Experimental demonstration of tunable graphene hyperbolic metamaterial

Previous theoretical work has suggested that actively tunable graphene elements can enable the tuning of the effective dielectric permittivity of metamaterials through the epsilon-near-zero regime at infrared wavelengths to yield transition from an elliptical to hyperbolic dispersion. Here, we experimentally realize and measure the response of a graphene/polar dielectric metamaterial using a graphene-SiO2 unit cell. This metamaterial exhibits epsilon-near-zero crossing and tunable electric properties from E_f =0 to E_f =0.5eV that are experimentally verified through spectroscopic ellipsometry and transmission measurements.

Metamaterials are artificial composite materials, with subwavelength elements, that exhibit electromagnetic responses unseen in the natural world. Research in the field has been mainly driven by the desire to tailor the optical response of materials 1-4 . Particularly interesting is the case of a permittivity (ε) near zero (ENZ) 5-7 , for which one can design materials with a high photonic density of states such as hyperbolic or indefinite metamaterials (HMMs) 8,9 . These are uniaxial metamaterials whose ordinary, in-plane (ε o ) and extraordinary, out-of-plane (ε e ) electrical permittivities have opposite signs. HMMs, unlike most natural materials, behave as metals along one coordinate direction and as dielectrics in the other, leading to dielectric permittivities of opposite sign in-plane (ε o ) and out-of-plane (ε e ).
Upon fixing the frequency and describing the wavenumber spatial distribution, unlike common materials with a circular isofrequency surface, they support open isofrequency surfaces with wavevectors extending to large values for a given energy. Owing to these novel optical properties, hyperbolic metamaterials can exhibit large Purcell factor enhancements and can serve as slow-light media 10 , enhancing dipole-dipole interactions 11 , increasing gain/length in lasing 12 , as well as enabling super-resolution 13 or sub-diffraction imaging 14 .
On the other hand, graphene is a well-studied monolayer material for electronics 15 and in infrared photonics 16 , Graphene is extensively being considered as an active metamaterial component, because its chemical potential can be actively modulated upon via a gate-bias 17 or via optical pumping 18 . Specifically, the dielectric properties of graphene can be dynamically tuned by chemical or electrostatic modulation of the carrier concentration 19 , allowing the design of graphene-dielectric layered metamaterials 8,20,21 . Additionally, it has been shown theoretically and experimentally that the plasmonic nature of graphene supports surface electromagnetic waves with extreme confinement 22  localization, together with the tunability of graphene, provides a promising platform for investigating tunable graphenebased HMMs. There has been considerable theoretic effort in the past decade to understand the properties of tunable graphene metamaterials. [24][25][26][27] . Graphene-based HMMs can further enhance the already strong field localization of graphene plasmons due to the opposing signs of dielectric permittivity along the different coordinate axes. Graphene heterostructures have been proposed for applications including thermophotovoltaics 28 , tunable absorbers 24 , thermal emission 29 , device applications 30 , boost terahertz emission 20 , and photonic logic switches 31 , and elliptichyperbolic transitions 21 .
Although previously graphene has been theoretically proposed as a tunable element in HMMs, until now, experimental demonstrations of tuning have not been reported. Fabrication challenges have hampered experimental realization of promising structures. As a two-dimensional material with weak out- 10 15 20 25 30 35 Wavelength (µm) 10   of-plane Van der Waals forces, graphene exhibit poor adhesion to most dielectric substrates. Moreover, it has been challenging to fabrication methods for dielectric overlayers on graphene which are sufficiently large in area to enable metamaterial characterization and which also avoid oxidization or other damage to the graphene structure.
In this Letter, we overcome these challenges and experimentally demonstrate a planar graphene-SiO 2 metamaterial, which is electrically gate-tunable with an external bias. A thin Al 2 O 3 layer encapsulates the graphene and enables adhesion of the top SiO 2 to realize symmetric dielectric heterostructures. This structure exhibits a tunable optical response in the long wavelength infrared range. We predict the tunable dielectric properties of our metamaterial and compare these prediction to experimental results obtained from spectroscopic ellipsometry and reflectometry, yielding a first experimental demonstration of a graphene metamaterial with a tunable unaxial near-zero permittivity.
Specifically, here We consider a metamaterial where monolayer graphene is sandwiched two polar dielectric materials a depicted in Fig. 1. Previous considerations assumed nondispersive dielectric media between graphene monolayers, as the insulating and dielectric component of the HMM 8 . How-ever, most naturally occurring dielectric materials exhibit lattice vibrations which are accompanied by strong frequency dispersion in the regime of interest (IR range), for which we account for in this report. Polar dielectric materials exhibit Reststrahlen bands of negative dielectric permittivity across the infrared range, which allow the near-zero crossing of the effective dielectric response of the heterostructure. By electrostatically tuning the graphene carrier density and permitittivity, we can shift the point at which Re(ε o ) crosses zero. Since the graphene response is uniaxial, we can shift the Re(ε o ) while leaving the extraordinary ENZ point unchanged.
The electrical modulation of permittivity occurs in the plane of the graphene sheet, and thus largely affects ε o . Outof-plane, the graphene has a constant ε o . The effective permittivity of the homogenized structure should consist of a tunable Re(ε o ) that crosses zero at a range of wavelengths for different Fermi level values and a static ε e that crosses zero at a fixed wavelength.
The substrate is a lightly-doped silicon wafer, with a 300nm thick layer of thermal oxide. On top of that oxide, we deposit 12.9nm of Al 2 O 3 by atomic layer deposition (ALD). CVDgrown graphene is transferred onto the stack. A 0.5nm aluminum layer is deposited on top of the graphene by electronbeam evaporation and oxidizes in ambient conditions. Another layer of 12.3nm Al 2 O 3 is deposited on top of the stack. The final layer is deposited by plasma-enhanced chemical vapor deposition (PECVD) and consists of 321nm of SiO 2 . Lithographically-defined patterns were used to deposit 3nm/100nm of Cr/Au contacts on the graphene layer and were used to gate the graphene against the silicon backgate. This allows for the electrical tuning of the effective ε o of the metamaterial. The effective Fermi level was calculated using a capacitor model based on the materials between the gate and the applied voltage 32 .
The location of the Dirac peak was experimentally determined using a capacitor model and the measured change in resistance. The thickness of the film layers were measured by both a thin film analyzer and visible ellipsometry with a qualitative agreement of 2nm. The previous absence of experimental demonstrations of graphene/dielectric tunable hyperbolic response can be attributed to several factors: First, large-area graphene sheets on the order of mm 2 's with gate-induced tunability are needed to perform metamaterial optical measurements. Exfoliated flakes are generally limited to sizes of 10s of µm, so largearea graphene samples grown by chemical vapor deposition and subsequently transferred from their growth substrates, are necessary. Second, deposition of large-area thin dielectric layers on graphene is challenging. Films prepared by electron-beam evaporation exhibit thermal stress-induced delamination 33 . . Films grown by atomic layer deposition (ALD) with an H 2 O precursors exhibit difficulty in bonding to chemically-inert hydrophobic graphene 34 , whereas ozonebased ALD processes oxidize the graphene sheet. A viable dielectric deposition method was developed consisting of functionalization of the surface by deposition of trimethylalu- Normalized to E f =0. Deviations arise due to hysteresis of the graphene induced by charge trapping minium (TMA) 35 or an aluminum nucleation layer 36 to create a seed layer for additional deposition. A suitably thin layer of aluminum is needed so that it can fully oxidize and not compromise the electrical gating of the graphene. In order to create a symmetric metamaterial unit cell, ALD AL 2 O 3 layers need to be deposited. We found that deposition of AL 2 O 3 via plasma-enhanced chemical vapor deposition (PECVD) resulted in reduced thermal stress and avoided delamination.
Metamaterial structures comprised of alternating layers of polar dielectric materials and graphene support high applied electric fields as they have a high electrical breakdown strengths. They allow for high contrast in the optical response of graphene. We use the Kubo formula 37 calculate the sheet conductance σ from the E f of graphene. This value can be used to compute the transfer matrix for graphene 38 .
We utilize the transfer matrix approach 39 , accounting for graphene via G, and obtain the complex scattering amplitudes of the fields. In turn, we use these to compute the effective permittivity via previously developed parameter retrieval approaches 40 . We measure individual layers of our sample with ellipsometry to obtain the ellipsometric parameters (ψ , ∆). Using oscillator models for the constituent materials, we transform ψ and ∆ into a complex ε using conventional ellipsometric fitting. From these values, we calculate transfer matrices of the dielectric layers. Combining these with the graphene transfer function, we obtain the transfer function of the composite medium 39 . This function gives us the complex scattering amplitudes of the fields for the structure. Using material parameter retrieval 40 , we can solve the inverse problem to compute effective ε o [see Fig. 2(a,b)] and ε e for a range of graphene Fermi levels.
Fourier-transform infrared spectroscopy (FTIR) was used to measure sample transmission and compare with predictions for ε calculated by material parameter retrieval. By tuning the graphene, we induce a change in transmission [See Fig.  3]. Our calculations predicted the experimentally-observed direction for ENZ wavelength shift. Graphene becomes more metallic at higher carrier concentration, thereby increasing in absorption. This shift of the graphene Drude conductivity causes modulation of the effective permittivity of the metamaterial. The graphene exhibits hystersis which attribute to defects induced by deposition of the Al layer, which may account for the discrepancies between experiment and theory. As the graphene is tuned, the Dirac peak shifts in the direc-tion of applied bias, causing the sample to experience a reduced E f , giving qualitative experimental agreement with theory without fitting parameters.
By tuning ε, we have interesting behavior that occurs at the ENZ points near the SiO 2 phonon at 22.0µm [see Fig. 2(c)]. The out-of-plane ε e extraordinary crossing at 19.7µm and 21.1µm, whereas the in-plane ordinary crossing occurs at a broader range of wavelengths dependent on the Fermi level of the graphene. From the 19.7µm ENZ point to 20.0µm, Re(ε o ) is greater than zero for E f =0eV, whereas Re(ε e ) is negative. This implies our heterostructure should behaves as Type I hyperbolic metamaterial (HMM). As the graphene Fermi level is raised to 0.2eV, this region shrinks. Above E f =0.2eV, the Re(ε o )<0 while Re(ε e )>0, as expected for a type II HMM. At 0.5eV, this phenomenon occurs in the wavelength range from 19.1µm to 19.7µm. This observation is consistent with an electrically tunable elliptic-to-hyperbolic transition in metamaterial dispersion for both type I and type II HMMs. For the longer wavelength crossings, the material should behave as a type I HMM for wavelengths in the range between 21.1µm and 21.6µm for E f = 0eV and up to 21.8µm for E f = 0.5eV.
In summary, we have experimentally demonstrated a graphene metamaterial with tunable epsilon-near-zero permittivity response. By tuning the graphene Fermi level, we can modulate the ENZ wavelength by up to 0.9µm. Ellipsometry was used to determine the optical properties of the constituent materials. Material parameter retrieval was used to calculate the constitutive electromagnetic response. These calculations closely matched the FTIR transmission measurements of the overall heterostructure, indicating a shift of the graphene permittivity near the ENZ point under electrical gate bias. Near 19.7µm we can tune electrically tune ε, which implies an elliptical to hyperbolic transition in dispersion.