Non-contact method for measurement of the microwave conductivity of graphene

We report a non-contact method for conductivity and sheet resistance measurements of graphene samples using a high Q microwave dielectric resonator perturbation technique, with the aim of fast and accurate measurement of microwave conductivity and sheet resistance of monolayer and few layers graphene samples. The dynamic range of the microwave conductivity measurements makes this technique sensitive to a wide variety of imperfections and impurities and can provide a rapid non-contacting characterisation method. Typically the graphene samples are supported on a low-loss dielectric substrate, such as quartz, sapphire or SiC. This substrate is suspended in the near-field region of a small high Q sapphire puck microwave resonator. The presence of the graphene perturbs both centre frequency and Q value of the microwave resonator. The measured data may be interpreted in terms of the real and imaginary components of the permittivity, and by calculation, the conductivity and sheet resistance of the graphene. The method has great sensitivity and dynamic range. Results are reported for graphene samples grown by three different methods: reduced graphene oxide (GO), chemical vapour deposition (CVD) and graphene grown epitaxially on SiC. The latter method produces much higher conductivity values than the others.Comment: 8 pages, 2 figures and 2 table

Metal-dielectric transition in Sn-intercalated graphene on SiC(0001)

The Sn intercalation into a buffer layer graphene grown on 4H-SiC(0001) substrate has been studied with spectroscopic photoemission and low energy electron microscope. Both SnSix and SnOx interfacial layers are found to form below the buffer layer, converting it into a quasi-free-standing monolayer graphene. Combining the various operation modes of the microscope allows a detailed insight into the formation processes of the interlayers and their thermal stability. In particular, at the interface we observed a reversible transition from silicide to oxide after exposure to ambient pressure and subsequent annealing. This metal-dielectric transition might be useful for interface engineering in graphene-based devices

Anomalously strong pinning of the filling factor nu=2 in epitaxial graphene

We explore the robust quantization of the Hall resistance in epitaxial graphene grown on Si-terminated SiC. Uniquely to this system, the dominance of quantum over classical capacitance in the charge transfer between the substrate and graphene is such that Landau levels (in particular, the one at exactly zero energy) remain completely filled over an extraordinarily broad range of magnetic fields. One important implication of this pinning of the filling factor is that the system can sustain a very high nondissipative current. This makes epitaxial graphene ideally suited for quantum resistance metrology, and we have achieved a precision of 3 parts in 10^10 in the Hall resistance quantization measurements

Long spin relaxation times in wafer scale epitaxial graphene on SiC(0001)

We developed an easy, upscalable process to prepare lateral spin-valve devices on epitaxially grown monolayer graphene on SiC(0001) and perform nonlocal spin transport measurements. We observe the longest spin relaxation times tau_S in monolayer graphene, while the spin diffusion coefficient D_S is strongly reduced compared to typical results on exfoliated graphene. The increase of tau_S is probably related to the changed substrate, while the cause for the small value of D_S remains an open question.Comment: 16 pages, 3 figures, 1 tabl

Magnetotransport in graphene on silicon side of SiC

We have studied the transport properties of graphene grown on silicon side of SiC. Samples under study have been prepared by two different growth methods in two different laboratories. Magnetoresistance and Hall resistance have been measured at temperatures between 4 and 100 K in resistive magnet in magnetic fields up to 22 T. In spite of differences in sample preparation, the field dependence of resistances measured on both sets of samples exhibits two periods of magneto-oscillations indicating two different parallel conducting channels with different concentrations of carriers. The semi-quantitative agreement with the model calculation allows for conclusion that channels are formed by high-density and low-density Dirac carriers. The coexistence of two different groups of carriers on the silicon side of SiC was not reported before.Comment: 5 pages, 6 figures, accepted for publication in the "IOP Journal of Physics: Conference series" as a contribution to the proceedings of the 20th International Conference on "High Magnetic Fields in Semiconductor Physics", HMF 2

Determination of the thickness distribution of a graphene layer grown on a 2" SiC wafer by means of Auger electron spectroscopy depth profiling

Auger electron spectroscopy (AES) depth profiling was applied for determination of the thickness of a macroscopic size graphene sheet grown on 2 inch 6H-SiC (0001) by sublimation epitaxy. The measured depth profile deviated from the expected exponential form showing the presence of an additional, buffer layer. The measured depth profile was compared to the simulated one which allowed the derivation of the thicknesses of the graphene and buffer layers and the Si concentration of buffer layer. It has been shown that the C made buffer layer contains about 30% unsaturated Si. The depth profiling was carried out in several points (diameter 50m), which permitted the constructing of a thickness distribution characterizing the uniformity of the graphene sheet

Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

Polarization selection rules for inter-Landau level transitions in epitaxial graphene revealed by infrared optical Hall effect

We report on polarization selection rules of inter-Landau level transitions using reflection-type optical Hall effect measurements from 600 to 4000 cm-1 on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and anti-symmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau level transitions, respectively. From field-dependent measurements we identify that transitions in decoupled graphene mono-layers are governed by polarization mixing selection rules, whereas transitions in coupled graphene mono-layers are governed by polarization preserving selection rules. The selection rules may find explanation by different coupling mechanisms of inter-Landau level transitions with free charge carrier magneto-optic plasma oscillations

Disorder induced Dirac-point physics in epitaxial graphene from temperature-dependent magneto-transport measurements

We report a study of disorder effects on epitaxial graphene in the vicinity of the Dirac point by magneto-transport. Hall effect measurements show that the carrier density increases quadratically with temperature, in good agreement with theoretical predictions which take into account intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. We deduce disorder strengths in the range 10.2 $\sim$ 31.2 meV, depending on the sample treatment. We investigate the scattering mechanisms and estimate the impurity density to be $3.0 \sim 9.1 \times 10^{10}$ cm$^{-2}$ for our samples. An asymmetry in the electron/hole scattering is observed and is consistent with theoretical calculations for graphene on SiC substrates. We also show that the minimum conductivity increases with increasing disorder potential, in good agreement with quantum-mechanical numerical calculations.Comment: 6 pages, 3 figure