Michael Hilke

Experimental Review of Graphene

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.

Graphene Conductance Uniformity Mapping

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.

A new transport regime in the quantum hall effect

Abstract A study of the temperature evolution of the recently discovered reflection symmetry of the diagonal resistivity, ϱ xx , near quantum Hall-to-insulator transitions, is presented. The data is found to follow a new phenomenological law over a broad range of temperatures, magnetic fields and samples. We note that this law is inconsistent with the scaling description of quantum Hall transitions and indicates the existence of a transport regime distinct from those considered previously.

Raman spectroscopy of the internal strain of a graphene layer grown on copper tuned by chemical vapor deposition

Strain can be used as an alternate way to tune the electronic properties of graphene. Here we demonstrate that it is possible to tune the uniform strain of graphene simply by changing the chemical vapor deposition growth temperature of graphene on copper. Due to the cooling of the graphene on copper system, we can induce a uniform compressive strain on graphene. The strain is analyzed by Raman spectroscopy, where a shift in the 2D peak is observed and compared to our ab initio calculations of the graphene on copper system as a function of strain.

Delocalization in continuous disordered systems

Continuous one-dimensional models supporting extended states are studied. These delocalized states occur at well-defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of {delta}-barrier potentials as well as alloys and liquids of quantum wells. The divergence of the localization length is studied and a critical exponent (2)/(3) is found for the {delta}-barrier case, whereas for the quantum wells we find an exponent of 2 or (2)/(3) depending on the well`s parameters. These results support the idea that correlations between random scattering sequences break Anderson localization. We further calculate the conductance of disordered superlattices. At the peak transmission the relative fluctuations of the transmission coefficient are vanishing. {copyright} {ital 1997} {ital The American Physical Society}

Electrically continuous graphene from single crystal copper verified by terahertz conductance spectroscopy and micro four-point probe.

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.

Frequency quenching of microwave-induced resistance oscillations in a high-mobility two-dimensional electron gas

The frequency dependence of microwave-induced resistance oscillations (MIROs) has been studied experimentally in high-mobility electron

Semicircle: An exact relation in the integer and fractional quantum Hall effect

\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}

Noninteracting electrons and the metal-insulator transition in two dimensions with correlated impurities.

structures to explore the limits at which these oscillations can be observed. It is found that in dc transport experiments at frequencies above

Localization properties of the periodic random Anderson model

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