A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian 1 . Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations 2-5 . Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, freestanding graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene.We investigated the reflectance R(ω) and transmission T (ω) of graphene samples on a SiO 2 /Si substrate (inset of Fig. 1a) as a function of gate voltage V g at 45 K (see the Methods section). We start with data taken at the charge-neutrality point V CN : the gate voltage corresponding to the minimum d.c. conductivity and zero total charge density (inset of Fig. 1c). Figure 1a shows R(ω) of a graphene gated structure (graphene/SiO 2 /Si) at V CN = 3 V normalized by reflectance of the substrate R sub (ω). R sub (ω) is dominated by a minimum around 5,500 cm −1 due to interference effects in SiO 2 . A remarkable observation is that a monolayer of undoped graphene markedly modifies the interference minimum of the substrate leading to a suppression of R sub (ω) by as much as 15%. This observation is significant because it enables us to evaluate the conductivity of graphene near the interference structure, as will be discussed below.Both reflectance and transmission spectra of graphene structures can be modified by a gate voltage. Figure 1b,c shows these modifications at various gate voltages normalized by data atThese data correspond to the Fermi energy E F on the electron side and similar behaviour was observed with E F on the hole side (not shown). At low voltages (<17 V), we found a dip in R(V )/R(V CN ) spectra. With increasing bias, this feature evolves into a peak-dip structure and systematically shifts to higher frequency. The T (V )/T (V CN ) spectra reveal a peak at all voltages, which systematically hardens with increasing bias. A voltage-induced increase in transmission (T (V )/T (V CN ) > 1) signals a decrease of the absorption with bias. Most interestingly, we observed that the frequencies of the main features in R(V )/R(V CN ) and T (V )/T (V CN ) all evolve approximately as √ V . To explore the quasiparticle dynamics under applied voltages, it is imperative to first discuss the two-dimensional (2D) optical conductivity of charge-neutral graphene, σ 1 (ω, V CN ) + iσ 2 (ω, V CN ), extracted from a multilayer analy...

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-1 QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.

Graphene nanoribbons will be essential components in future graphene nanoelectronics. However, in typical nanoribbons produced from lithographically patterned exfoliated graphene, the charge carriers travel only about ten nanometres between scattering events, resulting in minimum sheet resistances of about one kilohm per square. Here we show that 40-nanometre-wide graphene nanoribbons epitaxially grown on silicon carbide are single-channel room-temperature ballistic conductors on a length scale greater than ten micrometres, which is similar to the performance of metallic carbon nanotubes. This is equivalent to sheet resistances below 1 ohm per square, surpassing theoretical predictions for perfect graphene by at least an order of magnitude. In neutral graphene ribbons, we show that transport is dominated by two modes. One is ballistic and temperature independent; the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length--the ballistic mode at 16 micrometres and the other at 160 nanometres. Our epitaxial graphene nanoribbons will be important not only in fundamental science, but also--because they can be readily produced in thousands--in advanced nanoelectronics, which can make use of their room-temperature ballistic transport properties.