. The out-of-phase charge oscillation between the graphene and the gold surface confirms that an acoustic GP mode is observed.
To quantify the near-field distribution, in Fig. 3c we show the simulated near-field profiles of |Re(Ez)| (extracted along the dashed lines in Fig. 3a,b). We observe that the near field inside the bottom h-BN layer is about 36 times larger than the near field at the surface of the free-standing graphene. A strong near-field enhancement is also observed at the surface of the top h-BN layer, which is five times larger than on the free-standing graphene. For the out-of-plane decay length we find for free-standing graphene. It is reduced to δ2 = 0.26 μm for the heterostructure (Fig. 3c) owing to the short wavelength of the acoustic GPs.
We also studied the plasmon interference pattern (along the dashed black line in Fig. 1b) as a function of n2 (Fig. 4a). We observe that the fringe spacing (plasmon wavelength) increases with increasing carrier concentrations of both electrons and holes, demonstrating that acoustic GPs can be tuned by electrical gating, similar to plasmons in single-layer graphene4,6,7. However, in strong contrast to infrared GPs, we observe THz GPs at even the charge neutrality point (simultaneously probed by direct-current electrical measurements and indicated by a dotted white line in Fig. 4a). The photocurrent profile at the charge neutrality point (Fig. 4b) clearly shows weak oscillations near the graphene edge, revealing plasmons with λp ≈ 650 nm. We explain the existence of plasmons at the charge neutrality point by electron and hole populations that are thermally excited at room temperature26,27. Their energies, of about 25 meV, are large enough to support GPs at THz frequencies (3.11 THz = 13 meV). In Fig. 4c we compare experimental (symbols, extracted from Fig. 4a) and calculated (solid line, see Methods) plasmon wavelengths. The calculation of the plasmon dispersion is carried out by considering the conductivity of graphene at finite temperature28. The excellent agreement verifies both the electrical tunability of acoustic GPs and their existence at the charge neutrality point.
To study the acoustic plasmon amplitude decay time τp as a function of n2, we measure the decay length LPC of the photocurrent modulations in Fig. 4a by fitting a function that assumes both plasmon damping and radial-wave geometrical spreading (Supplementary Section 4). Although such fitting is consistent with previous near-field microscopy studies of GPs29, LPC provides only qualitative estimates for the GP propagation lengths LP owing to the more complex GP detection mechanism based on the heating of the p–n junction both by propagating GPs and via heat transfer from the hot spot below the tip14. However, as LPC scales with LP, the dependence of τp on the carrier density can be studied using the quantity LPC/vg. Note that in our work low-energy plasmons are studied, thus allowing the analysis of plasmon damping at very low carrier densities, down to the charge neutrality point. We find that LPC/vg increases with positive n2, from about 380 fs for n2 = 1.9 × 1011 cm−2 to about 600 fs for n2 = 7.7 × 1011 cm−2 (symbols in Fig. 4d). For negative n2, τp is almost constant with a value of about 500 fs. These observations are consistent with the expected competition of two types of plasmon damping mechanism: charge impurity and acoustic phonon scattering processes. For acoustic phonon scattering, a weak dependence of the GP lifetime on the carrier density is expected30, which has been experimentally demonstrated for mid-infrared plasmons at high carrier densities29. However, for charge impurity scattering, a strong dependence of the GP lifetime on the carrier density has been predicted31. Thus, for low carrier densities a cross-over is expected where charge impurity scattering dominates acoustic phonon scattering. We can qualitatively match the dependency of LPC/vg on the carrier concentration by microscopic plasmon lifetime calculations11 (solid lines in Fig. 4d), which fully take into account the layers of our heterostructure (see Supplementary Section 8). Importantly, in these calculations we only consider Coulomb impurities31 with a density nimp = 7×1010 cm–2, thus supporting the hypothesis that long-range scattering agents play a dominant role for plasmon damping at low carrier densities. This is in strong contrast to plasmon damping in encapsulated graphene samples at high carrier densities, which is dominated by intrinsic acoustic phonons rather than by impurities29.
The long-lived and strongly enhanced and confined fields of acoustic GPs could play an important role in fundamental studies of strong light–matter interactions at the nanoscale. Their linear dispersion could also offer manifold possibilities for the development of devices for detector, sensor and communication applications in the technologically important THz range, such as nanoscale waveguides or modulators. We also highlight that electrical detection of GPs constitutes an important technological advance in the field of graphene plasmonics, as purely on-chip functionalities can be now envisioned and developed. We finally stress that our imaging technique also enables the study and mapping of local THz photocurrents in semiconductor devices or 2D materials with nanoscale resolution.
Determination of the local carrier densities
The near-field photocurrent profiles shown in Fig. 2a were extracted at a distance of about 1 μm from the 50-nm-wide gap between the two gates, to ensure a well-defined and homogeneous carrier density in the graphene sheet. As can be seen in the Supplementary Section 4.2, the period of the signal oscillations (that is, the GP wavelength) is constant for all near-field photocurrent line profiles taken at distances d between 250 nm and 1,500 nm from the gap. Because the GP wavelength depends on the carrier concentration, we can conclude that the carrier concentration is well established at d = 1 μm.
The sheet carrier densities nL,R were obtained from the gate voltages UL,R according to nL,R = k(UL,R – Uoff) = (0.464 × 1016 m−2 V−1) (UL,R – 0.34 V). The offset voltage Uoff corresponds to the gate voltage for which the resistance of the graphene sheet is maximum. The coefficient k is the calculated electrostatic capacitance of the 42 nm h-BN layer, assuming dielectric constant of 3.56 for h-BN32,33.
Calculation of the acoustic GP dispersion
The graphene plasmon modes in both the thin-film stack of vacuum/SiO2(285 nm)/AuPd(10 nm)/h-BN(42 nm)/graphene/h-BN(13 nm)/vacuum and free-standing graphene (air/graphene/air) were calculated using the electromagnetic transfer matrix method. The finite-temperature local random phase approximation28 was used to calculate the graphene conductivity σ(ω) at room temperature. We assumed high-quality graphene15 with a mobility of 40,000 cm2 V–1 s–1 and utilized a permittivity model that has been used for the h-BN films29. The imaginary part of the Fresnel reflection coefficient is displayed as blue colour plot in Fig. 2b.
Numerical calculations of spatial near-field distributions
Finite-elements numerical simulations (Comsol software) were used to calculate the spatial distribution of the vertical near-field component in the heterostructure and around the free-standing graphene sheet, both shown in Fig. 3. The conductivity of graphene was calculated according to the local random phase approximation28. We assumed high-quality graphene15 with a mobility of 40,000 cm2 V–1 s–1. Further, we assumed a spatially constant carrier concentration (for justification see the Methods section ‘Determination of local carrier densities’). We also excluded reflection of GPs at the p–n junction, which we justify by the absence of photocurrent oscillations with half the GP wavelength perpendicular to the p–n junction. Because of the absence of GP reflections, the p–n junction essentially damps or transmits GPs. Altogether, we can conclude that the GP propagation parallel to the gap, and at 1 μm distance, is not affected by the p–n junction. In our numerical calculations we can thus model our experiment with a planar eterostructure with spatially uniform carrier concentration.
We thank C. Crespo for technical assistance with the THz laser. R.H., P.A-G. and A.N. acknowledge support from the Spanish Ministry of Economy and Competitiveness (national projects MAT2015-65525-R, FIS2014-60195-JIN and MAT2014-53432-C5-4-R, respectively). F.H.L.K. acknowledges support from the Fundacio Cellex Barcelona, the ERC Career integration grant (294056, GRANOP), the ERC starting grant (307806, CarbonLight), the Government of Catalonia through the SGR grant (2014-SGR-1535), the Mineco grants Ramón y Cajal (RYC-2012-12281) and Plan Nacional (FIS2013-47161-P) and project GRASP (FP7-ICT-2013-613024-GRASP). R.H., F.H.L.K., A.P. and M.P. acknowledge support by the EC under the Graphene Flagship (contract no. CNECT-ICT-604391). Y.G. and J.H. acknowledge support from the US Office of Naval Research (N00014-13-1- 0662).
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Nature Communications (2018)