Far-field excitation of single graphene plasmon cavities with ultracompressed mode volumes

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Science  12 Jun 2020:
Vol. 368, Issue 6496, pp. 1219-1223
DOI: 10.1126/science.abb1570

Light under compression

The ability to confine light to volumes much smaller than the wavelength produces high electromagnetic fields that can then be exploited in chemical and biological sensing and detection applications. Using silver nanocubes placed on a graphene surface, Epstein et al. developed a single, nanometer-scale acoustic graphene plasmon cavity device that can confine mid-infrared and terahertz radiation with mode volume confinement factors of 5 × 10–10. With the response being dependent on the size of the nanocube and electrically tunable, the results demonstrate a powerful platform with which to develop sensors in what has been a challenging wavelength regime where molecular fingerprints reside.

Science, this issue p. 1219


Acoustic graphene plasmons are highly confined electromagnetic modes carrying large momentum and low loss in the mid-infrared and terahertz spectra. However, until now they have been restricted to micrometer-scale areas, reducing their confinement potential by several orders of magnitude. Using a graphene-based magnetic resonator, we realized single, nanometer-scale acoustic graphene plasmon cavities, reaching mode volume confinement factors of ~5 × 10–10. Such a cavity acts as a mid-infrared nanoantenna, which is efficiently excited from the far field and is electrically tunable over an extremely large broadband spectrum. Our approach provides a platform for studying ultrastrong-coupling phenomena, such as chemical manipulation via vibrational strong coupling, as well as a path to efficient detectors and sensors operating in this long-wavelength spectral range.

Graphene plasmons (GPs) are propagating electromagnetic waves that are coupled to electron oscillations within a graphene sheet. As a result of their extraordinary properties of extreme confinement and low loss in the mid-infrared (MIR) to terahertz (THz) spectrum (16), they provide a platform to probe a variety of optical and electronic phenomena, including quantum nonlocal effects (7), molecular spectroscopy (8), and biosensing (9), and also enable access to forbidden transitions by bridging the scale between light and atoms (10). Furthermore, they offer a path toward miniaturizing optoelectronic devices in the long-wavelength spectrum, such as GP-based electro-optical detectors (11), modulators (12), and electrical excitation (13, 14).

The confinement of GPs can be increased even further by placing the graphene sheet close to a metallic surface (15). Such a structure supports a highly confined asymmetric mode, which is referred to as an acoustic graphene plasmon (AGP) because of its linear energy versus momentum dispersion. When the graphene-metal distance is very small, AGPs are confined in-plane extensively to almost 1/300 of their equivalent free-space wavelength (7) and are vertically confined to the spacing between the metal and graphene (16). This confinement is accompanied by very little contribution from the metal to the AGP damping, even when including the quantum nonlocal effects of the metal (17).

This ability of AGPs to confine light to small dimensions is pivotal for strong light-matter interactions, especially in the MIR and THz spectra, where the wavelength is inherently large and limits the electromagnetic field confinement. The latter is eminently important at this spectral region, as it is where molecular resonances reside, and the detection of their spectral fingerprints is a requirement for potential applications in industrial processes, medicine, biotechnology, and security (18, 19). Yet so far AGPs have only been observed over micrometer-scale areas, either as THz free-propagating waves (7, 15) or in MIR grating couplers (16, 20). Exploiting strong and ultrastrong light-matter interactions requires individual compact cavities for AGPs.

We realized single, nanometer-scale AGP cavities with ultrasmall mode volumes by the generation of a graphene plasmon magnetic resonance (GPMR), which enables the far-field excitation of AGP cavities over large areas without the need for lithographic patterning of either the surrounding environment or the graphene, and with no limitations on the light polarization. The GPMRs are formed by dispersing metallic nanocubes, with random locations and orientations, over a hexagonal boron nitride (hBN)/graphene van der Waals heterostructure.

In our GPMR device (Fig. 1A), nanometric silver nanocubes are randomly dispersed on top of a monolayer hBN/graphene heterostructure that is transferred onto a Si/SiO2 substrate (21), which acts as a back gate for electrically doping the graphene. The nanocubes are randomly scattered over the graphene surface. The Fourier-transform infrared spectroscopy (FTIR) extinction spectra, 1 – [T(V)/T(Vmax)], measured from the device for different back-gate voltages (colors), are shown in Fig. 1C, where T(V) is the transmission measured at a specific gate voltage V, and T(Vmax) is transmission measured for the maximal voltage (corresponding to the lowest doping due to the intrinsic doping of the chemical vapor–deposited graphene). Two resonances can be observed in the gate-dependent extinction (marked with triangles), on both sides of the SiO2 phonon absorption band (marked box). These resonances shift to higher frequencies with increasing graphene doping, which is consistent with the well-known behavior of plasmons in graphene (16, 22, 23). In addition, the supported surface phonons in the SiO2 and hBN (marked with arrows) lead to the typical surface phonon–graphene plasmon hybridization in this type of heterostructure (16, 2224).

Fig. 1 Structure and optical response of a GPMR device.

(A) Schematic of the GPMR device, which is composed of a Si/SiO2 substrate, graphene/0.8 nm monolayer hBN heterostructure, and silver nanocubes. The inset shows the cross section of a single GPMR structure and the generated magnetic resonance between the nanocube and the graphene. (B) SEM images of the actual device, showing the graphene edge and deposited nanocubes. The inset presents a zoomed-in image of the nanocubes (scale bars, 5 μm and 200 nm, respectively). (C) A typical GPMR device extinction spectra measured in an FTIR apparatus, for different gate voltages (colors). Each colored triangle marks an AGP peak and its evolution with gate voltage. The downward arrows mark the location of the hBN and SiO2 surface phonons. The solid and dotted lines correspond to the optical response for unpolarized and polarized light, respectively. The strong absorption band of the SiO2 phonon is also marked.

The effect of the polarization is shown for both polarized (solid curves) and unpolarized (dotted curves) illumination, and the two are nearly identical (Fig. 1C). Taking into account the fact that AGPs are transverse magnetic modes, this lack of preference on polarization in the response verifies the random nature of the nanocubes and implies a very weak interaction between neighboring nanocubes.

We further examined the device response by studying the gate-dependent extinction spectra obtained for different nanocube sizes and concentrations. The FTIR extinction spectrum was measured for three different nanocube sizes: 50 nm, 75 nm, and 110 nm (Fig. 2, A to C, respectively). For each nanocube size, two samples were fabricated and measured, one with a higher nanocube concentration (solid curves) and one with a lower nanocube concentration (dashed curves) (21). For all nanocube sizes, the resonances are seen to shift to higher frequencies with increasing graphene doping. An overall shift of the resonances to lower energies with increasing nanocube size can also be seen, which is attributed to the dispersive nature of AGPs (see below). In addition, a strong hybridization with the SiO2 surface phonon occurs when the resonance frequency is close to that of the SiO2 phonons; this is affected by the nanocube size and/or charge carrier density in graphene. This hybridization results in an enhancement of the peak around 1120 cm–1 as a result of the strong oscillator strength of the SiO2 phonon.

Fig. 2 Optical response for different nanocube sizes and concentrations.

(A to C) Gate-dependent extinction for nanocube sizes of 50 nm (A), 75 nm (B), and 110 nm (C), showing the change in spectral response with nanocube dimension. The solid and dashed curves correspond to higher and lower nanocube concentrations, respectively, and show that the change in the nanocube concentration corresponds to a change in the amplitude of the response without affecting its spectrum. The data for different gate voltages have been shifted for clarity. For simplicity, no hBN capping layer is used in these samples. (D) Calculated dispersion relation for an Ag/2 nm dielectric spacer/graphene/SiO2 structure, and extracted experimental results for nanocube sizes of 50 nm (black stars), 75 nm (red stars), and 110 nm (green stars). Graphene nonlocal conductivity was used, with Fermi level of 0.47 eV, lifetime of 10 fs, and T = 300 K for room temperature; the dashed orange curve represents the graphene Fermi velocity. The color scale corresponds to the imaginary part of the Fresnel reflection coefficient from the structure (the loss function).

The calculated and experimental dispersion relation (i.e., energy versus momentum dependence) shows good agreement (Fig. 2D). For simplicity, we calculate the dispersion for the layered structure without geometrical features (i.e., Ag/dielectric spacer/graphene/SiO2; color map), as in (16), and the experimental momentum (colored stars) is calculated by 2π/L, where L is the nanocube length. The resonances for the 75- and 110-nm nanocubes (green and red stars, respectively) lie very close to the SiO2 phonons, thus exhibiting a more phonon-like nature and confirming the strong hybridization mentioned above. The resonances for the 50-nm nanocubes (black stars), however, are farther away in frequency from the SiO2 phonons, thus displaying a more plasmon-like nature. This also explains the larger shift of the resonances with graphene doping that is obtained for the 50-nm nanocubes as compared to the 75- and 110-nm nanocubes, stemming from the fact that AGPs are doping-dependent whereas the SiO2 phonons are not. It is also seen that the calculated dispersion lies close to the graphene Fermi velocity, VF = 1 × 106 m/s (dashed orange line), which corresponds to the lowest achievable velocity of AGPs and to the maximal wavelength confinement of λ0/300. For the closest obtained experimental point (lower black star), we calculate an AGP velocity of ~1.42 × 106 m/s, denoting strong confinement of the optical field.

The results obtained in Fig. 2 further show that for different concentrations of the same nanocube size, one obtains the same spectral response but with different amplitude. On the other hand, different nanocube sizes generate an overall different spectral response. This implies that it is the properties of the single nanocube that determines the optical response of the device, whereas the amount (concentration) of nanocubes determines its amplitude. This is reinforced by the previous observation of the weak interaction between neighboring nanocubes. We can therefore conclude that a single nanocube/hBN/graphene structure actually acts as a single resonator. A further confirmation of the above conclusions is obtained from the 2D Fourier analysis of the scanning electron microscopy (SEM) images of the nanocubes, which distinctly show a lack of any other momentum contribution and/or periodical order in the samples’ k-space, except for that of the single nanocube (21).

We note that in these samples, the measured fill factor, which is the percentage of area covered by the nanocubes, ranges from 3 to 13% (21). Yet even with such low fill factors, the optical response is still comparable in magnitude to that obtained for grating couplers, with an equivalent fill factor of 50 to 85% (16). Furthermore, this robust scheme does not require any lithographic processes or patterning, and thus it both preserves the graphene quality and removes any limitation on the device area. To increase the number of devices per sample, we limited the graphene area to stripes of 200 μm × 2 mm; however, centimeter-scale devices were also fabricated and measured (21).

To corroborate the single-resonator nature of the behavior, we performed 3D simulations of a single nanocube close to a graphene sheet, illuminated by a far-field free-space beam (21). The spatial distribution of the electric field |Ey| shows that the field is mainly confined between the graphene and the nanocube (Fig. 3A), as expected for AGP modes (15, 16, 20). Figure 3, B and C, shows the obtained simulation results of the resonance frequency for different nanocube dimensions and Fermi levels, respectively. A linear dispersion relation is clearly seen in Fig. 3B, further corroborating the AGP nature of the resonance, together with a linear dependency on EF, which is characteristic of all plasmons in graphene. The field distribution obtained in Fig. 3A also exhibits the ability of the single structure to directly excite AGPs from the far field. However, there still remains an important question: What is the physical coupling mechanism that enables the far-field excitation of such high-momentum modes with a completely random structure that is built from single cavities?

Fig. 3 3D simulations and analysis of the generated electromagnetic fields of a single GPMR.

(A) The simulated |Ey| field distribution over the cross section of a single 3D nanocube. The intense electric field formed between the nanocube and the graphene is a signature of the generated AGPs (scale bar, 50 nm). (B and C) The expected linear dispersion of AGPs, as shown by the simulated resonance frequency obtained for different nanocube lengths L (40 to 90 nm) (B) and the square root of the Fermi level, EF (0.3 to 0.9 eV) (C). (D) The simulated magnetic field distribution, |Hz|, superimposed with the electric field lines, showing the generation of a magnetic dipole resonance at the graphene/nanocube interface. Vacuum is used as the environment; spacer thickness, 3 nm.

It can be argued that the average inter-nanocube spacing might lead to a certain periodicity in the system, which can contribute momentum similar to a grating coupler. However, we see no change in the spectral response of different concentrations (Fig. 2), which is contradictory to what has been observed for periodical structures with different periods (16, 20). This fact is further validated by the Fourier analysis of the nanocubes’ distribution and by examining the response of grating couplers (21). We can therefore rule out the existence of any order-based momentum-matching condition. A further examination of the magnetic field distribution of the single structure reveals its coupling nature. Figure 3D shows the spatial distribution of the magnetic field for a single nanocube close to a graphene sheet, superimposed with the electric field lines. The lines around the graphene-nanocube interface form a loop that is correlated with a strong magnetic field in its center, which has the shape of a magnetic dipole resonance. In the radio-frequency regime, this type of behavior occurs when a rectangular metallic patch is placed above a grounded conductive plane, and is known as the patch antenna. It supports Fabry-Perot–like resonances and can be described by a magnetic surface current. For a conductive patch and ground plane, this electromagnetic response is not constrained to a specific spectral band. Indeed, metal nanocubes placed close to a gold surface, known as the nanocube-on-metal (NCoM) system, had been previously shown to act as magnetic resonators in the visible spectrum (25, 26).

The optical response of the GPMR structure now becomes clear. Graphene, being a semimetal, can both act as a conductor and support AGPs when sufficiently doped. Thus, if a nanocube is placed in its vicinity, the illuminating far-field light can directly excite the GPMR patch antenna mode, which is associated with the excitation of an AGP between the nanocube and graphene, forming an optical cavity. The scalable nature of the patch antenna can also be observed in the GPMR spectral response for different nanocube sizes, where a larger nanocube size corresponds to a larger effective wavelength of the mode (see Fig. 2 and its discussion). We note that the remaining magnetic field within the top part of the nanocube in Fig. 3D is the part left unscreened by the graphene, owing to its small thickness and lower charge carrier density relative to a semi-infinite metal surface.

To corroborate the fact that the GPMR cavity is actually a graphene-based patch antenna in the MIR, we examined its scattering response. Owing to the similarity in the scattering response of patches and stripes (25, 27), for simplicity of simulations we show in Fig. 4A the simulated 2D scattering of a single GPMR structure for several Fermi levels, ranging from 0.1 eV to the recently achieved 1.8 eV (28). Scattering resonances that are correlated with the AGP resonances can be observed, thus validating the GPMR antenna nature. The response can be tuned from the far-infrared almost to the near-infrared spectrum solely by changing the charge carrier density in the graphene. Such an ultrabroad spectral response is remarkable to obtain from a single antenna. Although a variety of graphene-based antennas have been proposed, mainly in the MIR and THz (29, 30), they were found to be inefficient relative to their metallic counterparts. Thus, the GPMR might provide a different solution for realization of nanoantennas at these spectral bands.

Fig. 4 GPMR antenna response and mode volume calculation.

(A) Simulated 3D scattering from a single GPMR antenna for different graphene Fermi levels, showing that the scattering spectrum can be tuned from the far-infrared to almost the near-infrared. Inset: Zoom-in on the longer-wavelength spectrum. (B) Calculated normalized mode volume of the GPMR cavity in the MIR (blue curve) for different nanocube-graphene spacings d, and its comparison to the NCoM cavity in the visible spectrum (red curve), showing mode volumes that are smaller by four orders of magnitude with decreasing spacer thickness. See (21) for simulation details.

Finally, we used the quasi-normal mode theory to study the mode volumes achieved by the GPMR cavity (21, 31), neglecting nonlocal effects. Figure 4B shows the calculated normalized mode volume VGPMR30 (where λ0 is the free-space wavelength) of a single GPMR cavity with different hBN spacer thicknesses d (blue curve). Because similar plasmonic cavities in the visible spectrum have been shown to reach large confinement as well (32, 33), the GPMR cavity mode volume is compared with the equivalent NCoM patch antenna in the visible spectrum, where graphene is replaced by a gold surface (25) (red curve). It can be seen that even though the GPMR wavelength is about an order of magnitude larger than the NCoM wavelength, it is able to achieve a normalized mode volume that is four orders of magnitude smaller, reaching a normalized mode volume of ~4.7 × 10–10. These remarkable values can be directly attributed to the unique properties of AGPs and their ability to confine light to very small dimensions.

Although we can experimentally thin down the hBN spacer until the monolayer case (16), we note that below thicknesses of 1 to 2 nm, strong nonlocal effects in the graphene should be introduced (16, 34), given that we estimated the relative correction due to nonlocal effects to be ~23% in our experiment (21). In addition, we estimated the nonlocal response of the metal (17, 35, 36) and found it to be negligible above 1 nm (21). The inclusion of these requires a special treatment that cannot be introduced into our numerical simulations. Because it has been shown that AGPs can confine light to a monolayer hBN spacer and without increasing the losses (16), thinning down the spacer should continue and improve the achievable mode volume presented in Fig. 4B, accompanied by a spectral shift of the GPMR resonances and a saturation of the mode volume due to nonlocal effects (16).

The realization of single AGP cavities in the MIR spectrum with ultrasmall mode volumes, which are efficiently excited from the far field, provides a tunable platform for studying strong light-matter interactions in the MIR and THz spectra. One such important example is vibrational strong coupling (37) and its manipulation of chemical processes (38), which can be studied by introducing molecular substances or gas absorption layers between graphene and the nanocubes (33). In addition, it opens up possibilities for efficient AGP-based devices in this long-wavelength spectrum, such as photodetectors, biological and chemical sensing devices, and graphene-based tunable optical nanoantennas.

Supplementary Materials

Materials and Methods

Figs. S1 to S13

Table S1

References (3944)

References and Notes

  1. See supplementary materials.
Acknowledgments: I.E. thanks E. J. C. Dias and F. Vialla for fruitful discussions. Funding: Supported by U.S. Air Force Office of Scientific Research (AFOSR) grants FA9550-12-1-0491 and FA9550-18-1-0187 (D.R.S.); AFOSR Foldable and Adaptive 2D Electronics Multidisciplinary University Research Initiative grant FA9550-15-1-0514 (J.-Y.H. and J.K.); the European Commission through the project “Graphene-Driven Revolutions in ICT and Beyond” (Ref. use CORE 3 reference, not CORE 2) (N.M.R.P.); COMPETE 2020, PORTUGAL 2020, FEDER, and the Portuguese Foundation for Science and Technology (FCT) through project POCI-01-0145-FEDER-028114 (N.M.R.P. and T.G.R.); and the Government of Catalonia through an SGR grant and the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” Programme for Centres of Excellence in R and D (SEV-2015-0522), Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA program, and Mineco grant Plan Nacional (FIS2016-81044-P), and Agency for Management of University and Research Grants (AGAUR) 2017 SGR 1656 (F.H.L.K.). Furthermore, the research leading to these results has received funding from the European Union Seventh Framework Programme under grant agreements 785219 and 881603 Graphene Flagship. This work was supported by the ERC TOPONANOP under grant agreement 726001. Author contributions: I.E. conceived the idea and performed simulations, experiments, and analysis of the results; D.A., A.K., and V.-V.P. fabricated devices and assisted in measurements; Z.H. and X.M.D. performed nanocube deposition and analysis; T.K. assisted in device fabrication; N.M.R.P., T.G.R., and J.-P.H. assisted in numerical simulations; J.-Y.H. and J.K. provided the monolayer hBN; and N.M.R.P., D.R.S., and F.H.L.K. supervised the project. All authors contributed to the writing of the manuscript. Competing interests: The authors have no competing interests. Data and materials availability: All data are available in the manuscript or the supplementary materials.

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