We have measured the quantum-Hall activation gaps in graphene at filling factors ν = 2 and ν = 6 for magnetic fields up to 32 T and temperatures from 4 K to 300 K. The ν = 6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at ν = 2 is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields B > 20 T and temperatures T > 100 K. We explain this surprising behavior by a narrowing of the lowest Landau level. The quantum Hall effect (QHE) observed in twodimensional electron systems (2DESs) is one of the fundamental quantum phenomena in solid state physics. Since its discovery in 1980 [1] it has been important for fundamental physics [2] and application to quantum metrology [3]. Recently a new member joined the family of 2DESs: graphene, a single layer of carbon atoms [4,5,6,7,8]. Graphene displays a unique charge carrier spectrum of chiral Dirac fermions [9,10] and enriches the QHE with a half integer QHE of massless relativistic particles observed in single-layer graphene [11,12,13,14] and a novel type of integer QHE of massive chiral fermions in bilayers [15,16]. Moreover, the band structure of graphene even allows the observation of the QHE up to room temperature [17]. Since localization in conventional quantum Hall systems is already fully destroyed at moderate temperatures, no QHE has been observed at temperatures above 30 K until very recently. Therefore, understanding a room temperature QHE in graphene goes far beyond our comprehension of the traditional QHE.In order to access this intriguing phenomenon in more detail we report here systematic measurements of the inter Landau level activation gap in graphene for magnetic fields up to 32 T. We will show that the gap between the zeroth and the first Landau level approaches the bare, unbroadened Landau-level separation for high magnetic fields and we explain these findings by a much narrower lowest Landau level compared to the other ones. In contrast, for higher Landau levels, the measured activation gap behaves as expected for equally broadened states.The single-layer graphene samples (Fig. 1c) were made by the micromechanical exfoliation of crystals of natural graphite, followed by the selection of single-layer flakes using optical microscopy and atomic force microscopy [4,5]. A large enough single-layer flake is contacted by Au electrodes and patterned into a Hall bar by ebeam lithography with subsequent reactive plasma etching. The structures are deposited on a SIMOX-substrate with a 300 nm thick SiO 2 layer on top of heavily doped Si. The Si is used as a backgate allowing to tune the carrier concentration n to either holes (n < 0) or electrons (n > 0) with a mobility µ = 15000 cm 2 (Vs) −1 at 4.2 K. Due to the presence of surface impurities on the graphene sheet [18] the devices are generally stronglyhole doped with a charge neutrality point situated at a positive back-gate voltage. In order to restore a pristine undoped situation we...

We have measured a strong increase of the low-temperature resistivity ρxx and a zero-value plateau in the Hall conductivity σxy at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in ρxx and the anomalous ν = 0 plateau in σxy in terms of coexisting electrons and holes in the same spin-split zero-energy Landau level.PACS numbers: 71.70.Di In a magnetic field, graphene displays an unconventional Landau-level spectrum of massless chiral Dirac fermions [1,2,3,4]. In particular, a Landau level shared equally between electrons and holes of opposite chirality exists at zero-energy around the charge neutrality point (CNP). Due to the coexistence of carriers with opposite charge, graphene behaves as a compensated semimetal at the CNP with a finite resistivity ρ xx and a zero Hall resistivity ρ xy .Recently, the nature of the CNP in high magnetic fields has attracted considerable theoretical interest (see Ref.[5] and references there in). Experimentally, in the metallic regime, the transport behavior around the CNP can be explained using counter-propagating edge channels [6]. On the other hand, the high-field resistivity at the CNP was shown to diverge strongly, an effect recently analyzed in terms of a Kosterlitz-Thouless-type localization behavior [7]. In high quality graphene samples, made from Kish-graphite, Zhang et al. [8,9] have observed an additional fine structure of the lowest Landau level in the form of a ν = ±1 state. The existence of this state is proposed to be caused by a spontaneous symmetry breaking at the CNP and an interaction-induced splitting of the two levels resulting from this.Here we present an experimental study of the transport properties of the zero-energy Landau level in high magnetic fields and at low temperatures. Calculating the conductivities from an increasing magneto-resistance at the CNP and a zero-crossing of the Hall resistance yields a zero minimum in the longitudinal conductivity σ xx and a quantized zero-plateau in the Hall-conductivity σ xy . The temperature dependence of the σ xx -minimum displays an activated behavior. We explain this transition with a simple model involving the opening of a spingap (30 K at 30 T) in the zeroth Landau level. We do not observe any indication for a spontaneous symmetry breaking and an interaction-induced splitting at ν = ±1 as reported in Refs. 8 and 9 and we tentatively assign this to the relatively larger disorder in our samples made from natural graphite.The monolayer graphene devices (see top left inset Fig. 1a) are deposited on Si/SiO 2 substrate using methods as already reported elsewhere [10,11]. The doped Si acts as a back-gate and allows to adjust the chargecarrier concentration in the graphene film from highly hole-doped to highly electron-doped. Prior to the experiments the...

We use an atomic force microscope (AFM) to manipulate graphene films on a nanoscopic length scale. By means of local anodic oxidation with an AFM we are able to structure isolating trenches into single-layer and few-layer graphene flakes, opening the possibility of tabletop graphene based device fabrication. Trench sizes of less than 30 nm in width are attainable with this technique. Besides oxidation we also show the influence of mechanical peeling and scratching with an AFM of few layer graphene sheets placed on different substrates.

Due to the predominantly surface character of graphene, it is highly suitable for functionalization with external atoms and/or molecules leading to a plethora of new and interesting phenomena. Here we show ferromagnetic properties of hydrogenfunctionalized epitaxial graphene on SiC. Ferromagnetism in such a material is not directly evident as it is inherently composed of only non-magnetic constituents. Our results nevertheless show strong ferromagnetism, which cannot be explained by simple magnetic impurities. The ferromagnetism is unique to hydrogenated epitaxial graphene on SiC, where interactions with the interfacial buffer layer play a crucial role. We argue that the origin of the observed ferromagnetism is governed by electron correlation effects of the narrow Si-dangling-bond (Si-DB) states in the buffer layer exchangecoupled to localized states in the hydrogenated graphene layer. This forms a quasithree-dimensional ferromagnet with a Curie temperature higher than 300 K.Owing to its capability of ballistic transport over micrometer distances 1 , as well as its very long spin relaxation time and spin relaxation length 2, 3 , graphene represents a close-to-ideal material for spintronic applications 4 . In this context, considerable effort has recently been directed to rendering graphene ferromagnetic via chemical modification. Thus far, ferromagnetic order in graphene has been attained through covalent functionalization, involving the linkage of radical species like the spin-bearing carbon atom of an organic molecule or hydrogen atoms to the graphene layer [5][6][7][8][9][10][11][12][13][14][15][16][17] . Along these lines, functionalization of epitaxial graphene by aryl radicals has been reported to yield disordered magnetism, comprising a mixture of ferromagnetic, superparamagnetic and antiferromagnetic regions 18 .With the aid of combined atomic and magnetic force microscopy, it could be proven that these randomly dispersed regions are constituted by the attached moieties. This lack of a periodic functionalization pattern of the graphene sheet prevents the achievement of long range ferromagnetic order, thus limiting the use of such samples in spintronic devices.Furthermore, room temperature ferromagnetism has been detected in partially hydrogenated epitaxial graphene grown on silicon carbide (SiC), and attributed to hydrogen monomers bonded to the graphene sheet 12 . Despite these accomplishments, however, both the mechanism underlying the ferromagnetic ordering, and the role played by the SiC substrate used for the epitaxial graphene growth, has not yet been clarified. Here, we experimentally demonstrate that spin ordering within hydrogenated epitaxial graphene critically depends on the presence of the underlying buffer layer. In addition, it is shown that the created magnetic 3 areas are distributed over the entire graphene sheet, thus enabling to effectively tune the overall magnetization through the density of attached hydrogen atoms.To explore the ferromagnetism in epitaxial graphene, we use samples ...

Quantum dots of around 20 nm in size are fabricated using local anodic oxidation. The behavior of the smallest dots in a magnetic field (see image) allows the identification of the charge‐neutrality point and distinguishing of the states with one electron, no charge, and one hole left inside the quantum dot.

No abstract

Graphene antidot lattices (GALs) offer an attractive approach to band-gap engineering in graphene. Theoretical studies indicate that the size of the opened gap is sensitive to the shape, size, and architecture of the nanoholes introduced into the graphene sheet. We have investigated the temperature-dependent electrical conductivity of GALs comprising 50-nm-diameter nanoholes with a pitch of 80, 100, and 200 nm, respectively. The data reveal the presence of localized states within a transport gap, whose interactions lead to a soft Coulomb gap and associated Efros-Shklovskii variable range hopping (ES-VRH). This conduction type is preserved upon application of magnetic fields up to 1 Tesla, above which a transition to Mott variable range hopping occurs. Such a crossover can alternatively be introduced at zero magnetic fields by increasing either the nanohole spacing or the gate-controlled carrier concentration. Furthermore, at intermediate magnetic fields, the hopping exponent assumes a value of 2/3, as predicted by percolation theory for ES-VRH under this condition.

We have performed a metrological characterization of the quantum Hall resistance in a 1 µm wide graphene Hall-bar. The longitudinal resistivity in the center of the ν = ±2 quantum Hall plateaus vanishes within the measurement noise of 20 mΩ upto 2 µA. Our results show that the quantization of these plateaus is within the experimental uncertainty (15 ppm for 1.5 µA current) equal to that in conventional semiconductors. The principal limitation of the present experiments are the relatively high contact resistances in the quantum Hall regime, leading to a significantly increased noise across the voltage contacts and a heating of the sample when a high current is applied. The Hall resistance in two-dimensional electron systems (2DESs) is quantized in terms of natural constants only, R H = h/ie 2 with i an integer number [1]. Due to its high accuracy and reproducibility this quantized Hall resistance in conventional 2DESs is nowadays used as a universal resistance standard [2].Recently a new type of half-integer quantum Hall effect [3,4] was found in graphene, the purely twodimensional form of carbon [5]. Its unique electronic properties [6] (mimicking the behavior of charged chiral Dirac fermions [7,8]) allow the observation of a quantized Hall resistance up to room-temperature [9, 10], making graphene a promising candidate for a high-temperature quantum resistance standard. Although the quantized resistance in graphene around the ν = 2 plateau is generally believed to be equal to h/2e 2 , up to now it has not been shown to meet a metrological standard. In this Letter we present results of the first metrological characterization of the quantum Hall resistance in graphene. In particular, we will address the present accuracy of quantization (15 ppm) and the experimental conditions limiting this accuracy.Our sample consists of a graphene Hall-bar on a Si/SiO 2 substrate forming a charge-tunable ambipolar field-effect transistor (A-FET), where the carrier concentration can be tuned with a back-gate voltage V g [11]. In order to remove most of the surface dopants that make graphene generally strongly hole doped and limit its mobility, we have annealed the sample in-situ for several hours at 380 K prior to cooling it down slowly (∆T /∆t < 3 K/min) to the base temperature (0.35 K) of a toploading 3 He-system equipped with a 15 T superconducting magnet. After annealing, the charge neutrality point in the A-FET was situated at 5 V and the sample dis- * Electronic address: J.Giesbers@science.ru.nl † Electronic address: U.Zeitler@science.ru.nl 2 µm