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Letter
Propagating plasmons in a charge-neutral quantum tunneling transistor Achim Woessner, Abhishek Misra, Yang Cao, Iacopo Torre, Artem Mishchenko, Mark Lundeberg, Kenji Watanabe, Takashi Taniguchi, Marco Polini, Kostya Novoselov, and Frank H.L. Koppens ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01020 • Publication Date (Web): 30 Oct 2017 Downloaded from http://pubs.acs.org on November 1, 2017
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ACS Photonics
Propagating plasmons in a charge-neutral quantum tunneling transistor Achim Woessner,1 Abhishek Misra,2 Yang Cao,3 Iacopo Torre,4, 5 Artem Mishchenko,2, 3 Mark B. Lundeberg,1 Kenji Watanabe,6 Takashi Taniguchi,6 Marco Polini,5 Kostya S. Novoselov,2, 3 and Frank H.L. Koppens1, 7, ∗ 1
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain 2 School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK 3 National Graphene Institute, The University of Manchester, Booth St. E, Manchester M13 9PL, UK 4 NEST, Scuola Normale Superiore, I-56126 Pisa, Italy 5 Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy 6 National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 7 ICREA – Institució Catalana de Recerça i Estudis Avancats, Barcelona, Spain
The ultimate limit of control of light at the nanoscale is the atomic scale. By stacking multiple layers of graphene on hexagonal boron nitride (h-BN), heterostructures with unique nanophotonic properties can be constructed, where the distance between plasmonic materials can be controlled with atom-scale precision. Here we show how an atomically-thick tunable quantum tunnelling device can be used as building block for quantum plasmonics. The device consists of two layers of graphene separated by one nanometer (three monolayers) of h-BN, and a bias voltage between the layers generates an electron gas coupled to a hole gas. We show that even though its total charge is zero, this system is capable of supporting propagating graphene plasmons. Keywords: graphene plasmons; graphene tunneling device; s-SNOM; nano-optics; highly doped graphene Heterostructures of graphene and related twodimensional materials, such as the insulator hexagonal boron nitride (h-BN) or the semiconducting transition metal dichalcogenides (TMDs), are a promising new material system with virtually unlimited possibilities.1 Such heterostructures allow a full bottom-up control of their physical properties and have generated tremendous interest because they display novel physical phenomena and allow for the construction of novel opto-electronic devices with specific functionalities2 that cannot be realized with bulk materials. Heterostructures of two-dimensional (2d) materials are also an appealing toolbox for nanophotonic devices, with prospects to bring the confinement and control of plasmons to the atomic scale and to study quantum plasmonic effects.3 So far, only the most simple heterostructure – graphene encapsulated in h-BN – has been studied and showed a much longer plasmon lifetime than previously reported,4 as well has hybrid plasmon-phonon modes,5 and many other exotic phenomena.6,7 Plasmons in bilayer graphene have been studied,8 as well as globally gated graphene plasmons with a spacing layer.9 Because the two graphene layers are electrically shorted the effects of quantum tunnelling could not be studied. Tunnelling effects in metallic plasmonic systems have been studied extensively,10,11 and the atomic control of 2d material heterostructures offers an ideal testbed for detailed physics studies on quantum tunnelling and many-body effects in plasmonics. Here, we make the first steps towards more advanced nanophotonic 2d material heterostructures and report on the plasmonic properties of a quantum tunnelling transistor.12–14 The device is constructed from two graphene monolayers (GML), separated by 3 layers of h-BN. The two GMLs are contacted individually, allowing for control of the bias voltage between the two graphene layers. This bias voltage leads to a tunnelling
current but also induces carriers of opposite polarity in the two layers. Thus effectively, we obtain an electron gas coupled to a hole gas (see Fig. 1b). We find that even though the total charge carrier density of this device is zero, clear propagating plasmon modes with long lifetimes are supported. The plasmonic mode of our device is schematically illustrated in Fig. 1c. Usually, two-dimensional doublelayer electron systems host two collective (i.e. selfsustained) modes. When inter-layer tunnelling is weak, the two modes can be classified classically as in-phase and out-of-phase oscillations of the charge carrier densities in the two layers. If both layers are doped with charges of the same sign, say both host electrons or holes, the in-phase mode is an ordinary 2d plasmon15 with a dispersion relation that at long wavelengths depends on the square root of the in-plane plasmon wave vector q. On the other hand, the out-of-phase mode is an acoustic plasmon mode, whose existence outside the intraband particle-hole continuum depends on details of the band structure of the electron system in each layer.16–19 The situation is the opposite if one of the two layers is electron doped and the other is hole doped (Fig. 1b), as is the case for our device. In this case, despite the overall charge of the double-layer electron system being zero, plasmons still can be excited. This time it is the in-phase mode that has an acoustic dispersion in the long-wavelength limit, while the out-of-phase mode is the ordinary 2d charged plasmon. To the best of our knowledge, however, exper√ imental signatures of the ordinary q-dispersing, or optical, plasmon modes in electrically-neutral double layers have not been reported in the literature. The device structure, as shown in Fig. 1a, is obtained by transferring graphene monolayers and h-BN with the dry transfer technique.20,21 The tunnel junction between the two graphene layers is created by a 3-layer-thick h-BN
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Figure 1 | Microscope image of the device and sketch of the observed plasmon mode. a Microscope image of the device with the tunnel junction region highlighted. The contacts at which the bias voltage Vb is applied are indicated. The thickness of the h-BN substrate is 60 nm. The total overlap area of the tunnel junction is 45 µm2 . b Sketch of the gating scheme. A voltage is applied between the top and bottom graphene leading to an induced carrier density in the graphene layers. By changing the voltage the carrier density can be tuned. The total carrier density of the system however is always zero. c Sketch of the in-plane component of the electric field and field lines of the measured optical plasmon mode. The mode of the separated double layer graphene has the charges in the top and bottom layer of the graphene oscillating out-of-phase. For the sake of clarity the bottom h-BN layer is not indicated in this sketch, but is included in all the simulations.
flake and the whole stack is placed on top of a h-BN substrate (60 nm) for increased electrical quality.14 The two GML layers are contacted individually by evaporation of 5 nm Cr and 50 nm Au. Even though a global backgate voltage could be applied between the Si and graphene, we focus in this work only on the effect of a bias voltage Vb that is applied between the two graphene layers. As the h-BN is only ∼ 1 nm thick, even a small bias voltage (of order millivolts) induces a measurable tunnelling current, but the bias voltage also induces charge carriers in both of the two GMLs. As the GMLs are undoped (apart from thermally induced carriers) for zero bias voltage, it is clear from symmetry arguments that the total carrier density of the system is zero when a bias voltage is applied, while the two graphene layers obtain charges of
opposite polarity. We image propagating plasmons in the tunnel junction region with a scattering-type scanning near-field optical microscope (s-SNOM).4,22,23 A continuous wave infrared CO2 laser with a wavelength of λ0 = 10.6 µm is focussed onto a metallized atomic force microscope probe tip. The light interacts with the probe tip leading to a strongly confined field (of ∼ 30 nm) near the apex of the tip. The sharpness of the tip and the associated confined field provide the necessary momentum for graphene plasmon excitation, overcoming the momentum mismatch between far-field light and plasmons.24 The excited plasmons, which propagate away from the tip radially, are then partially reflected by the edge of the tunnel junction as well as wrinkles and folds. These reflected plasmons interact with the tip and are partially scattered out as light into the far-field, which is detected by a cooled HgCdTe detector. Fig. 2a shows this detected optical signal versus tip position, for the region where the tunnel junction is formed (as indicated in Fig. 1a), while a bias voltage of Vb = −1.5 V is applied. On the top and the bottom (left and right) of the darker region of the tunnel junction a brighter region is visible, which is associated to the optical signal from the top (bottom) graphene. In these regions, the signal is more or less featureless. The four corners show a different but also featureless optical signal as there is no graphene in these regions. Within the darker region (corresponding to the tunnel junction area) a characteristic fringe pattern is observed. These fringes are more clearly visible in the higher resolution image shown in Fig. 2b, obtained by zooming the s-SNOM at the top right corner. As the fringe spacing is λp /2 ≈ 162 nm, where λp is the plasmon wavelength, we attribute these fringes to plasmon interference. These interferences occur not only due to reflections from the edges of the tunnel junction, but also due to reflections from wrinkles and folds. The details of the dependence of the plasmon properties (wavelength and damping) on bias voltage are shown in Fig. 3b and are obtained by scanning the s-SNOM along the dashed line indicated in Fig. 2a. By changing the bias voltage, the fringe spacing and thus the plasmon wavelength are changed (Fig. 3b). This is attributed to bias-induced charges in each of the layers. Clearly, propagating plasmon modes are supported for a wide range of Vb , typically above +1 V or below −1 V where interband losses are suppressed by the induced charges in each of the layers. At the highest applied bias voltages carrier densities of almost 15 × 1012 cm−2 are reached. The inverse damping ratio4 extracted from these data is γp−1 ∼ 20 and rather independent of Vb (see supporting information), which is comparable to other measurements of encapsulated high quality graphene samples.4 The tunnelling current is monitored at the same time as the s-SNOM signal, and is shown in Fig. 3a. Due to the alignment of the two graphene sheets with respect to each other but not with respect to the h-BN, a negative differential resistance is observed.14 The alignment,
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however, does not seem to influence the observed outof-phase mode significantly. This can be qualitatively understood since this mode has a vanishing electric field between the two graphene layers for plasmon wavelengths much longer than the spacer thickness (see Eqs. (S3-S11) in the supporting information). For this reason no additional tunneling takes place due to the plasmon field, carriers perform in-plane oscillation only, and these oscillations are therefore insensitive to the tunneling characteristics of the junction. Conversely, the acoustic mode has a significant electric field in the spacer region. This implies that carriers can also be exchanged between the two layers during oscillations, and makes the frequency of these oscillations sensitive to the tunneling coupling between the two layers, and, therefore, to flakes alignment, as explained in Ref. 25. The symmetric behaviour around Vb = 0 V indicates that the graphene top and bottom layers do not have any appreciable intrinsic doping. This symmetry allows us to analytically calculate the carrier density of the top and bottom graphene layers taking into account the quantum capacitance of the system:26 (1)
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Figure 2 | Optical near-field images of the device. a Overview scan of the device showing plasmon fringes reflected from the edges of the tunnel junction region and wrinkles and folds. The uniformity of the fringe spacing indicates a uniform gating efficiency of the device. b Zoom at the top right corner of a shows the plasmon fringes more detailed. The applied bias voltage is Vb = −1.5 V and the laser wavelength is λ0 = 10.6 µm in a and b. The white dashed line indicates where the measurement in Fig. 3b was taken.
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Figure 3 | Carrier density dependence of the plasmon wavelength. a Tunnelling current I as a function of applied bias voltage Vb . The alignment between the two graphene sheets leads to the observed negative differential resistance.14 b Background subtracted optical signal from scan of tip position perpendicular to the graphene edge (dashed-dotted line) shows the bias voltage dependence of the plasmon fringes. c Calculated voltage dependence of the plasmon wavelength for N = 3 layers (blue shaded) and measured plasmon wavelength (red dots). For comparison the expected wavelength for N = 2, 4 layers is shown. The mode with the longer wavelength is the optical and the one with the shorter wavelength the acoustic mode.
where Vb is the bias voltage applied between top and bottom graphene, e the elementary charge, EF the Fermi energy, ED the Dirac point energy, and n the carrier density per layer. In order to correctly calculate the capacitance of the system we include a vacuum gap with a thickness of dgap and a permittivity of vac between the graphene and the h-BN.3 The thickness of this gap is half the interlayer spacing of graphene between the top graphene and the top h-BN layer and half the layer spacing between the bottom graphene and the bottom h-BN layer. In total this leads to dvac = 0.33 nm and vac = 1. The thickness of the h-BN is dBN = N × 0.33 nm, where N is the number of h-BN layers (N = 3 for the shown measurements) and BN = 3.56 is the out-of-plane component of the DC permittivity of h-BN.4 Assuming no thermal smearing and undoped top and bottom graphene at Vb = 0 V the quantum capacitance effect is captured by the addition
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Figure 4 | Dependence of the plasmon wavelength on the h-BN spacing layer. For an increasing spacing layer thickness and a fixed bias voltage the expected plasmon wavelength of the optical mode is reduced. The expected plasmon wavelength and the extracted wavelength for a spacing layer thickness of N = 3 are in good agreement.
(once for each layer) of EF − ED in the r.h.s. of eq. 1 with: p EF − ED = sgn(n)¯hvF π|n| , (2) where vF ' c/300 is the graphene Fermi velocity. This allows us to translate the applied Vb into a carrier density n per layer. Initially, we model the collective mode using the transfer matrix method and the relation between Vb and n as obtained above. We show the imaginary part of the Fresnel reflection coefficient as the blue shaded curve in Fig. 3c, which reflects the two plasmon modes: the optical plasmon mode with higher λp and an acoustic mode with λp below 50 nm. The measured plasmon wavelength, displayed by red dots, is obtained by fitting a decaying oscillatory function to the data. We find a good agreement between the theoretically obtained optical plasmon mode and the measured plasmon wavelength for the measured layer thickness of N = 3. The dashed curves show the expected plasmon wavelength for 2 and 4 layers and no agreement is found. This shows that the plasmon wavelength is extremely sensitive on the thickness of the spacer due to the induced carrier density in the two graphene layers being thickness dependent (see eq. (1)). In order to better understand the behaviour and the important parameters of the plasmon modes we have developed a fully analytical model of the two expected plasmon modes. This model assumes that the plasmon wavelength is much larger than the spacing layer thickness between the two graphene sheets, which is fully satisfied in our system. Furthermore in our case the plasmon outof-plane decay length is short compared to the bottom h-BN thickness. The acoustic plasmon mode is described by (see supporting information): λP− (ω) =
2πvF 1 + 4α− (ω)dkF p ω 1 + 8α− (ω)dkF
(3)
where q is the plasmon momentum, d is the thickness of the h-BN spacing layer, α− (ω) = e2 /[¯hv√F zz (ω)] is the graphene fine structure constant, kF = πn the Fermi momentum and zz the out-of-plane permittivity of hBN. The linear frequency dispersion of this mode can be directly seen from the equation as well as the dependence on the thickness of the spacer layer. We note that this dispersion relation is identical to that of acoustic plasmons in graphene near a perfectly conducting gate positioned at a distance d/2 from the graphene flake.3,27 This acoustic mode is predicted both in the analytical as well as in the transfer matrix model however it is not observed in measurements. This is most likely due to a combination of two effects. First, the plasmon wavelength of this mode is extremely short and thus the probe tip does not couple well to it24 It could be possible to use a tip with a smaller tip radius, such as a carbon nanotube, in order to overcome this.28 Second, the electric field of this mode is mainly concentrated between the two graphene sheets and thus coupling to the tip is weak. The optical plasmon mode can then be described by (see supporting information): λP+ (ω) =
8πvF2 kF α+ (ω) ω2
(4)
where α+ (ω) = 2e2 /[¯hvF ((ω) + 1)] is the modified √ graphene fine structure constant with = xx zz the effective permittivity of the h-BN substrate, with xx being the in-plane permittivity of h-BN. This equation reflects the typical square root dispersion of optical graphene plasmons.29 This dispersion can also be seen as the standard 2d plasmon dispersion but with double the optical conductivity due to having two graphene layers conducting in parallel.9 Eq. (4) shows that the plasmon wavelength of the optical mode is independent of the spacing layer thickness at a fixed carrier density n (and thus fixed kF ). However, the plasmon wavelength is not independent of Vb . That is because Eq. (4) does not include the dependence of the carrier density on Vb . Including this effect via the capacitance model described in eq. 1, we find that for a constant Vb the plasmon wavelength should change significantly for a changing layer thickness, as shown in Fig. 4. This could allow for measuring the spacer thickness with atomic precision using graphene plasmons as a probe. In summary, we have shown the first graphene plasmon quantum tunnelling device, and find propagating plasmon modes in a charge-neutral system. This type of device can also be used to greatly increase the graphene plasmon wavelength as much larger carrier densities can be induced than with the typical electrostatic gating technique. We exploit the fact that one graphene layer can efficiently modify the carrier density of the other layer and we reach carrier densities of almost 15×1012 cm−2 , much higher than previously reported for gate tunable graphene plasmonic devices. The large plasmon wavelength is also due to the doubling of the optical
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conductivity due to the two graphene layers. Furthermore the tunnelling current in such devices could be exploited to electrically excite plasmons in the graphene.30 Finally, this type of nanophotonic heterostructures may reveal several new physical phenomena. For example, in the case in which inter-layer tunnelling is not negligible, the in-phase mode (for a charge-neutral system) is usually gapped in the long-wavelength limit, the q = 0 gap coinciding in the random phase approximation (RPA) with the bare inter-layer tunnelling gap. Beyond RPA, this gap is dressed by many-body effects and the mode acquires an intrinsic lifetime due to the production of double particle-hole pairs, akin to Gilbert damping in ferromagnets.25
Simulations. The theoretical model of plasmon modes was calculated using a classical electromagnetic transfer matrix method, with a thin-film stack of metal-SiO2 (285 nm)h-BN(60 nm)-graphene-air(0.165 nm)-h-BN(0.99 nm)air(0.165 nm)-graphene. The zero-temperature random phase approximation result31,32 was used for the graphene nonlocal conductivity σ(k, ω). The graphene is modelled as a two dimensional conductor with zero thickness. The h-BN permittivity used is xx = 8.34+0.023i and zz = 1.93+0.006i at 10.6 µm.4 In Fig. 3a, the colour quantity plotted is the imaginary part of the reflection coefficient of evanescent waves, evaluated at the top graphene surface.
Device fabrication. METHODS Measurement details. The s-SNOM used was a NeaSNOM from Neaspec GmbH, equipped with a CO2 laser operated at 10.6 µm. The laser power used was approximately 20 mW. The probes were commercially-available metallized atomic force microscopy probes with an apex radius of approximately 25 nm. The tip height was modulated at a frequency of approximately 250 kHz with a 60–80 nm amplitude. The probe tip was electrically grounded. The measurements were performed at room temperature in ambient atmosphere.
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[email protected] Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–25 (2013). Novoselov, K. S. et al. 2D materials and van der Waals heterostructures. Science 353, 6298 (2016). Lundeberg, M. B. et al. Tuning quantum nonlocal effects in graphene plasmonics. Science 357, 187–191 (2017). Woessner, A. et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nature Mater. 14, 421–425 (2015). Dai, S. et al. Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial. Nature Nanotech. 10, 682–686 (2015). Basov, D. N., Fogler, M. M. & Garcia de Abajo, F. J. Polaritons in van der Waals materials. Science 354, 1992 (2016). Low, T. et al. Polaritons in layered two-dimensional materials. Nature Mater. 16, 182–194 (2017). Fei, Z. et al. Tunneling Plasmonics in Bilayer Graphene. Nano Lett. 15, 4973–4978 (2015). Rodrigo, D. et al. Double-layer graphene for enhanced tunable infrared plasmonics. Light Sci. Appl. 6, e16277 (2017). Romero, I., Aizpurua, J., Bryant, G. W., De Abajo, F. J. G. & García De Abajo, F. J. Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers. Opt. Express 14, 9988–9999 (2006). Savage, K. J. et al. Revealing the quantum regime in tun-
The heterostructures are made by means of a standard drytransfer procedure of mechanically exfoliated graphene and hBN layers.14,21 The lattices of the top and bottom graphene flakes are aligned to within 2◦ of each other. For an improved electronic quality, the bottom graphene electrode is placed on a thick layer of h-BN on top of a the SiO2 /Si substrate. The two graphene layers were contacted with Cr/Au. Supporting information. Derivation of the analytical formulas provided; Comparison between analytical model and transfer-matrix model; Plasmon loss
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ACKNOWLEDGEMENTS Open source software was used (www.matplotlib.org, www.python.org, www.inkscape.org). F.H.L.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the "Severo Ochoa" Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, the ERC Career integration grant (294056, GRANOP), the ERC starting grant (307806, CarbonLight), the Government of Catalonia trough the SGR grant (2014-SGR-1535), the Mineco grants Ramón y Cajal (RYC-2012-12281) and Plan Nacional (FIS2013-47161P), and project GRASP (FP7-ICT-2013-613024-GRASP). F.H.L.K. acknowledges support by the E.C. under Graphene Flagship (contract no. CNECT-ICT-604391). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI Grant Numbers JP15K21722 and JP25106006.
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