NHMFL Research Report

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					                                NATIONAL HIGH MAGNETIC FIELD LABORATORY
                                         2010 RESEARCH REPORT

Microwave Measurements of Graphene Conductance
P. Jiang (NHMFL and Princeton U.); A. F. Young, W. Chang P. Kim, (Columbia U);
L. W. Engel (NHMFL); and D. C. Tsui (Princeton U.)

Graphene [1,2] is an important new material, both for fundamental physics and for possible applications. We have
developed microwave conductance spectroscopy as a quantitative tool for measuring small graphene samples [3].
A carefully characterized structure, shown schematically in Fig. 1, connects a pair of contacts on a small
graphene sample to coaxial cables, which in turn connect to a room-temperature microwave network analyzer.

Results and Discussion
We measured relatively low-mobility (1000 cm /V-s) samples of graphene mechanically exfoliated on to SiO2. The
carrier sign and density of the graphene depend on the backgate voltage Vg, which is applied between the Si
substrate and the graphene.
     Fig. 2 shows G(Vg)=G(Vg)-G(VCN), for several frequencies at a magnetic field, B, of 8 T. VCN is the voltage
required to bring the graphene to its charge neutral point and can readily be identified as the voltage that
produces a minimum in dc conductance (measurable in the same set-up) for B=0. The inset of Fig. 2 shows G
vs Vg for B=0. G is calculated from the microwave transmission based on a calibration standard detailed in ref. 3.
     Fig. 2 shows clear quantum oscillations, and is marked with the Landau level filling factors, Possibly due
to the low mobility of our samples, G does not exhibit quantized values as would be expected [4] if the quantum
Hall effect were fully developed. We find the real microwave conductivity to have no measurable frequency
dependence for frequencies between dc and 8 GHz, and for any B up to 8 T. Though we measure G only, its
frequency independence is a reliable indicator that the absolute conductance G must be frequency independent
as well. The frequency-independent behavior of graphene conductance is consistent with the low frequency limit,
2f<<1, where t is the transport relaxation time of the graphene carriers.

                                                       Fig. 1. a) Schematic of measurement of
                                                       graphene flake. The orange areas are
                                                       fabricated in metal film on SiO2 coating
                                                       doped Si. b) enlarged area of rectangle
                                                       of a), showing graphene in the slot.

                                                       Fig. 2. Graphene change in conductance
                                                       (DG) from charge-neutral point vs gate
                                                       voltage (Vg), for dc and several
                                                       frequencies for magnetice field B= 8 T.
                                                       Inset: DG vs Vg for B=0.

                                                   1. K. S. Novoselov, A. K Geim, A. K. Morozov, D. Jiang, Y.
                                                   Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science
                                                   306, 666 (2004) .
                                                   2. A. K. Geim, Science 324, 1530 (2009).
                                                   3. P. Jiang, A. F. Young, W. Chang P. Kim, L. W. Engel, and D.
                                                   C. Tsui, Applied Physics Letters 97, 062113 (2010).
                                                   4. D. A. Abanin and L. S. Levitov, Phys. Rev. B 78, 035416

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