ARTICLE https://doi.org/10.1038/s41467-020-18544-z OPEN Plasmonic antenna coupling to hyperbolic phonon-polaritons for sensitive and fast mid-infrared photodetection with graphene Sebastián Castilla 1,12, Ioannis Vangelidis2,12, Varun-Varma Pusapati 1, Jordan Goldstein 3, Marta Autore4, Tetiana Slipchenko5, Khannan Rajendran1, Seyoon Kim1, Kenji Watanabe 6, Takashi Taniguchi 6, Luis Martín-Moreno 5, Dirk Englund 3, Klaas-Jan Tielrooij 7, Rainer Hillenbrand 8,9, Elefterios Lidorikis 2,10 ✉ & Frank H. L. Koppens 1,11 ✉ 1234567890():,; Integrating and manipulating the nano-optoelectronic properties of Van der Waals hetero- structures can enable unprecedented platforms for photodetection and sensing. The main challenge of infrared photodetectors is to funnel the light into a small nanoscale active area and efficiently convert it into an electrical signal. Here, we overcome all of those challenges in one device, by efficient coupling of a plasmonic antenna to hyperbolic phonon-polaritons in hexagonal-BN to highly concentrate mid-infrared light into a graphene pn-junction. We bal- ance the interplay of the absorption, electrical and thermal conductivity of graphene via the device geometry. This approach yields remarkable device performance featuring room pffiffiffiffiffiffi temperature high sensitivity (NEP of 82 pW= Hz) and fast rise time of 17 nanoseconds (setup-limited), among others, hence achieving a combination currently not present in the state-of-the-art graphene and commercial mid-infrared detectors. We also develop a mul- tiphysics model that shows very good quantitative agreement with our experimental results and reveals the different contributions to our photoresponse, thus paving the way for further improvement of these types of photodetectors even beyond mid-infrared range. 1 ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain. 2 Department of Materials Science and Engineering, University of Ioannina, Ioannina 45110, Greece. 3 Department of Electrical Engineering and Computer Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 4 CIC nanoGUNE BRTA, Donostia-San Sebastián 20018, Spain. 5 Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, Zaragoza 50009, Spain. 6 Advanced Materials Laboratory, National Institute for Material Science, Tsukuba 305-0044, Japan. 7 Catalan Institute of Nanoscience and Nanotechnology (ICN2), Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, Barcelona 08193, Spain. 8 IKERBASQUE, Basque Foundation for Science, Bilbao 48013, Spain. 9 CIC nanoGUNE BRTA and Department of Electricity and Electronics, UPV/EHU, Donostia-San Sebastián 20018, Spain. 10 University Research Center of Ioannina (URCI), Institute of Materials Science and Computing, Ioannina 45110, Greece. 11 ICREA - Institució Catalana de Recerca i Estudis Avançats, Barcelona 08010, Spain. 12These authors contributed equally: Sebastián Castilla, Ioannis Vangelidis. ✉email: elidorik@uoi.gr; frank.koppens@icfo.eu NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18544-z H yperbolic phonon-polaritons (HPPs) are hybridized Results modes of ionic oscillations and light present in polar Device operation principle. Our design (depicted in Fig. 1a–c) dielectric materials, such as hexagonal-BN (hBN)1–7 that combines several mechanisms to achieve high field concentration show interesting optical properties such as extreme sub- for both incident light polarizations. Specifically, when light is wavelength ray-like propagation and sub-diffraction light polarized parallel to the bow-tie antenna axis (transverse mag- confinement (~λ0/100)1,8–11, among others. In fact, novel nano- netic, TM-polarization, Fig. 1d), it excites its localized surface optoelectronic platforms can be attained by merging HPPs plasmon resonance (LSPR) spectrally located at λ ≈ 5–7 μm functionalities with other 2D materials-based devices, such as (Supplementary Figs. 1 and 2a). As a result, the antenna con- graphene photodetectors governed by the photothermoelectric centrates the incoming mid-IR light into its gap that is situated (PTE) effect. This mechanism generates a photoresponse in just above the graphene pn-junction (i.e. the detector photoactive graphene pn-junctions12–19 driven by a temperature gradient and area)16. At the same time, the near-fields produced within the Fermi level asymmetry across the channel. Nevertheless, one of antenna hot-spot contain high momenta and thus efficiently the limitations of these detectors is the low light absorption of launch HPPs ascribed to the spectral overlap of the antenna’s graphene, especially for mid-IR frequencies where the photon LSPR with the hBN upper reststrahlen band (RB) range energy becomes comparable to the typical doping level of gra- (λ ≈ 6–7 μm. These HPPs propagate as guided modes and inter- phene reaching the Pauli blocking regime20,21. This is further fere within the graphene pn-junction, producing high absorption exacerbated by the small photoactive area of graphene pn- across this small localized region. Likewise, when light is polarized junctions16,22, limited by the cooling length of the hot carriers perpendicularly to the bow-tie antenna axis (transverse electric, (0.5–1 μm)13,14,22,23. These limitations can be overcome by TE-polarization, Fig. 1e), it produces strong light concentration in exciting HPPs and focusing them towards the photoactive area the gap of the H-shaped antenna, acting as the split-gate, ascribed and consequently absorbing them in graphene. However, efficient again to its LSPR spectrally located at λ ≈ 5.5–7.5 μm (Supple- exploitation of HPPs for mid-IR photodetection still remains mentary Figs. 2b and 3). This phenomenon will also launch hBN unexplored24,25. In this work, we embed hBN and graphene HPPs at the gate edges, which will be guided and interfered within within metallic antennas in order to couple their plasmonic the photoactive area. interactions with HPPs and achieve highly concentrated mid-IR The absorption process in the graphene is mediated mostly by light on a graphene pn-junction for sensitive and fast mid-IR interband transitions, which mainly occur in the regions within photodetection. the gap of the gates where the graphene doping is sufficiently a b Antenna c Source Drain x Right gate 17 nm Alumina Source y top hBN 11 nm Rigjht gate Left gate Source Drain Bottom hBN 15 nm Left gate Right gate 30 nm Drain Antenna z Left gate SiO2 (substrate) VL 0.5 μm IPTE VR x y d 300 TM-polarization Antenna branch Antenna branch E/E0 2 77 z 20 Right gate y e 1000 TE-polarization Antenna E/E0 2 63 z Left gate Right gate 4 x Fig. 1 Device schematic and operation principle. a Schematic representation of the photodetector consisting of H-shaped resonant gates of 4.2 μm of total length, with a hBN-encapsulated H-shaped graphene channel transferred on top, contacted by source and drain electrodes. A bow-tie antenna of 2.7 μm of total length is placed on top of the 2D stack. The local gates serve to create a pn-junction in the central part of the graphene channel (by applying voltages VL and VR), where the antenna gap and gate gap are located. Both narrow gaps are on the order of ~100 nm. The scale bar corresponds to 0.5 μm. b Side view of the device design (not to scale) with indications of the materials' thicknesses. c Optical image of the photodetector. The dashed lined circle indicates the typical beam spot size obtained at λ = 6.6 μm. The scale bar corresponds to 2.5 μm. d Cross section view of the simulated total electric field intensity (∣E∣2) normalized to the incident one (∣E0∣2) along the antenna main axis when light is polarized parallel to the bow-tie antenna (TM-polarization) axis as indicated in the illustration on the left. The white scale bar corresponds to 250 nm. e Same as (d) but for light polarization perpendicular to the bow- tie antenna (TE-polarization) and parallel to the local gates as shown in the schematic on the left. 2 NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18544-z ARTICLE small to avoid Pauli blocking (Supplementary Figs. 4 and 5). The photocurrent mechanism and optimal doping level. We find that excited carriers quickly relax (<100 fs)23 into a local hot when sweeping the gate voltages independently, the photocurrent equilibrium Fermi–Dirac distribution by electron–electron scat- follows several sign changes resulting in a 6-fold pattern, which tering. Subsequent cooling mechanisms include electron–phonon indicates that the photodetection is driven by the PTE effect, as scattering (~1 ps)13,14,22,23,26 and heat diffusion away from the also shown in other studies in the mid-IR range24,27,28. The junction area. As a result, a symmetric electronic temperature highest values of photocurrent occur at pn or np configuration, profile Te(x) is produced in the graphene junction13,14,24, giving specifically at VL = 1.6 V (170 meV) and VR = −0.82 V rise to a thermoelectric voltage VPTE ∝ S(x) ∇Te(x), where x runs (−130 meV), which are relatively low doping levels. We note that along the graphene channel and S(x) represents the Seebeck when applying a voltage bias in the graphene channel, the pho- coefficient which is tunable by the gates. Since ∇Te(x) is tocurrent remains constant while the source-drain current antisymmetric, an antisymmetric S(x) is also needed to maximize increases linearly with bias (Supplementary Fig. 6). This allows us the net PTE response, which is achieved by applying opposite to discard other mechanisms such as photogating and bolometric voltages to the two gates (Supplementary Figs. 4 and 5). In effects that would increase significantly with voltage bias. addition to HPPs promoting absorption in graphene, they also To determine the photodetector spectral response, we measure absorb light themselves. However, due to the large (~103) heat the TM-polarization (Fig. 2c) external responsivity (see Methods) capacitance mismatch between graphene electrons and lattice, the as a function of excitation wavelength. We obtain high values up HPP absorption does not amount to any meaningful temperature to 15 mA/W within 6–7 μm at the hBN RB. On the other hand, rise and thus does not contribute to the device PTE response. for TE-polarization (Fig. 2d), we observe two responsivity peaks, the first one (up to 22 mA/W) again within the hBN RB (6–7 μm) and a second peak (3.5 mA/W) around 8 μm. We also plot the Photocurrent characterization and spectral response. To reveal simulated responsivity that is extracted from the multiphysics the spatial intensity profile of the beam focus at λ = 6.6 μm, we simulations, which considers the exact geometry of the photo- scan the sample with xyz-motorized stages and measure the detector and the whole device photoresponse (optical excitation, photocurrent (IPTE) as shown in Fig. 2a. As a result, we observe carrier distribution and relaxation, heat diffusion and thermo- the Airy pattern of the beam, which implies that we obtain a well- electric current collection. See further details in Supplementary focused beam (see Methods) and high sensitivity at this wave- Notes 1–4). We observe very good qualitative and quantitative length considering the small irradiance input of 0.2 μW/μm2. agreement between experimental and theoretical responsivity, Next, we investigate the photoresponse as a function of the two which we explore in the following by analyzing each component gate voltages (VL and VR), shown in Fig. 2b, which reveals the involved in the photoresponse. a b 1.5 15 10 6 1 5 2 0.5 IPTE (nA) IPTE (nA) VR (V) 0.8 0 0 0.3 –0.5 –5 0.1 –1 –10 0.04 0.01 –1.5 –1.5 –1 –0.5 0 0.5 1 1.5 VL (V) c d 15 TM experiment 25 TE experiment Responsivity (mA/W) Responsivity (mA/W) TM simulations TE simulations 20 10 15 10 5 5 0 0 6 7 8 9 10 6 7 8 9 10 Wavelength (μm) Wavelength (μm) Fig. 2 Photocurrent generation and spectral photoresponse. a Scanning photocurrent map (log scale) across the mid-IR beam focus at λ = 6.6 μm. The white scale bar corresponds to 20 μm. We obtain a FWHM of 6.1 μm. We use a small input power (Pin) of 13.7 μW (irradiance of 0.2 μW/μm2). b Photocurrent map as a function of the two gate voltages at λ = 6.6 μm. c Experimental (dots) and theoretical (dashed lines) spectral external responsivity of the device for TM-polarization and (d) for TE-polarization. The highlighted region corresponds to the hBN RB (λ = 6.2–7.3 μm). For (c and d), we set the gate voltages to a pn-junction configuration close to the optimal with VL = 0.5 V (97 meV) and VR = −0.5 V ( −100 meV). We use the same doping level for the theoretical simulations. NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications 3 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18544-z a b 10 TM TE λTO, SiO G G 2 140 200 Wavelength (μm) 9 12 14 SiO2 PPs 8 1 1 λTO, hBN λTO, hBN 7 hBN HPPs hBN HPPs 6 c d 10 TM TE λTO, SiO G G 2 100 80 Wavelength (μm) 9 10 9 SiO2 PPs 8 1 1 7 LSPR LSPR 6 –0.4 –0.2 0.0 0.2 0.4 –0.4 –0.2 0.0 0.2 0.4 x (μm) x (μm) Fig. 3 Absorption enhancement spectra. Simulations of the absorption enhancement in graphene (G) along the source-drain direction (x direction as shown in Fig. 1a, b, where x = 0 is located at the center of the gate gap) as a function of the wavelength, for TM (a) and TE-polarization (b). (c) and (d) correspond to (a) and (b), respectively, but with wavelength-independent refractive index for hBN (n = 2.4). Spectral and spatial analysis of the photoresponse. We first For TE-polarization (Fig. 3b), we find the maximum values of identify the behavior of the resonant mechanisms, in terms of G between 6.2 and 6.6 μm due to the gate LSPR hybridization field intensity enhancement and spatial localization by studying with HPPs and their strong constructive interference at x = 0. the absorption enhancement in graphene (G) across the channel For longer wavelengths, we identify a G peak centered at 8.5 μm in the x direction (averaging over 500 nm in the y direction, see that corresponds to SiO2 phonon-polaritons (PPs) hybridization Fig. 1a, b for axis definition) and as a function of the wavelength with the gate LSPR as presented in Supplementary Figs. 2 and 9. as shown in Fig. 3. We define G as follows: G(λ, r) = To further elucidate the role of the antennas in G, we simulate Absdevice(λ, r)/Absair(λ, r), which is the ratio between the gra- the system without the contribution of the HPPs using phene absorption incorporating all the elements of the device (e.g. wavelength-independent refractive index values for the hBN antenna, contacts, etc.) to that of suspended graphene as a (Fig. 3c, d). For TM-polarization (Fig. 3c), we observe a peak function of λ and the position vector r. G and responsivity are around 6 μm that corresponds to the antenna LSPR and its proportionally related via the electronic temperature gradient as resonance tail extending up to 8 μm. For TE-polarization, in shown in Supplementary Fig. 5 and Supplementary Note 2. contrast, Fig. 3d shows high values of G across a broader In the TM-polarization case shown in Fig. 3a, we observe very wavelength range (5.5–7.5 μm) due to the complex shape of the high G values at the antenna LSPR (λ ~ 6 μm). The value of G gates and their interactions with the source–drain contacts peaks around 6.8 μm due to the hybridization of the hBN HPPs (Supplementary Fig. 3). Although in Fig. 3d we observe lower G with the antenna LSPR and to the constructive interference of values compared to Fig. 3c (Supplementary Fig. 2), we obtain the propagating HPPs occurring at x ~ ±100 nm. In fact, higher values of G in TE-polarization when combining the gate the different spatial patterns of G arise from the wavelength LSPR with HPPs (Fig. 3b) ascribed to its higher spectral overlap dependence of the HPP propagation angle in hBN following the qffiffiffiffiffiffiffiffiffiffiffiffiffi with the hBN RB and due to the stronger constructive pffiffiffiffiffiffiffiffiffiffiffi interferences of the HPPs excited by the gates. equation tan θðωÞ ¼ i εx;y ðωÞ= εz ðωÞ (refs. 1,24,29). For longer To evaluate the coupling between the bow-tie antenna LSPR wavelengths, we find a negligible G between 7 and 7.3 μm that and the hBN HPPs, we study the responsivity as a function of the corresponds to the hBN transverse optical (TO) phonon. We antenna length for TM-polarization as shown in Fig. 4a observe that the highest G values are only found for the spatially (Supplementary Fig. 10). We observe some hBN HPP excitation confined region (from x ~ −100 to 100 nm) where the antenna when using an antenna non-resonant (green line) within the hBN and gates overlap, which is designed to coincide with the RB range, in which case we obtain a maximum responsitivity of 4 graphene pn-junction (see Supplementary Figs. 7, 8 and 17–23 mA/W. In the case of the semi-resonant antenna (experimental regarding the Supplementary Discussion 1). Nevertheless, in the antenna, shown in blue line), whose LSPR partially overlaps with hBN RB we find large G values outside this tightly localized the RB spectral range25, the responsivity increases to 17 mA/W, region due to HPP propagation. respectively. However, this can be significantly improved if we use 4 NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18544-z ARTICLE a b 240 c 180 TM-polarization TE-polarization TE-polarization 35 60 λ = 6.5 μm 30 λ = 6.5 μm Responsivity (mA/W) Responsivity (mA/W) Responsivity (mA/W) 50 150 30 Antenna length L = 4.8 μm NEP (pW/Hz0.5) NEP (pW/Hz0.5) 180 25 40 25 120 30 20 20 20 120 15 90 L = 2.7 μm 15 10 L = 1.8 μm 60 10 60 10 6 7 8 9 10 0 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 2.0 2.4 Wavelength (μm) Gate tip width (μm) Gate tip length (μm) Fig. 4 Dependence of the simulated responsivity and NEP on the geometry of the antenna and H-shaped gates. a Simulations of responsivity for TM- polarization for different antenna lengths. Different cases are presented: non-resonant antenna within the hBN RB spectral range (antenna total length of L = 1.8 μm, shown in green), semi-resonant antenna (L = 2.7 μm shown in blue, which corresponds to the experimental antenna) and resonant antenna (L = 4.8 μm, shown in red). b Simulations of responsivity and NEP as a function of gate tip width and graphene (following the exact shape of the gates) as shown in the schematic for TE-polarization at λ = 6.5 μm. The tip length is 855 nm, which includes the gap between the gates of 155 nm. The source-drain distance is 2.6 μm and electrodes width is 2 μm as in the measured device. c Same as b but as a function of the gate tip length as shown in schematic. The tip width is 500 nm. pffiffiffiffiffiffi a longer antenna (red line) such that its LSPR peak fully overlaps equivalent-power of 82 pW/ Hz (refs. 24,30–33), assuming the with the hBN HPPs peak, thus obtaining 65 mA/W. graphene thermal noise as the dominating noise source16,34,35. Next, we examine the impact of the H-shaped gates excited at We emphasize that the zero-bias operation leads to low noise λ = 6.5 μm with TE-polarization on the responsivity and NEP levels and a very low power consumption, which is given by the (noise-equivalent power, see Methods) by varying the width and voltage applied to the gates. Furthermore, our design allows length of the gate tip and graphene, while keeping the source- sensitive detection in different polarizations (Supplementary drain distance and width fixed as indicated in Fig. 4b, c. Fig. 4b Fig. 14), which is a limitation for the mentioned graphene shows that the responsivity (NEP) increases (decreases) when detectors24,30–32. Additionally, our device exhibits a wide decreasing the tip width down to an optimal value of 500 nm dynamic range by showing linear photoresponse over three (same as the experimental value). This is ascribed to the balancing orders of magnitude as shown in Fig. 5b, which is an issue for act of absorption, electrical resistance and thermal conductance: other types of graphene detectors31 and commercial detectors larger absorption and lower thermal conductance increase the such as MCT36. It also has a very small active area given by the temperature gradients, but a smaller electrical conductance also antennas’ cross-sections, which implies high spatial resolution reduces the photocurrent and thus the responsivity (Supplemen- and opens the possibility of arranging it into high density tary Fig. 11 and Supplementary Discussion 1). Note that electrical photodetector pixels30,37 that are CMOS compatible38. All of and thermal conductivity are ultimately proportional through the these performance parameters combined make our device an Wiedemann-Franz law. For the case of the gate tip length, interesting platform that fulfills the ongoing trend of decreasing however, the optimum is found around 1.45 μm, which is larger the size, weight and power consumption (SWaP) of infrared than the experimental one (855 nm), pointing to future design imaging systems36. and performance improvements (Supplementary Figs. 3 and 11). These results highlight the importance of the gate and graphene Discussion channel shapes on PTE performance and the vital role of The device concept introduced in this work can be extended to multiphysics modeling in understanding and optimizing such a detectors for other wavelengths or more specific functionalities complex device. such as hyperspectral imaging and spectroscopy. Our approach can also be combined with HPPs in other regions of the mid-IR Speed, sensitivity, and device benchmark. Now we discuss the and long-wave infrared range such as MoO3 (refs. 39–41). Addi- technological relevance of our photodetector. First, we measure the tional tuning and wavelength sensitivity can be realized by con- photodetection speed by using as reference a commercial fast trolling the hyperbolic material’s thickness24,42 or shape1,43–45. mercury–cadmium–telluride (MCT) detector. We plot in Fig. 5a the quantum cascade laser (QCL) voltage (brown line) together with Methods the photoresponses of the MCT (blue line) and our device (black Device fabrication. First, we fabricate the H-shaped local gates structure with a circles). The signal of the MCT detector reveals the pulse shape of total length of 4.2 μm, a total width of 2 μm and a narrow width region (tip) of 500 the laser. We fit an exponential function to the initial peak to nm on a Si/SiO2 substrate using electron beam lithography (EBL) followed by evaporation of titanium (2 nm)/gold (30 nm). The gap between the gates is 155 nm. determine the rise time (shown in red lines), obtaining a value of Afterwards, we transfer a hBN/graphene/hBN stack onto the metallic gates. We 9.5 ns, which is close to its datasheet value of 4.4 ns. In the case of cleave and exfoliate the top and bottom hBN and the graphene onto freshly cleaned our photodetector, we find a rise time of 17 ns (22 MHz) when Si/SiO2 substrates, stack them following the Van der Waals assembly technique46,47 using a current amplifier with 14 MHz bandwidth. This suggests and release onto the gates. We then use EBL with a PMMA 950 K resist film to pattern source and drain electrodes and expose the device to a plasma of CHF3/O2 that our time-resolved measurements are limited by the current gases to partially etch the Van der Waals stack. Subsequently, we deposit side amplifier bandwidth (Supplementary Fig. 12), meaning that the contacts of chromium (5 nm)/gold (80 nm) and lift off in acetone as described in actual rise time may be shorter. In fact, our theoretical calculations ref. 46. We then etch the hBN-encapsulated graphene into an H-shape using a predict a speed of 53 ps (Supplementary Note 5). CHF3/O2 plasma and deposit 17 nm of Al2O3 using atomic layer deposition (ALD). Finally we pattern the bow-tie antenna of 2.7 μm total length (L) and with a small The sensitivity of the detector is best expressed in terms of gap of 200 nm between its branches with EBL and deposit titanium (2 nm)/gold external responsivity, which the maximum measured value is (80 nm). We point out that the bow-tie antenna and gate dimensions were selected 27 mA/W (92 V/W, Supplementary Fig. 13), yielding a noise- based on preliminary optical simulations based on a simplified device, ignoring NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications 5 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18544-z a reflective objective with a numerical aperture (NA) of 0.5. We measure the mid-IR Device 1.0 power using a thermopile detector from Thorlabs placed at the sample position. MCT For the time-resolved measurements, we set the QCL wavelength to λ = 6.6 μm QCL with a pulse width of 496 ns. We use a MCT as a reference detector from VIGO Fits System model PCI-2TE-13. We measure the photoresponse using a current Norm. photovoltage (a.u.) Norm. voltageQCL (a.u.) 1.0 amplifier from FEMTO model DHPCA-100 with switchable gain and acquire the signal with an oscilloscope from Teledyne Lecroy model HDO6000. 0.5 Responsivity and NEP calculation. The external responsivity is given by: 0.5 Responsivity = (IPTE/Pin) × (Afocus/Adiff)16,34,48,49, where Pin is the power measured by the commercial power meter, Afocus is the experimental beam area at the mea- sured wavelength and Adiff is the diffraction-limited spot size. We measure the photocurrent pffiffi IPTE from the output signal of the lock-in amplifier VLIA considering 0.0 I PTE ¼ 2π4ξ 2 V LIA (refs. 34,48,49), where ξ is the gain factor in V/A (given by the lock- 0.0 in amplifier). We use the ratio Adiff/Afocus for estimating the power reaching our photodetector since Adiff is the most reasonable value one can attain when con- sidering the detector together with an optimized focusing system (e.g. using hemispherical lens) and it is widely used in the literature for comparing the per- formances among photodetectors16,34,48,49. Note that this simple geometrical scaling 0 200 400 600 800 is not used here to predict the exact performance at a hypothetical diffraction- Time (ns) limited spot but rather as clear performance benchmark so to consistently compare different device architectures measured at differed focusing conditions. We usually w20;diff b have a ratio of Afocus/Adiff ≈ 7. This ratio is given by Adiff =Afocus ¼ w . In order to 0;x w0;y 100 obtain w0,x and w0,y we use our experimental observation that the photocurrent is 8 μm 6.54 μm linear in laser power and measure the photocurrent while scanning the device in the 6.6 μm x- and y-direction. Consequently, the photocurrent is described by Gaussian dis- tributions / e2x =w0;x and / e2y =w0;y , where w0,x and w0,y are the respectively 2 2 2 2 obtained spot sizes (related to the standard deviation via σ = w0/2 and to the Photocurrent (nA) pffiffiffiffiffiffiffiffiffiffiffiffiffi FWHM = 2ln ð2Þw0 ). We usually achieve w0,x = 5.05 μm and w0,y = 5.40 μm at λ = 6.6 μm (Supplementary Fig. 13b). For the diffraction-limited spot, we consider w0;diff ¼ πλ, with λ the mid-IR laser wavelength. The diffraction-limited area is hence 10 taken as Adiff ¼ πw20;diff ¼ λ2 =π. Additionally, the noise-equivalent power (NEP) that characterizes the sensitivity of the photodetector is defined as NEP = Inoise/ Responsivity and considering that our unbiased photodetector has a very low noise current qthat isffi limited by Johnson noise, we use a noise spectral density ffiffiffiffiffiffiffi 4kB T I noise ¼ RD , where kB corresponds to the Boltzmann constant, T is the operation temperature (300 K) and RD the device resistance. 1 Data availability 0.1 1 10 The data that support the plots within this paper and other findings of this study are Pdiff (μW) available from the corresponding author upon reasonable request. Fig. 5 Photodetection speed and power dependence. a Time-resolved Received: 4 April 2020; Accepted: 24 August 2020; photodetection traces at λ = 6.6 μm, compared with a MCT detector (both plotted in black dots and blue line respectively) and the respective QCL voltage signal (brown line). The QCL pulse width corresponds to 496 ns. 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Compact mid-infrared graphene thermopile enabled by a financial support from the Spanish Ministry of Economy and Competitiveness, through nanopatterning technique of electrolyte gates. N. J. Phys. 20, 083050 (2018). the “Severo Ochoa” Programme for Centres of Excellence in R& D (SEV-2015-0522), 18. Schuler, S. et al. Graphene photodetector integrated on a photonic crystal support by Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA defect waveguide. ACS Photonics 5, 4758–4763 (2018). program, and the Agency for Management of University and Research Grants (AGAUR) 19. Muench, J. E. et al. Waveguide-integrated, plasmonic enhanced graphene 2017 SGR 1656. Furthermore, the research leading to these results has received funding photodetectors. Nano Lett. 19, 7632–7644 (2019). from the European Union Seventh Framework Programme under grant agreement no. 20. Li, Z. Q. et al. Dirac charge dynamics in graphene by infrared spectroscopy. 785219 and no. 881603 Graphene Flagship for Core2 and Core3. ICN2 is supported by Nat. Phys. 4, 532–535 (2008). the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). K.J.T. 21. Low, T. & Avouris, P. Graphene plasmonics for terahertz to mid-infrared acknowledges funding from the European Union’s Horizon 2020 research and innova- applications. ACS Nano 8, 1086–1101 (2014). tion programme under Grant Agreement No. 804349. R.H. acknowledges financial 22. Tielrooij, K.-J. et al. Out-of-plane heat transfer in van der Waals stacks through support from the Spanish Ministry of Science, Innovation and Universities (national electron-hyperbolic phonon coupling. Nat. Nanotechnol. 13, 41–46 (2018). project RTI2018-094830-B-100 and the project MDM-2016-0618 of the Marie de Maeztu 23. Tielrooij, K. J. et al. Generation of photovoltage in graphene on a femtosecond Units of Excellence Program) and the Basque Government (grant No. IT1164-19). S.C. timescale through efficient carrier heating. Nat. Nanotechnol. 10, 437–443 (2015). acknowledges financial support from the Barcelona Institute of Science and Technology 24. Woessner, A. et al. Electrical detection of hyperbolic phonon-polaritons in (BIST), the Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixe- heterostructures of graphene and boron nitride. npj 2D Mater. Appl. 1, 25 ment de la Generalitat de Catalunya and the European Social Fund (L’FSE inverteix en el (2017). teu futur)—FEDER. D.E. acknowledges partial support from the Army Research Office 25. Pons-Valencia, P. et al. Launching of hyperbolic phonon-polaritons in h-BN MURI “Ab-Initio Solid-State Quantum Materials” Grant No. W911NF18-1-0431. J.G. slabs by resonant metal plasmonic antennas. Nat. Commun. 10, 3242 (2019). was supported by the ARL-MIT Institute for Soldier Nanotechnologies (ISN). T.S. and 26. Bistritzer, R. & MacDonald, A. H. Electronic cooling in graphene. Phys. Rev. L.M.M. acknowledge support by Spain’s MINECO under Grant No. MAT2017-88358- Lett. 102, 13–16 (2009). C3-1-R and the Aragon Government through project Q-MAD. 27. Herring, P. K. et al. Photoresponse of an electrically tunable ambipolar graphene infrared thermocouple. Nano Lett. 14, 901–907 (2014). Author contributions 28. Hsu, A. L. et al. Graphene-based thermopile for thermal imaging applications. F.H.L.K., R.H., M.A., and S.C. conceived the project. S.C. fabricated the device and Nano Lett. 15, 7211–7216 (2015). performed the experiments. V.P. assisted in device fabrication and experiments. M.A. 29. Dai, S. et al. Subdiffractional focusing and guiding of polaritonic rays in a supported the device fabrication. I.V. and E.L. performed the simulations and developed natural hyperbolic material. Nat. Commun. 6, 1–7 (2015). the multiphysics model. S.C., T.S., and L.M.-M. assisted in the modeling. S.C., K.R., J.G. 30. Guo, Q. et al. Efficient electrical detection of mid-infrared graphene plasmons and M.A. performed preliminary optical simulations. S.C., I.V., E.L., and F.H.L.K. wrote at room temperature. Nat. Mater. 17, 986–992 (2018). the manuscript. J.G., S.K., and K.-J.T. assisted with measurements and discussion of the 31. Cakmakyapan, S., Lu, P. K., Navabi, A. & Jarrahi, M. Gold-patched graphene results. K.W. and T.T. synthesized the hBN crystals. D.E., R.H., K.-J.T., E.L., and F.H.L.K. nano-stripes for high-responsivity and ultrafast photodetection from the supervised the work and discussed the results. All authors contributed to the scientific visible to infrared regime. Light Sci. Appl. 7, 20 (2018). discussion and manuscript revisions. S.C. and I.V. contributed equally to the work. 32. Sassi, U. et al. Graphene-based mid-infrared room-temperature pyroelectric bolometers with ultrahigh temperature coefficient of resistance. Nat. Commun. 8, 14311 (2017). Competing interests 33. Yu, X. et al. Narrow bandgap oxide nanoparticles coupled with graphene for The authors declare no competing interests. high performance mid-infrared photodetection. Nat. Commun. 9, 1–8 (2018). 34. Vicarelli, L. et al. Graphene field-effect transistors as room-temperature terahertz detectors. Nat. Mater. 11, 865–871 (2012). Additional information Supplementary information is available for this paper at https://doi.org/10.1038/s41467- 35. Generalov, A. A., Andersson, M. A., Yang, X., Vorobiev, A. & Stake, J. A 400- 020-18544-z. GHz Graphene FET Detector. IEEE Trans. Terahertz Sci. Technol. 7, 614–616 (2017). Correspondence and requests for materials should be addressed to E.L. or F.H.L.K. 36. Rogalski, A. Graphene-based materials in the infrared and terahertz detector families: a tutorial. Adv. Opt. Photonics 11, 314 (2019). Peer review information Nature Communications thanks Nezih Yardimci and the other, 37. Rogalski, A., Martyniuk, P. & Kopytko, M. Challenges of small-pixel infrared anonymous reviewers for their contribution to the peer review of this work. detectors: a review. Rep. Prog. Phys. 79, 046501 (2016). 38. Goossens, S. et al. Broadband image sensor array based on graphene-CMOS Reprints and permission information is available at http://www.nature.com/reprints integration. Nat. Photonics 11, 366–371 (2017). 39. Ma, W. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in van der Waals crystal. Nature 562, 557–562 (2018). published maps and institutional affiliations. 40. Zheng, Z. et al. Highly confined and tunable hyperbolic phonon polaritons in van der waals semiconducting transition metal oxides. Adv. Mater. 30, 1–9 (2018). 41. Zheng, Z. et al. 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J. et al. Deeply subwavelength phonon-polaritonic crystal article’s Creative Commons license and your intended use is not permitted by statutory made of a van der Waals material. Nat. Commun. 10, 42 (2019). regulation or exceeds the permitted use, you will need to obtain permission directly from 45. Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field the copyright holder. To view a copy of this license, visit http://creativecommons.org/ optical imaging and focusing. Nat. Commun. 6, 1–9 (2015). licenses/by/4.0/. 46. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–7 (2013). 47. Pizzocchero, F. et al. The hot pick-up technique for batch assembly of van der © The Author(s) 2020 Waals heterostructures. Nat. Commun. 7, 11894 (2016). NATURE COMMUNICATIONS | (2020)11:4872 | https://doi.org/10.1038/s41467-020-18544-z | www.nature.com/naturecommunications 7