This review examines the properties of graphene from an experimental perspective. The intent is to review the most important experimental results at a level of detail appropriate for new graduate students who are interested in a general overview of the fascinating properties of graphene. While some introductory theoretical concepts are provided, including a discussion of the electronic band structure and phonon dispersion, the main emphasis is on describing relevant experiments and important results as well as some of the novel applications of graphene. In particular, this review covers graphene synthesis and characterization, field-effect behavior, electronic transport properties, magnetotransport, integer and fractional quantum Hall effects, mechanical properties, transistors, optoelectronics, graphene-based sensors, and biosensors. This approach attempts to highlight both the means by which the current understanding of graphene has come about and some tools for future contributions.

We demonstrate a combination of micro four-point probe (M4PP) and non-contact terahertz time-domain spectroscopy (THz-TDS) measurements for centimeter scale quantitative mapping of the sheet conductance of large area chemical vapor deposited graphene films. Dual configuration M4PP measurements, demonstrated on graphene for the first time, provide valuable statistical insight into the influence of microscale defects on the conductance, while THz-TDS has potential as a fast, non-contact metrology method for mapping of the spatially averaged nanoscopic conductance on wafer-scale graphene with scan times of less than a minute for a 4-in. wafer. The combination of M4PP and THz-TDS conductance measurements, supported by micro Raman spectroscopy and optical imaging, reveals that the film is electrically continuous on the nanoscopic scale with microscopic defects likely originating from the transfer process, dominating the microscale conductance of the investigated graphene film.

The general theoretical de®nition of an insulator is a material in which the conductivity vanishes at the absolute zero of temperature. In classical insulators, such as materials with a band gap, vanishing conductivities lead to diverging resistivities. But other insulators can show more complex behaviour, particularly in the presence of a high magnetic ®eld, where different components of the resistivity tensor can display different behaviours: the magnetoresistance diverges as the temperature approaches absolute zero, but the transverse (Hall) resistance remains ®nite. Such a system is known as a Hall insulator 1 . Here we report experimental evidence for a quantized 2 Hall insulator in a two-dimensional electron systemÐcon®ned in a semiconductor quantum well. The Hall resistance is quantized in the quantum unit of resistance h/e 2 , where h is Planck's constant and e the electronic charge. At low ®elds, the sample reverts to being a normal Hall insulator.Experimentally, the identi®cation of an insulating phase is based on extrapolating the measured magnetoresistance, r xx (T), at ®nite temperature (T) to T 0. This is always an ambiguous process. However, when r xx is exponentially increasing as T ! 0, the state is usually considered to be an insulator. Unfortunately, the divergent r xx seriously hinders the determination of the Hall resistivity, r xy , as even small Hall-contact misalignment will result in a large overriding signal from the diverging r xx . It is possible, to a certain degree, to circumvent this dif®culty by symmetrizing the measurement. This can be achieved by reversing the magnetic ®eld (B) orientation, as the contribution of r xx is symmetric in B as opposed to antisymmetric for r xy . The effectiveness of this procedure is demonstrated in the inset of Fig. 1, where we show measurements made in a twodimensional hole system con®ned in a 150-A Ê -thick strained Ge layer sandwiched in between Si 0.4 Ge 0.6 layers with boron modulation doping. More details of this system are given in ref. 3. The Hall resistances obtained for the two opposite B-®eld directions are in dotted lines and the average, that is r xy , is shown with a solid line. All Hall resistivities discussed here are obtained by this method.We now turn to discuss our results, where our ®rst task is to identify the different phases. The transition between insulating and quantum Hall phases can be characterized by a critical B-®eld value, for which r xx is T-independent and where the derivative of the Tdependence changes sign on each side of the transition. By plotting r xx at two different values of T, we can therefore extract the transition points. In Fig. 1 we have plotted r xy together with r xx as a function of B. With increasing B, transition points at B 2:2 T and at B B C 6:06 T can be identi®ed from the crossing of the two r xx curves obtained at different values of T. Between these transitions we have the usual quantum Hall state, which is bordered on both sides by insulators. For clarity, r xx is normalized to r c r xx B C 4 ...

Our evolving understanding of the dramatic features of charge-transport in the quantum Hall (QH) regime has its roots in the more general problem of the metal-insulator transition. Conversely, the set of conductivity transitions observed in the QH regime provides a fertile experimental ground for studying many aspects of the metal-insulator transition. While earlier works [1,2] tend to concentrate on transitions between adjacent QH liquid states, more recent works [3-8] focus on the transition from the last QH state to the high-magnetic-field insulator. Here we report on measurements that identified a novel transport regime which is distinct from both, the fully developed QH liquid, and the critical scaling regime believed to exist asymptotically close to the transition at very low temperatures (T 's).This new regime appears to hold in a wide variety of samples and over a large range of magnetic field (B) and temperature. It is characterized by a remarkably simple phenomenological scaling of the longitudinal resistivity (ρ xx ), which is the center of this letter, and is not understood theoretically.We begin by focusing on a recent set of observations that directly begot some of the results presented here. In Refs. [9,10], the observation of a new symmetry was reported, relating the transport properties of the QH liquid to those of the adjacent insulator. For the case of the ν = 1 to insulator transition, this symmetry is summarized by:where ν is the Landau level filling factor, ∆ν = ν −ν c and ν c is the critical ν of the transition (see the inset of Fig. 1 for the identification of ν c ). Remarkably, a similar symmetry holds at transitions from the 1/3 fractional quantum Hall (FQH) state to the insulator, if one replaces the ν's in Eq. 1 with those of composite fermions [11]. In addition, in ref.[9] we showed that a generalized relation holds, within experimental error, even for the non-linear regime of transport, and suggested the possibility that duality symmetry underlies this relation [9,12]. More recently, a similar relation was observed in Si-MOSFET samples near the B = 0 conductor-insulator transition [13], which raises the question whether a more general explanation may exist for the symmetry [14].In the remainder of this paper we shall present and discuss a view of the ρ xx data where the symmetry of Eq. 1 is a straightforward ingredient. We begin by plotting, in Fig. 1, ρ xx vs. ν for a low mobility (µ = 30000 cm 2 /Vsec), low density (n = 3 · 10 10 cm −2 ), InGaAs/InP sample, in the range of 0.4 < ν < 0.8 which includes the ν = 1-to-insulator transition (ν = 0.562), at several T 's between 0.072 and 2.21 K. Rather than plotting the data using the conventional linear ordinate (see inset of Fig. 1), we chose a log scale, which clearly reveals a distinct ν dependence of ρ xx :where ρ xx is measured in units of its critical value, ρ xxc (= 29.6 kΩ for this sample), a normalization which we adopt throughout this letter, and ν 0 (T ) is a T -dependent logarithmic slope, introduced here for the first time....

The electrical performance of graphene synthesized by chemical vapor deposition and transferred to insulating surfaces may be compromised by extended defects, including for instance grain boundaries, cracks, wrinkles, and tears. In this study, we experimentally investigate and compare the nano- and microscale electrical continuity of single layer graphene grown on centimeter-sized single crystal copper with that of previously studied graphene films, grown on commercially available copper foil, after transfer to SiO2 surfaces. The electrical continuity of the graphene films is analyzed using two noninvasive conductance characterization methods: ultrabroadband terahertz time-domain spectroscopy and micro four-point probe, which probe the electrical properties of the graphene film on different length scales, 100 nm and 10 μm, respectively. Ultrabroadband terahertz time-domain spectroscopy allows for measurement of the complex conductance response in the frequency range 1-15 terahertz, covering the entire intraband conductance spectrum, and reveals that the conductance response for the graphene grown on single crystalline copper intimately follows the Drude model for a barrier-free conductor. In contrast, the graphene grown on commercial copper foil shows a distinctly non-Drude conductance spectrum that is better described by the Drude-Smith model, which incorporates the effect of preferential carrier backscattering associated with extended, electronic barriers with a typical separation on the order of 100 nm. Micro four-point probe resistance values measured on graphene grown on single crystalline copper in two different voltage-current configurations show close agreement with the expected distributions for a continuous 2D conductor, in contrast with previous observations on graphene grown on commercial copper foil. The terahertz and micro four-point probe conductance values of the graphene grown on single crystalline copper shows a close to unity correlation, in contrast with those of the graphene grown on commercial copper foil, which we explain by the absence of extended defects on the microscale in CVD graphene grown on single crystalline copper. The presented results demonstrate that the graphene grown on single crystal copper is electrically continuous on the nanoscopic, microscopic, as well as intermediate length scales.