Electronic transport in graphene

This dissertation focuses on the electronic transport properties of graphene, a single atomic layer of graphite. Graphene is a novel two-dimensional system in which electron transport is effectively governed by the relativistic quantum theory. We discover a variety of new phenomenon which stem from the "relativistic" nature of the electron dynamics in graphene.; An unusual quantum Hall (QH) effect is discovered in graphene at low temperatures and strong magnetic fields. Unlike conventional two-dimensional electron systems, in graphene the observed quantization condition is characterized by half integers rather than integers. Our investigation of the magneto-oscillations in resistance reveals a Berry's phase of pi associated with the electron motion in graphene. The half-integer quantization, as well as the Berry's phase, is attributed to the peculiar topology of the graphene band structure with a linear dispersion relation and vanishing mass near the Dirac point, which can be described by relativistic quantum electrodynamics. This is further confirmed by our measurement of the effective carrier mass, m*, which obeys Einstein's equation: E = m*c*2 where c* ≈ c/300 is the effective speed of light for electrons in graphene.; The availability of high magnetic fields up to 45 Tesla allows us to study the magneto-transport in graphene in the extreme quantum limit. Under such condition, we discover new sets of QH states at filling factors nu = 0, +/-1, +/-4, indicating the lifting of the four-fold degeneracy of the previously observed QH states at nu = +/-4(|n|+1/2), where n is the Landau level index. In particular, the presence of the nu = 0, +/-1 QH states indicates that the Landau level at the charge neutral Dirac point splits into four sub-levels, lifting both sublattice and spin degeneracy, thereby potentially indicating a many-body correlation in this LL. The QH effect at nu = +/-4 is investigated in tilted magnetic fields and is attributed to lifting of the n = +/-1 spin-degeneracy of the Landau level.; We devote one chapter to the investigation of multi-layer graphene. Strong conductance modulation as a function of gate voltage is observed in the thin crystallite devices (thickness ∼ 12 nm). The temperature-dependent resistivity data are analyzed in the frame work of the simple two-band (STB) model. They indicate more boundary scattering contribution in the thinner graphite samples. Galvanomagnetic transport study those samples shows strong modulation of the Hall resistance as well as the magneto-resistance, a phenomena that was not observed before in the bulk, has been observed as the applied gate voltage changes. The Landau level formation of electron and hole carriers is also tuned by the gate. The observed phenomenon can be well described by the STB model, taking into account the carrier density gradient induced by the gate electrode. By fitting the temperature damping of the magneto-resistance oscillations, we obtain the effective carrier masses in the mesoscopic graphite samples.