Since the celebrated discovery of graphene 1,2 , the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors 3 , Ising superconductors 4-6 that can be tuned into a quantum metal 7 , possible Mott insulators with tunable charge-density waves 8 , and topological semi-metals with edge transport 9,10 . Despite this progress, there is still no 2D crystal with intrinsic magnetism 11-16 , which would be useful for many technologies such as sensing, information, and data storage 17 . Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem 18 . However, magnetic anisotropy removes this restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase transition, showcasing the hallmark thickness-dependent physical properties typical of van der Waals crystals 19-21 . Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect 22 , while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics 13,23 , and van der Waals engineering for novel interface phenomena 17 . Extended DataFigure 1 | Atomic force microscopy (AFM) and magneto-optic Kerr effect (MOKE) measurements of graphite-encapsulated few-layer CrI3. a, Optical microscope image of a bilayer CrI3 flake on 285 nm SiO2. b, AFM data for the CrI3 flake in a encapsulated in graphite, showing a line cut across the flake with a step height of 1.5 nm. c, Optical microscope image of a tri-layer CrI3 flake on 285 nm SiO2. d, AFM data for the CrI3 flake shown in c encapsulated in graphite. A line cut taken across the flake shows a step height of 2.2 nm. All scale bars are 2 µm in length. e and f show the MOKE signal as a function of applied magnetic field for the encapsulated bilayer in b and the encapsulated trilayer in d respectively. Extended Data Figure 2 | Magneto-optical Kerr effect experimental setup. Schematic of the optical setup used to measure Magneto-optical Kerr effect in CrI3 samples. 633 nm optical excitation is provided by a power-stabilized HeNe laser. A mechanical chopper and photoelastic modulator provide intensity and polarization modulation, respectively. The modulated beam is directed through a polarizing beam splitter to the sample, housed in a closed-cycle cryostat at 15 K. A magnetic field is applied at the sample using a 7 T solenoidal superconducting magnet in Farad...

We have achieved mobilities in excess of 200,000 cm 2 V −1 s −1 at electron densities of ∼2×10 11 cm −2 by suspending single layer graphene. Suspension ∼150 nm above a Si/SiO2 gate electrode and electrical contacts to the graphene was achieved by a combination of electron beam lithography and etching. The specimens were cleaned in situ by employing current-induced heating, directly resulting in a significant improvement of electrical transport. Concomitant with large mobility enhancement, the widths of the characteristic Dirac peaks are reduced by a factor of 10 compared to traditional, non-suspended devices. This advance should allow for accessing the intrinsic transport properties of graphene. Graphene, the latest addition to the family of twodimensional (2D) materials, is distinguished from its cousins by its unusual band structure, rendering the quasiparticles in it formally identical to massless, chiral fermions. The experimental realization of graphene thus presents tantalizing opportunities to study phenomena ranging from the topological phase resulting in exotic quantum Hall states [1,2] to the famous Klein paradox -the anomalous tunneling of relativistic particles [3]. However, despite tremendous interest and concerted experimental efforts , the presence of strong impurity scattering -which limits the electron mean free path to less than a micron -has been a major barrier to progress. At the same time, there is strong evidence that graphene is a nearly perfect crystal free of the structural defects [4,5] that characterize most conductors. As a result, it has been put forth that the scattering of charge carriers stems from extrinsic sources [7,8,9,10].Although the exact nature of the scattering that limits the mobility of graphene devices remains unclear, evidence has mounted that interactions with the underlying substrate are largely responsible. Surface charge traps [6,7,8,9], interfacial phonons [11], substrate stabilized ripples [5,10,12], and fabrication residues on or under the graphene sheet may all contribute. Consequently, improving substrate quality or eliminating the substrate altogether by suspending graphene over a trench seems a promising strategy towards higher quality samples. While devices suspended over the substrate were achieved in the past [12,13], they lacked multiple electrical contacts thus precluding transport measurements.In this Letter we report the fabrication of electrically contacted suspended graphene and achieve a tenfold improvement in mobility as compared to the best values reported in the literature for traditional devices fabricated on a substrate. Besides opening new avenues for studying the intrinsic physics of Dirac fermions, this improvement demonstrates the dominant role played by extrinsic scattering in limiting the transport properties of unsuspended graphene samples.The fabrication of a suspended graphene device starts with optically locating a single-layer mechanically exfoliated graphene flake on top of a silicon substrate covered with 300 nm of SiO 2 . Singl...

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The quantum Hall effect (QHE), one example of a quantum phenomenon that occurs on a truly macroscopic scale, has been attracting intense interest since its discovery in 1980 (1). The QHE is exclusive to two-dimensional (2D) metals and has elucidated many important aspects of quantum physics and deepened our understanding of interacting systems. It has also led to the establishment of a new metrological standard, the resistance quantum h/e 2 that contains only fundamental constants of the electron charge e and the Planck constant h (2). As many other quantum phenomena, the observation of the QHE usually requires low temperatures T, typically below the boiling point of liquid helium (1). Efforts to extend the QHE temperature range by, for example, using semiconductors with small effective masses of charge carriers have so far failed to reach T above 30K (3,4). These efforts are driven by both innate desire to observe apparently fragile quantum phenomena under ambient conditions and the pragmatic need to perform metrology at room or, at least, liquid-nitrogen temperatures. More robust quantum states, implied by their persistence to higher T, would also provide added freedom to investigate finer features of the QHE and, possibly, allow higher quantization accuracy (2). Here, we show that in graphene -a single layer of carbon atoms tightly packed in a honeycomb crystal lattice -the QHE can be observed even at room temperature. This is due to the highly unusual nature of charge carriers in graphene, which behave as massless relativistic particles (Dirac fermions) and move with little scattering under ambient conditions (5). Figure 1 shows the room-T QHE in graphene. The Hall conductivity σxy reveals clear plateaux at 2e 2 /h for both electrons and holes, while the longitudinal conductivity ρxx approaches zero (<10Ω) exhibiting an activation energy ∆E ≈600K (Fig. 1B). The quantization in σxy is exact within an experimental accuracy of ≈0.2% (see Fig. 1C Fig. 1B). This implies that, in our experiments at room temperature, ω h exceeded the thermal energy kBT by a factor of 10. Importantly, in addition to the large cyclotron gap, there are a number of other factors that help the QHE in graphene to survive to so high temperatures. First, graphene devices allow for very high carrier concentrations (up to 10 13 cm -2 ) with only a single 2D subband occupied, which is essential to fully populate the lowest LL even in ultra-high B. This is in contrast to traditional 2D systems (for example, GaAs heterostructures) which are either depopulated already in moderate B or exhibit multiple subband occupation leading to the reduction of the effective energy gap to values well below ω h . Second, the mobility µ of Dirac fermions in our samples does not change appreciably from liquid-helium to room temperature. It remains at ≈10,000 cm 2 /Vs, which yields a scattering time of 13 10 − τ sec so that the high field limit 1 >> ⋅ = B µ ωτ is reached in fields of several T. These characteristics of graphene foster hopes for the room-T QHE obs...

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...

2The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical (NEMS) applications. We demonstrate fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the MHz range. The strong dependence of the resonant frequency on applied gate voltage can be fit to a membrane model, which yields the mass density and built-in strain. Upon removal and addition of mass, we observe changes in both the density and the strain, indicating that adsorbates impart tension to the graphene. Upon cooling, the frequency increases; the shift rate can be used to measure the unusual negative thermal expansion coefficient of graphene. The quality factor increases with decreasing temperature, reaching ~10 4 at 5 K. By establishing many of the basic attributes of monolayer graphene resonators, these studies lay the groundwork for applications, including high-sensitivity mass detectors.Since its discovery in 2004 1 , graphene has attracted attention because of its unusual two dimensional (2D) structure and potential for applications [2][3][4] . Due to its exceptional mechanical properties 5 and low mass density, graphene is an ideal material for use in nanoelectromechanical systems (NEMS), which are of great interest both for fundamental studies of mechanics at the nanoscale and for a variety of applications, including force 6 , position 7 and mass 8 sensing. Recent studies using optical and scanned probe detection have shown that micron-size graphene flakes can act as MHz-range NEMS resonators 9,10 . Electrical readout of these devices is important for integration and attractive for many applications. In addition, characterization of the basic attributes of these devices, including their response to applied voltage, added mass, and changes 3 in temperature, allows detailed modeling of their behavior, which is crucial for rational device design.Samples are fabricated by first locating monolayer graphene flakes on Si/SiO 2 substrates, then patterning metal electrodes and etching away the SiO 2 to yield suspended graphene. The ability to choose monolayers in advance provides control of device properties and facilitates electrical readout. The fabrication method also provides control over the lateral dimensions; devices can be either micron-wide sheets (Fig. 1a) or lithographically defined nanoribbons (Fig.1b). Because the etchant diffuses freely under the sheets, the SiO 2 is removed at the same rate everywhere under the graphene, so that the distance between the substrate and the suspended sheet is constant (~100 nm) across each device. For the same reason, the portion of each electrode that contacts the graphene is also suspended 11,12 , as depicted in Fig. 1c.Following previous work 13-15 , we implemented an all-electrical high-frequency mixing approach ( Fig. 1d) and 5). In addition to being of fundamental interest as a coupled nanoscale-microscale system, these resonances demonstrate that grap...

The resistivity of ultra-clean suspended graphene is strongly temperature (T ) dependent for 5 K< T < 240 K. At T ∼ 5 K transport is near-ballistic in a device of ∼ 2 µm dimension and a mobility ∼ 170, 000 cm 2 /Vs. At large carrier density, n > 0.5×10 11 cm −2 , the resistivity increases with increasing T and is linear above 50 K, suggesting carrier scattering from acoustic phonons. At T = 240 K the mobility is ∼ 120, 000 cm 2 /Vs, higher than in any known semiconductor. At the charge neutral point we observe a non-universal conductivity that decreases with decreasing T , consistent with a density inhomogeneity <10 8 cm −2 .

An even-denominator rational quantum number has been observed in the Hall resistance of a twodimensional electron system. At partial filling of the second Landau level v=2+ y = y and at temperatures below 100 mK, a fractional Hall plateau develops at p xy =(h/e 2 )/y defined to better than 0.5%. Equivalent even-denominator quantization is absent in the lowest Landau level under comparable conditions.