Electrical spectroscopy of polaritonic nanoresonators

Abstract

One of the most captivating properties of polaritons is their capacity to confine light at the nanoscale. This confinement is even more extreme in two-dimensional (2D) materials. 2D polaritons have been investigated by optical measurements using an external photodetector. However, their effective spectrally resolved electrical detection via far-field excitation remains unexplored. This hinders their exploitation in crucial applications such as sensing, hyperspectral imaging, and optical spectrometry, banking on their potential for integration with silicon technologies. Herein, we present the electrical spectroscopy of polaritonic nanoresonators based on a high-quality 2D-material heterostructure, which serves at the same time as the photodetector and the polaritonic platform. Subsequently, we electrically detect these mid-infrared resonators by near-field coupling to a graphene pn-junction. The nanoresonators simultaneously exhibit extreme lateral confinement and high-quality factors. This work opens a venue for investigating this tunable and complex hybrid system and its use in compact sensing and imaging platforms.

Fig. 1. Configurations of devices, transmission and photocurrent measurements, and optical simulation.

a Schematic representation of the measured devices (not to scale) consisting of two main configurations depending on the experiment. The 1^st configuration (left panel) corresponds to that used exclusively for transmission measurements in Fourier Transform Infrared spectroscopy (FTIR), with the top metallic nanorods and the 2D stack below. A mercury-cadmium-telluride (MCT) detector is required to perform mid-infrared (mid-IR) spectroscopy. Devices 1 and 4 have this configuration. The 2^nd configuration (right panel) consists of two grating bottom gates with a top 2D stack. Devices 2, 3, and 5 comprise this 2^nd configuration. Devices 2 and 3 are measured using electrical spectroscopy, whereas device 5 is measured using FTIR. b The signal-to-noise ratio (SNR) of the five devices was measured using the corresponding technique, either by FTIR or photocurrent measurements (electrical spectroscopy). The noise level dashed line corresponds to an SNR of 1. The inset shows a Scanning electron microscopy (SEM) image of the metallic nanorod array with a central gap for configuration 2, corresponding to devices 2, 3, and 5. c Extinction (1-T/T_CNP) spectrum of device 1 measured using FTIR, where T and T_CNP are the transmittances of the device at a certain gate voltage and at charge neutrality point (CNP), respectively. The curves correspond to several Fermi levels, as indicated in the legend. The inset shows the optical image of the device 1. The white scale bar corresponds to 30 μm. The three columns above the 2D stack are arrays of 100 nm wide metal nanorods with a 50 nm gap between them. A and B arrows indicate the polaritonic resonances described in the main text. d Finite-difference time-domain (FDTD) simulated extinction spectra of device 1 for several Fermi levels. e Optical image and device circuitry of configuration 2, which corresponds to device 3 used for photocurrent measurements. f Scanning photocurrent map (in absolute value) of device 3 at the incident wavelength (λ) of 6.6 μm. The gates are set to GG1 at 0.4 V and GG2 at − 0.25 V, thus creating a pn-junction.

Fig. 2. Electrical spectroscopy measurements and simulations.

a Normalized photocurrent spectrum of device 2 at several Fermi energies. The photocurrent spectra are normalized to the spectrum at the charge neutrality point (CNP). The polaritonic peaks are labeled by red arrows. The highlighted spectral regions in green correspond to the upper and lower reststrahlen bands (RB) of hBN and, in yellow to the SiO₂ RB. The curves are offset for clarity. b Optical (FDTD) simulation of the graphene absorption spectrum for different Fermi energies normalized to the spectrum at CNP. We label the identified peaks in the same manner as the experimental ones in panel (a). c–f Cross-sectional view of the simulated electric field intensity normalized to the incident one across a region containing two metal nanorods, for wavelengths 10.2, 11.9, 12.2, and 13.3 μm corresponding to peaks 4, 5, 6, and 8, respectively in panel (a). The x − (horizontal) and z − (vertical) directions are defined in Fig. 1e. The white scale bar corresponds to 40 nm. The calculations consider a non-uniform graphene Fermi level with a value of 0.4 eV above the metal (for a detailed doping profile, see Supplementary Fig. 2). g–j Same as panels (c–f), but the simulations instead show the cross-sectional view of the x-component of the electric field normalized to the incident one. The black scale bar corresponds to 40 nm. k Dispersion relation of the polaritonic modes with the respective harmonic diffraction orders (2πn/D). The three horizontal dashed lines correspond to the defect resonance (n = 1/2), first (n = 1), and second (n = 2) diffraction order resonances launched by the metal rod array, respectively. The marked red dots represent the experimental values, which the numeric labels are defined in Fig. 2a. The graphene Fermi level is 0.4 eV. At the hBN RBs (green highlighted regions), the black, blue, orange, and purple lines correspond to the 1^st, 2^nd, 3^rd, and 4^th hybridized polaritonic modes, respectively. In yellow is highlighted the SiO₂ RB.

Fig. 3. Normalized photocurrent spectra of device 3 at the hBN RBs.

a Normalized photocurrent spectra at the upper RB of hBN for several gate voltages. The photocurrent spectra are normalized to the spectrum at CNP. The polaritonic peaks are labeled by red arrows. The 0.20 eV curve is slightly shifted (divided by 1.05) for illustration. The Fermi energies are presented in absolute values. b Same as panel (a) but for the lower RB range. c Optical simulation of graphene absorption at the upper RB spectral region for different Fermi energies normalized to the spectrum at CNP. We label the identified peaks in the same manner as the experimental ones. d Same as panel (c) but for the lower RB range. e Cross-sectional view of the electric field intensity normalized to the incident one. The x − (horizontal) and z − (vertical) directions are defined in Fig. 1e. The simulations correspond to a non-uniform graphene Fermi level at 0.35 eV at wavelength 6.91 μm (corresponding to peak 1' in panel (a). The white scale bar corresponds to 20 nm. f Same as panel (e) but for a lower RB range at wavelength 12.37 μm (corresponding to peak 4' in Fig. 3b).

Fig. 4. Spatial field distribution and dispersion of hBN equivalent geometry and Q-factor spectrum of the 2D polaritonic nanoresonators.

Cross-sectional view of the spatial x − component of the electric field as a function of the wavelength for (a) 3^rd and (b) 5^th mode of the hybridized polariton. The graphene doping is 0.4 eV. The vertical black scale bar corresponds to 10 nm for panels (a–d). c and d correspond to the first and second order mode, respectively, of the bottom hBN (6 nm thick) of the equivalent system (E.S.) geometry consisting of the bottom hBN embedded by two gold layers of 10 nm without the presence of graphene and the top hBN as shown in the illustrations on the top part of the figure. e Dispersion relation of the investigated modes of the two systems. f Q-factor spectrum of the measured 2D polaritonic nanoresonators. The regions highlighted in green correspond to the RBs of hBN.