The focus of this thesis is on the electronic properties of graphene. Specifically, the 1/f noise and carrier density modulations under large bias were experimentally investigated and theoretically studied. The novel electronic transport properties were analyzed by Boltzmann transport theory. Some preliminary results regarding the topological properties of antidot graphene are discussed.

The 1/f noise study is important for the potential industrial application, since it largely affects the performance of the device. The 1/f noise in graphene was measured on both the longitudinal and Hall resistances. We carried out simultaneous measurements on longitudinal and Hall signals. The major discovery has been that there is a negative correlation between carrier density and mobility fluctuatio...[ Read more ]

The focus of this thesis is on the electronic properties of graphene. Specifically, the 1/f noise and carrier density modulations under large bias were experimentally investigated and theoretically studied. The novel electronic transport properties were analyzed by Boltzmann transport theory. Some preliminary results regarding the topological properties of antidot graphene are discussed.

The 1/f noise study is important for the potential industrial application, since it largely affects the performance of the device. The 1/f noise in graphene was measured on both the longitudinal and Hall resistances. We carried out simultaneous measurements on longitudinal and Hall signals. The major discovery has been that there is a negative correlation between carrier density and mobility fluctuations. This discovery was proved by two experimental results. The first is that the normalized power spectrum density (PSD) of Hall noise, i.e. carrier density noise, can exceed that of the longitudinal noise. The second is that the governing relation between transient carrier density and mobility can differ significantly from the relation between their mean values. We propose a single parameter theory whose underlying physics is the screening effect of the trapping and de-trapping of the charge carriers. This can alter the effective density of long-range scattering impurities in a transient manner, leading to the fluctuations of mobility. The model also requires zero cross correlation between longitudinal and Hall voltage fluctuations, which was verified by experiments.

Graphene with electric field has attracted many attentions, since it opens the window for studying electron-phonon interactions, which are almost absent for low field measurement. When graphene is under a large electric field, we discovered that the carrier density can exhibit spatial variations. This behavior is quantitatively explained by the back-gate tuning model. We directly measure the carrier density's spatial variation by detecting the differential Hall resistance at different pairs of side-electrodes. Our first observation is that carrier density modulation depends on the sign and magnitude of the bias current, which rules out the possibility of heating effects. The carrier density modulations are well fitted by the gate tuning model. Moreover, the shifts of CNP were observed from the measured longitudinal and Hall resistances. In addition, the I-V curves were quantitatively analyzed by solving the Boltzmann equation self-consistently, by including the induced carrier density modulation. The spatial modulation of charge carrier density is especially significant when the back gate is not far away from CNP.

The last part of the thesis discusses some preliminary results on antidot graphene. Since graphene is a gapless material, a gap will open by introducing the antidot, and antidot graphene turns out to be a semiconductor which is of potential industrial application. We present the bandstructure of antidot graphene by two different methods. One is the continuum model with the Weyl Hamiltonian, which can be solved by the commercial software COMSOL. The other is the tight-binding model solved by numerically diagonalizing the matrix of the antidot graphene Hamiltonian. Both models yield the conclusion that a band gap is opened at Dirac point, and also indicate a nonzero Berry curvature in the antidot graphene. The nonzero Berry curvature is experimentally verified by detecting the topological current through nonlocal measurements. When filling the holes of antidot graphene with some magnetic clusters, an edge state is observed under numerical calculations. More experimental and theoretical works are required for further investigating the topological properties in antidot graphene.