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Chemically decorated graphene

• Electron Localization in Metal-decorated Graphene

* (W. Li, Y.H. He, L. Wang, G.H. Ding, Z.Q. Zhang, R. W. Lortz, P. Sheng and N. Wang, Phys. Rev. B84 (2011)045431)



Due to the chirality nature of charge carriers and the “pseudospin” quantum number, single-layer graphene sheets show distinct quantum interference effects compared with the conventional two-dimensional (2D) systems. In ordinary 2D metals, the localization properties (either weak localization (WL) or weak anti-localization (AL)) are controlled by impurity scattering with spin-orbit interaction. As a result of two sublattices in graphene’s honeycomb crystal structure, charge carriers in single-layer graphene have a Berry phase of π and their backscattering is effectively suppressed because the two opposing interfering trajectories pick up a phase difference of π, resulting in a destructive interference and a positive correction to the conductivity. Therefore, electrons in graphene have a strong tendency not to localize.


Anderson Localization:


About the conductance of electrons in solid materials, traditionally, the quantum theory of electronic conductivity was built on the picture of an electron being multiply scattered by impurities and diffusing through the solid. 

At low temperature, electrons behave as wave and elastically scattered by the impurity. Anderson (Anderson, P. W. Phys. Rev. 109 (1958) 1492) showed that at sufficiently strong disorder, the interferences can start to dominate the transport. In this regime, the electrons in a disordered material can lose their mobility because of constructive interference of backscattering and the material may become an insulator. 

The chiral charge carriers in single-layer graphene reside in two inequivalent valleys at the K and K’ points of the first Brillouin zone. In the absence of intervalley scattering, single layer graphene would not display any WL. However, it has been reported theoretically and experimentally that WL and magnetoresistance (MR) effect in graphene can be achieved in samples with sufficiently strong intervalley scattering. Therefore, by introducing point defects or lattice disorders, the intervalley scattering can be enhanced and constructive interference of back scattering which favors WL can be restored. So far, the scattering mechanism which determines the transport properties in graphene samples containing disorders has not unambiguously been identified.

Strong Localization induced by metal clusters:

Recently, we studied the electron localization phenomena in metal-decorated graphene (Phys. Rev. B, 2011, in press). We demonstrated that Ag clusters (Au and Pt showed similar behavior) introduced disorders and scattering centers in graphene and a strong interaction between the clusters and graphene was observed. Upon increasing the density of the metal clusters, the graphene devices transformed from WL to SL regime. A large negative MR effect (up to 80% at 12T) has been observed. We show that the localized states in the energy spectrum of carriers in graphene are tunable by changing the density of Ag clusters. In addition, the samples containing strong scattering centers behave as insulators at low temperature and their transport can be described by hopping conductance in accordance with the 2D variable-range hoping mechanism.

Our Experimental Approach:images/stories/GrapheneB.jpg

High-quality graphene devices were fabricated by conventional electron beam lithography (Raith e_LiNE). Single-layer graphene samples were prepared by mechanical exfoliation of graphite on a heavily doped Si substrate coated with SiO2 (300nm thick). The electrodes were Cr(5nm)/Au(40nm) prepared by electron-beam thermal evaporation. The quality of the single layer graphene samples were first verified by micro Raman spectroscopy. The graphene devices were then characterized using four-probe configuration at cryogenic temperature (from 1.8K to room temperature) before metal decoration. All transport measurements were carried out using lock-in technique (Stanford Research System SR830) with an AC current source (Keithley model 6221). The frequency of the AC bias current (<10nA) was 4.7Hz. 

Quantum Hall Effect observed in our pristine graphene devices:


All graphene devices used in this study showed good homogeneity with the Dirac point close to zero back gate voltage. The conductivity at high gate regions showed nonlinearity. By considering short range scattering, the electron mobility of the pristine graphene devices was estimated to be about 19,500cm2/Vs and its electrical conductance at the Dirac point was about 1.18x(4e2/h) which is close to the minimum conductance of monolayer graphene.

At 2K, the pristine graphene device showed clear fractional quantum Hall effect and electron mobility obtained from the Hall effect measurement is close to the value mentioned above. These results indicated that the quality of the pristine graphene devoces are very good before conducting metal decoration.

Metal decoration of graphene devices were performed in a DC plasma sputtering system. A cap with a small hole was used to allow the metal cluster flux to pass and deposit only on the graphene device. The structure of the metal clusters was characterized by a scanning tunneling microscope and a high-resolution transmission electron microscope.

For slightly Ag coating samples, the average separation between Ag clusters was about 20nm. The average cluster diameters were about 4images/stories/GrapheneE.jpgnm. By increasing the deposition duration, the size of Ag clusters increased to about 6nm. The cluster density increased significantly. The structure of the Ag clusters also characterized by HRTEM. The Ag clusters are crystalline with clear facets and the lattice plane spacing measured from the HRTEM image matched the d-spacing of (111) plane of Ag face-center-cubic structure fairly well. The Ag clusters resulted in significant changes of the graphene conductivity. The resistance of the devices usually increased about one order of magnitude at room temperature (a maximum of 3 orders of increase has been observed) and the mobility was largely reduced after Ag decoration. The Dirac point shifted slightly and the conductivity became very sensitive to temperature. At low temperatures (down to 1.8K), the conductivities of Ag decorated devices decreased drastically and the heavily decorated devices often behaved as insulators. Ag clusters introduced strong disorder scattering centers and caused localized states. Therefore, the transport of the graphene devices at low temperature followed the variable-range hopping (VRH) conductance model. For Mott’s VRH process, an electron could hop from one localized site to another when receiving energy and the resistivity in the Miller-Abrahams network can be expressed by:


The dependence of the resistivity on temperature will be determined by how the density of states at the Fermi level depended on energy. For a constant density of states at the Fermi energy, the resistivity is described as ρ(T)∝〖exp⁡(T0/T)〗^(1/(1+d)), where d = 2 for a 2D system. Here T0 inversely proportional to the density of states.

The dependence of the resistivity on temperature will be determined by how the density of states at the Fermi level depended on energy. For a constant density of states at the Fermi energy, the resistivity is described as ρ(T)∝〖exp⁡(T0/T)〗^(1/(1+d)), where d = 2 for a 2D system. Here T0 inversely proportional to the density of states.


To understand the transport properties of the Ag-decorated graphene, we have systematically investigated the MR effects in the presence of a magnetic field perpendicular to the graphene layer. Different from pristine graphene, the graphene devices displayed large negative MR effects. Their MRs were gate-voltage dependent. The maximum MR effect was achieved with the lowest carrier density when Vg was approaching the Dirac point. To verify the 2D quantum interferences of localization effects in Ag decorated samples, we also performed MR measurement with a magnetic field parallel to the graphene surface. The negative MR effect was much weaker than that in the same sample recorded with a perpendicular magnetic field. The MR effect at 6T was about -10%, while under the perpendicular magnetic field, the MR effect was about -70%. This strong magnetic-field direction dependence of the negative MR effect indicated a major localization effect which might arise from the quantum interference between the charge carrier paths.


The observation of VRH behavior suggests strong localization. It is known that in the weak magnetic field regime where the magnetic length is larger than the localization length, there can be a negative MR.

The dependence of the MR on -B^(1/2) in our samples agrees with the orbital mechanism of 2D VRH fairly well. By estimating the electron diffusion constant, we obtained the changes of the density of states versus gate voltages. Then, we estimated the localization length based on the 2D VRH model. For Sample A, the localization length at the gate voltage far away from the Dirac point (Vg= -50V) is about 394nm, about 50 times of the separation distance of the Ag clusters. At the Dirac point, the localization length is about 88nm (see Table 1). For Sample B and C, the localization lengths largely decrease. Because the uncertainty of the estimated density of states is large, the localization lengths listed in Table 1 can be considered as a reference.

We have measured the differential conductance of the samples under different biases and gate voltages. The mapping of differential conductance of mild and heavily Ag-decorated devices for different temperatures is obtained. Because the samples are in the SL regime, no obvious MR effect was observed under a magnetic field up to 6T. Oscillations in the differential conductance become pronounced when the sample temperature is below 100K. The oscillation is temperature dependent and very obvious during variation of drain-source voltage (Vds) for a fixed gate voltage (Vg) (see the right side column). There seems to be no rigorous periodicity of the oscillation. The right column shows the variation of the differential conductances versus Vds for certain gate voltages. The oscillation of the differential conductance versus Vds is clearly visible for 50K. For high temperature (>120K), the oscillation gradually disappears.


The lattice disorder introduced by noble metal cluster decoration largely changed the transport properties of graphene. A strong interaction between metal clusters and graphene has been evidenced by micro Raman scattering. The metal-decorated graphene transformed from weak localization to strong localization by increasing the density of the metal clusters. At low temperature, the heavily Ag-decorated graphene behaved as an insulator and its transport property was in accordance with the 2D variable-range hoping mechanism. The large MR effect observed in the samples showed obvious dependence of ρ ∞ exp(-B^1/2) which agreed with the orbital mechanism of 2D VRH fairly well.



















 *W. Li, Y.H. He, L. Wang, G.H. Ding, Z.Q. Zhang, R. W. Lortz, P. Sheng and N. Wang*, Phys. Rev. B84 (2011) 045431.













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