While metal is the most common conducting constituent element in the fabrication of metamaterials, graphene provides another useful building block, that is, a truly two-dimensional conducting sheet whose conductivity can be controlled by doping. Here we report the experimental realization of a multilayer structure of alternating graphene and Al2O3 layers, a structure similar to the metal-dielectric multilayers commonly used in creating visible wavelength hyperbolic metamaterials. Chemical vapour deposited graphene rather than exfoliated or epitaxial graphene is used, because layer transfer methods are easily applied in fabrication. We employ a method of doping to increase the layer conductivity, and our analysis shows that the doped chemical vapour deposited graphene has good optical properties in the mid-infrared range. We therefore design the metamaterial for mid-infrared operation; our characterization with an infrared ellipsometer demonstrates that the metamaterial experiences an optical topological transition from elliptic to hyperbolic dispersion at a wavelength of 4.5 μm.

The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier–carrier interactions and carrier–phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of observed signals within phenomenological frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated experimental and theoretical programme, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modelling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amounts of disorder and with either high or low doping levels. The theory reproduces the observed dynamics quantitatively without the need to invoke any fitting parameters, phenomenological models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier–carrier scattering, which maintains a thermalized carrier distribution, and carrier–optical–phonon scattering, which removes energy from the carrier liquid.

A method for analysis of spectroscopic ellipsometry data is demonstrated to extract the optical conductivity of mono-and bilayer chemical-vapor-deposited graphene. We model graphene as a truly two-dimensional (2D) material with a sheet conductivity, rather than a phenomenological effective refractive index as has been used in the literature. This technique measures both the real and imaginary part of the optical conductivity, which is important for graphene optoelectronics and metamaterials. Using this method, we obtain broadband measurements of the complex optical conductivity for mono-and bilayer graphene from ultraviolet to mid-infrared wavelengths. We also study how chemical doping with nitric acid modifies the complex optical conductivity.

transfer was repeated several times (typically ∼3) in order to further improve the conductance of the electrodes, therefore forming a multilayer graphene (MLG) stack. An optical graph of the glass substrate with the MLG fi lm on top is displayed in Figure 1 b, showing high transparency. Subsequently, the MLG fi lm was patterned into bottom electrodes (BEs) with widths of 1-5 µm by photolithography and O 2 plasma etching (Figure 1 a2). Au/Ti metal contacts (B1 and B2) were then deposited onto the two ends of the MLG BE afterwards to minimize the contact resistance to the external probes in electrical measurements (Figure 1 a3). Following BE defi nition, a bilayer oxide structure consisting of an oxygen rich Ta 2 O 5-x layer (∼5 nm) and an oxygen defi cient TaO y layer (∼40 nm) serving as the switching medium of the RRAM devices was successively deposited by radio-frequency (RF) sputtering and reactive sputtering (400 °C, O 2 /Ar = 3%), respectively, without breaking the vacuum (Figure 1 a4). Similar to steps 1-3 in Figure 1 a, multiple monolayer graphene transfer, O 2 plasma etching and Au/Ti metal contacts deposition were conducted again to fabricate the top electrodes (TEs) that complete the crossbar memory structure ( Figure 1 a5-7). Finally, a pad opening step was performed through a timed reactive ion etching (RIE) process to remove the Ta 2 O 5-x /TaO y bilayer on top of the bottom contact Au/Ti pads (Figure 1 a8). The sizes of the RRAM devices in this work range from 1-5 µm × 1-5 µm, and during measurements the voltage was applied on the TE with the BE grounded. Since resistive switching in Ta 2 O 5-x /TaO y bilayer devices is driven by internal oxygen vacancy redistribution, the change in deposition sequence should in principle only lead to a reversal of the switching polarity, as has been verifi ed by studies on devices with inert metal electrodes. [ 25 ] However, in the case of devices with MLG electrodes, the stacking sequence of the bilayer was found to be critical in determining the device behavior, as shown in Figure 1 d,e. When the Ta 2 O 5-x layer was deposited fi rst on the graphene BE followed by TaO y deposition, the MLG/TaO y /Ta 2 O 5-x /MLG (top to bottom) devices exhibited conventional bipolar resistive switching characteristics similar to the results obtained with metal electrodes, [ 25,26 ] as shown in Figure 1 d. Such switching behavior can be well understood in the picture of V O exchange between the Ta 2 O 5-x and the V O -rich TaO y layers, [ 8,26,27 ] and the switching polarity with positive SET and negative RESET voltages is a natural result of the device confi guration since the V O reservoir (the oxygen defi cient TaO y layer) sits on top in this case. The linear on-state behavior is also consistent with Ohmic conduction for the V O -based conducting fi laments in Ta 2 O 5-x /TaO y RRAMs. [ 8,26,27 ] Driven by the continuing demand for improved computing capability, the semiconductor industry has been constantly looking for a fast, reliable, scalable yet nonvolatile memory technolo...