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Patterning graphene with a spatially periodic potential provides a powerful means to modify its electronic properties1–3. In particular, in twisted bilayers, coupling to the resulting moire superlattice yields an isolated flat band that hosts correlated many-body phases4,5. However, both the symmetry and strength of the effective moire potential are constrained by the constituent crystals, limiting its tunability. Here, we have exploited the technique of dielectric patterning6 to subject graphene to a one-dimensional electrostatic superlattice (SL)1. We observed the emergence of multiple Dirac cones and found evidence that with increasing SL potential the main and satellite Dirac cones are sequentially flattened in the direction parallel to the SL basis vector, behaviour resulting from the interaction between the one-dimensional SL electric potential and the massless Dirac fermions hosted by graphene. Our results demonstrate the ability to induce tunable anisotropy in high-mobility two-dimensional materials, a long-desired property for novel electronic and optical applications7,8. Moreover, these findings offer a new approach to engineering flat energy bands where electron interactions can lead to emergent properties9. Dielectric patterning allows tunable anisotropy in high-mobility one-dimensional graphene electrostatic superlattices.

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of $Z\approx 0.4$, that remain superconducting under magnetic fields larger than $18$ T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the $\nu = 4$ Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\nu }}={{0}},\pm {{1}}$$\end{document}ν=0,±1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields., The broken-symmetry edge states that are the hallmark of the quantum Hall effect in graphene have eluded spatial measurements. Here, the authors spatially map the quantum Hall broken-symmetry edge states using atomic force microscopy and show a gapped ground state proceeding from the bulk through to the quantum Hall edge boundary.

When light-matter polaritons travel in periodic media, they acquire properties akin to Bloch quasi-particles in crystals., Efficient control of photons is enabled by hybridizing light with matter. The resulting light-matter quasi-particles can be readily programmed by manipulating either their photonic or matter constituents. Here, we hybridized infrared photons with graphene Dirac electrons to form surface plasmon polaritons (SPPs) and uncovered a previously unexplored means to control SPPs in structures with periodically modulated carrier density. In these periodic structures, common SPPs with continuous dispersion are transformed into Bloch polaritons with attendant discrete bands separated by bandgaps. We explored directional Bloch polaritons and steered their propagation by dialing the proper gate voltage. Fourier analysis of the near-field images corroborates that this on-demand nano-optics functionality is rooted in the polaritonic band structure. Our programmable polaritonic platform paves the way for the much-sought benefits of on-the-chip photonic circuits.

Significance Micrometer-sized uniform four-layer (ABCA) rhombohedral graphene is realized by introducing a small twist angle between two bilayers of Bernal graphene. By means of scanning tunneling spectroscopy we observe an extremely sharp van Hove singularity of 3–5-meV half-width and a correlated many-body gap of 9.5 meV at neutrality, thus making small twisted double-bilayer graphene a unique platform to realize electronic correlations in the absence of a moiré potential. Furthermore, ABCA graphene domain walls display tunable topological edge states, of great interest in Floquet engineering., Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl3, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl3 interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl3 at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: EF = 0.6 eV (n = 2.7 × 1013 cm–2). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl3 giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping., Research at Columbia was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. J.Z., L.X., and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056 - 390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19) and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL). J.Z., L.X., and A.R. would like to acknowledge Nicolas Tancogne-Dejean for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. Work at ORNL was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant JPMXP0112101001, JSPS KAKENHI Grant JP20H00354, and the CREST (JPMJCR15F3), JST. S.E.N. was supported by the Division of Scientific User Facilities of the U.S. DOE Basic Energy Sciences. M.M.F. acknowledges support from the Office of Naval Research Grant N00014-18-1-2722. D.N.B. is the Vannevar Bush Faculty ONR-VB: N00014-19-1-2630 and Moore investigator in Quantum Materials EPIQS program #9455. A.S.M acknowledges support from award 80NSSC19K1210 under the NASA Laboratory Analysis of Returned Samples program.

Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with an extraordinary degree of control and tunability. In graphene-based moir\'e heterostructures, the correlated phase diagram and band topology depend strongly on the number of graphene layers, their relative stacking arrangement, and details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer-bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as well as topological magnetic states. Because of its low symmetry, the phase diagram of tMBG approximates that of twisted bilayer graphene when an applied perpendicular electric field points from the bilayer towards the monolayer graphene, or twisted double bilayer graphene when the field is reversed. In the former case, we observe correlated states which undergo an orbitally driven insulating transition above a critical perpendicular magnetic field. In the latter case, we observe the emergence of electrically tunable ferromagnetism at one-quarter filling of the conduction band, with a large associated anomalous Hall effect. Uniquely, the magnetization direction can be switched purely with electrostatic doping at zero magnetic field. Our results establish tMBG as a highly tunable platform for investigating a wide array of tunable correlated and topological states., Comment: 21 Pages, 20 Figures

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe2, with signatures of collective phases observed over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. At a 5.1° twist, zero-resistance pockets were observed on doping away from half filling at temperatures below 3 K, which indicates a possible transition to a superconducting state. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice., Studies of the tunable correlated states in the twisted bilayer WSe2 were supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. The synthesis of the WSe2 crystals was supported by the NSF MRSEC programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The theoretical work was supported by the European Research Council (ERC-2015-AdG694097), cluster of Excellence AIM, SFB925 and Grupos Consolidados (IT1249-19). The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck–New York Center for Non-Equilibrium Quantum Phenomena.

Graphene-based heterostructures display a variety of phenomena that are strongly tunable by electrostatic local gates. Monolayer graphene (MLG) exhibits tunable surface plasmon polaritons, as revealed by scanning nano-infrared experiments. In bilayer graphene (BLG), an electronic gap is induced by a perpendicular displacement field. Gapped BLG is predicted to display unusual effects such as plasmon amplification and domain wall plasmons with significantly larger lifetime than MLG. Furthermore, a variety of correlated electronic phases highly sensitive to displacement fields have been observed in twisted graphene structures. However, applying perpendicular displacement fields in nano-infrared experiments has only recently become possible [Li, H.; Nano Lett. 2020, 20, 3106-3112]. In this work, we fully characterize two approaches to realizing nano-optics compatible top gates: bilayer MoS2 and MLG. We perform nano-infrared imaging on both types of structures and evaluate their strengths and weaknesses. Our work paves the way for comprehensive near-field experiments of correlated phenomena and plasmonic effects in graphene-based heterostructures.

Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable band gap and strong spin-orbit coupling hold promise for properties beyond graphene. Measurements under large magnetic fields have revealed an unusual LL structure, distinct from other 2D electron systems. However, owing to limited sample quality and poor electrical contact, probing the lowest Landau levels (LLs) has been challenging, and observation of electron correlations within the fractionally filled LLs regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of ML WSe$_2$ in the extreme quantum limit, and observe fractional quantum Hall (FQH) states in the lowest three LLs. The odd-denominator FQH sequences demonstrate a systematic evolution with the LL orbital index, which has not been observed in any other system but is consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime., typos in v1 corrected

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing 1 , topological protection2,3 and dipole-forbidden absorption 4 . A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes 5 . Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial 8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications. The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

Photonic crystals are commonly implemented in media with periodically varying optical properties. Photonic crystals enable exquisite control of light propagation in integrated optical circuits, and also emulate advanced physical concepts. However, common photonic crystals are unfit for in-operando on/off controls. We overcome this limitation and demonstrate a broadly tunable two-dimensional photonic crystal for surface plasmon polaritons. Our platform consists of a continuous graphene monolayer integrated in a back-gated platform with nano-structured gate insulators. Infrared nano-imaging reveals the formation of a photonic bandgap and strong modulation of the local plasmonic density of states that can be turned on/off or gradually tuned by the applied gate voltage. We also implement an artificial domain wall which supports highly confined one-dimensional plasmonic modes. Our electrostatically-tunable photonic crystals are derived from standard metal oxide semiconductor field effect transistor technology and pave a way for practical on-chip light manipulation., Traditional photonic crystals consist of periodic media with a pre-defined optical response. Here, the authors combine nanostructured back-gate insulators with a continuous layer of graphene to demonstrate an electrically tunable two-dimensional photonic crystal suitable for controlling the propagation of surface plasmon polaritons.

Controlling two-dimensional twist In heterostructures assembled from two-dimensional materials such as graphene, electron tunneling between layers varies strongly with the rotation angle between the crystal lattices. Usually, the twist angle between layers is fixed after assembly. Ribeiro-Palau et al. encapsulated graphene with boron nitride, but the top boron nitride flake was shaped so that an atomic force microscope tip could push on it to vary the twist angle by as little as 0.2°. They observed variations with twist angle in properties such as the charge neutrality point, which would be difficult to observe in static rotated structures. Science , this issue p. 690

In heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch or rotation between the layers results in long-wavelength moir\'e superlattices. These moir\'e patterns can drive significant band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity, magnetism, fractional Chern insulating states, and moir\'e excitons. Here, we investigate monolayer graphene encapsulated between two crystals of boron nitride (BN), where the rotational alignment between all three components can be varied. We find that band gaps in the graphene arising from perfect rotational alignment with both BN layers can be modified substantially depending on whether the relative orientation of the two BN layers is 0 or 60 degrees, suggesting a tunable transition between the absence or presence of inversion symmetry in the heterostructure. Small deviations ($, Comment: 14 Pages, 12 Figures

International audience; We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N=2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell’s law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.

Andreev reflection occurs at the interface of a metal and a superconductor when an incident electron in the metal gets ‘reflected’ as a hole travelling on the same path. Replace the metal with graphene and specular reflection may instead take place. Electrons incident from a normal metal onto a superconductor are reflected back as holes—a process called Andreev reflection1,2,3. In a normal metal where the Fermi energy is much larger than a typical superconducting gap, the reflected hole retraces the path taken by the incident electron. In graphene with low disorder, however, the Fermi energy can be tuned to be smaller than the superconducting gap. In this unusual limit, the holes are expected to be reflected specularly at the superconductor–graphene interface owing to the onset of interband Andreev processes, where the effective mass of the reflected holes changes sign4,5. Here we present measurements of gate-modulated Andreev reflections across the low-disorder van der Waals interface formed between graphene and the superconducting NbSe2. We find that the conductance across the graphene–superconductor interface exhibits a characteristic suppression when the Fermi energy is tuned to values smaller than the superconducting gap, a hallmark for the transition between intraband retro Andreev reflections and interband specular Andreev reflections.

Mixing interactions and superlattices Under the influence of an external magnetic field, the energies of electrons in two-dimensional systems group into the so-called Landau levels. In the cleanest samples, interactions among electrons lead to fractional quantum Hall (FQH) states. If such a system is then subjected to a superlattice potential, it is unclear whether the fragile FQH states will survive. To address this question, Wang et al. sandwiched graphene between two layers of hexagonal boron nitride. Transport measurements on the superlattice showed that some FQH states did survive. Furthermore, the interplay between interactions and the superlattice potential produced additional, anomalous states. Science , this issue p. 1231

We present the characterization of ballistic graphene field-effect transistors (GFETs) with an effective oxide thickness of 3.5 nm. Graphene channels are fully encapsulated within hexagonal boron nitride, and self-aligned contacts are formed to the edge of the single-layer graphene. Devices of channel lengths ( $L_{G})$ down to 67 nm are fabricated, and a virtual-source transport model is used to model the resulting current–voltage characteristics. The mobility and source-injection velocity as a function of $L_{G}$ yields a mean-free-path, ballistic velocity, and effective mobility of 850 nm, $9.3\times 10^{7}$ cm/s, and 13 700 cm2/Vs, respectively, which are among the highest velocities and mobilities reported for GFETs. Despite these best-in-class attributes, these devices achieve transconductance ( $g_{m})$ and output conductance ( $g_{{\mathrm{ds}}})$ of only 600 and 300 $\mu \text{S}/\mu \text{m}$ , respectively, due to the fundamental limitations of graphene’s quantum capacitance and zero-bandgap. $g_{m}$ values, which are less than those of comparable ballistic silicon devices, benefit from the high ballistic velocity in graphene but are degraded by an effective gate capacitance reduced by the quantum capacitance. The $g_{{\mathrm{ds}}}$ values, which limit the effective power gain achievable in these devices, are significantly worse than comparable silicon devices due to the properties of the zero-bandgap graphene channel.

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry., Main text: 5 pages, 3 Figures. Supplements: 8 pages, 5 figures

Heterostructures of atomically-thin materials have attracted significant interest owing to their ability to host novel electronic properties fundamentally distinct from their constituent layers. In the case of graphene on boron nitride, the closely-matched lattices yield a moir\'e superlattice that modifies the graphene electron dispersion and opens gaps both at the primary Dirac point (DP) and the moir\'e-induced secondary Dirac point (SDP) in the valence band. While significant effort has focused on controlling the superlattice period via the rotational stacking order, the role played by the magnitude of the interlayer coupling has received comparatively little attention. Here, we modify the interaction between graphene and boron nitride by tuning their separation with hydrostatic pressure. We observe a dramatic enhancement of the DP gap with increasing pressure, but little change in the SDP gap. Our surprising results identify the critical role played by atomic-scale structural deformations of the graphene lattice and reveal new opportunities for band structure engineering in van der Waals heterostructures., Comment: 26 Pages, 16 Figures. (v2) Main text and figures are updated

The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and SL fabrication processes, we address the intractable tradeoff between device processing and mobility degradation that constrains SL engineering in conventional systems. The improved electrostatics of atomically thin materials moreover allows smaller wavelength SL patterns than previously achieved. Replica Dirac cones in ballistic graphene devices with sub 40nm wavelength SLs are demonstrated, while under large magnetic fields we report the fractal Hofstadter spectra from SLs with designed lattice symmetries vastly different from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability., 15 pages, 4 figures

Coulomb interaction between two closely spaced parallel layers of electron system can generate the frictional drag effect by interlayer Coulomb scattering. Employing graphene double layers separated by few layer hexagonal boron nitride (hBN), we investigate density tunable magneto- and Hall-drag under strong magnetic fields. The observed large magneto-drag and Hall-drag signals can be related with Laudau level (LL) filling status of the drive and drag layers. We find that the sign and magnitude of the magneto- and Hall-drag resistivity tensor can be quantitatively correlated to the variation of magneto-resistivity tensors in the drive and drag layers, confirming a theoretical formula for magneto-drag in the quantum Hall regime. The observed weak temperature dependence and $\sim B^2$ dependence of the magneto-drag are qualitatively explained by Coulomb scattering phase-space argument., 5 pages, 3 figures

We present a detailed study of gaseous Br2 adsorption and charge transfer on graphene, combining in situ Raman spectroscopy and density functional theory (DFT). When graphene is encapsulated by hexagonal boron nitride (h-BN) layers on both sides, in a h-BN/graphene/h-BN sandwich structure, it is protected from doping by strongly oxidizing Br2. Graphene supported on only one side by h-BN shows strong hole doping by adsorbed Br2. Using Raman spectroscopy, we determine the graphene charge density as a function of pressure. DFT calculations reveal the variation in charge transfer per adsorbed molecule as a function of coverage. The molecular adsorption isotherm (coverage versus pressure) is obtained by combining Raman spectra with DFT calculations. The Fowler-Guggenheim isotherm fits better than the Langmuir isotherm. The fitting yields the adsorption equilibrium constant (∼0.31 Torr(-1)) and repulsive lateral interaction (∼20 meV) between adsorbed Br2 molecules. The Br2 molecule binding energy is ∼0.35 eV. We estimate that at monolayer coverage each Br2 molecule accepts 0.09 e- from single-layer graphene. If graphene is supported on SiO2 instead of h-BN, a threshold pressure is observed for diffusion of Br2 along the (somewhat rough) SiO2/graphene interface. At high pressure, graphene supported on SiO2 is doped by adsorbed Br2 on both sides.

High electron mobility is one of graphene's key properties, exploited for applications and fundamental research alike. Highest mobility values are found in heterostructures of graphene and hexagonal boron nitride, which consequently are widely used. However, surprisingly little is known about the interaction between the electronic states of these layered systems. Rather pragmatically, it is assumed that these do not couple significantly. Here we study the unoccupied band structure of graphite, boron nitride and their heterostructures using angle-resolved reflected-electron spectroscopy. We demonstrate that graphene and boron nitride bands do not interact over a wide energy range, despite their very similar dispersions. The method we use can be generally applied to study interactions in van der Waals systems, that is, artificial stacks of layered materials. With this we can quantitatively understand the ‘chemistry of layers' by which novel materials are created via electronic coupling between the layers they are composed of., Heterostructures of graphene and hexagonal boron nitride have great potential for high-mobility electronics, yet little is known about the electronic interaction between these two atomically thin materials. Here, the authors perform angle-resolved reflected-electron spectroscopy to unveil their interplay.

Better Contact Along the Edge Electrical contact to graphene is normally done with metal contacts on its flat face, where there are few strong bonding sites for the metal. Wang et al. (p. 614 ) encapsulated graphene with hexagonal boron nitride sheets and made metal contacts along its edge, where bonding orbitals are exposed. The resulting heterostructures had high electronic performance, with room-temperature carrier mobilities near the theoretical phonon-scattering limit.

Kelvin probe microscopy in ultrahigh vacuum is used to image the local electrostatic potential fluctuations above hexagonal boron nitride (h-BN) and SiO2, common substrates for graphene. Results are compared to a model of randomly distributed charges in a two-dimensional (2D) plane. For SiO2, the results are well modeled by 2D charge densities ranging from 0.24 to 2.7 × 10(11) cm(-2), while h-BN displays potential fluctuations 1-2 orders of magnitude lower than SiO2, consistent with the improvement in charge carrier mobility for graphene on h-BN compared to SiO2. Electron beam exposure of SiO2 increases the charge density fluctuations, creating long-lived metastable charge populations of ~2 × 10(11) cm(-2) at room temperature, which can be reversed by heating.

Two-dimensional atomic sheets of graphene represent a new class of nanoscale materials with potential applications in electronics. However, exploiting the intrinsic characteristics of graphene devices has been problematic due to impurities and disorder in the surrounding dielectric and graphene/dielectric interfaces. Recent advancements in fabricating graphene heterostructures by alternately layering graphene with crystalline hexagonal boron nitride (hBN), its insulating isomorph, have led to an order of magnitude improvement in graphene device quality. Here, recent developments in graphene devices utilizing boron-nitride dielectrics are reviewed. Field-effect transistor (FET) characteristics of these systems at high bias are examined. Additionally, existing challenges in material synthesis and fabrication and the potential of graphene/BN heterostructures for novel electronic applications are discussed.

A quantum phase transition from an antiferromagnetic to a ferromagnetic state is now measured in graphene bilayers. This observation supports the idea that bilayer graphene can sustain counter-propagating spin-polarized edge modes in analogy to the quantum spin Hall effect seen in topological insulators.

We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in graphene and related topological states in other two-dimensional electron systems., Comment: 4 figures

Spatially indirect excitons can be created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite Boson. Because there is no recombination pathway such excitons are long lived making them accessible to transport studies. Moreover, the ability to independently tune both the intralayer charge density and interlayer electron-hole separation provides the capability to reach the low-density, strongly interacting regime where a BEC-like phase transition into a superfluid ground state is anticipated. To date, transport signatures of the superfluid condensate phase have been seen only in quantum Hall bilayers composed of double well GaAs heterostructures. Here we report observation of the exciton condensate in the quantum Hall effect regime of double layer structures of bilayer graphene. Correlation between the layers is identified by quantized Hall drag appearing at matched layer densities, and the dissipationless nature of the phase is confirmed in the counterflow geometry. Independent tuning of the layer densities and interlayer bias reveals a selection rule involving both the orbital and valley quantum number between the symmetry-broken states of bilayer graphene and the condensate phase, while tuning the layer imbalance stabilizes the condensate to temperatures in excess of 4K. Our results establish bilayer graphene quantum wells as an ideal system in which to study the rich phase diagram of strongly interacting Bosonic particles in the solid state., 7 pages, 4 figures. Main text and figures are updated

Robust electrical contact of bulk conductors to two-dimensional (2D) material, such as graphene, is critical to the use of these 2D materials in practical electronic devices. Typical metallic contacts to graphene, whether edge or areal, yield a resistivity of no better than 100 Ω μm but are typically >10 kΩ μm. In this Letter, we employ single-crystal graphite for the bulk contact to graphene instead of conventional metals. The graphite contacts exhibit a transfer length up to four-times longer than in conventional metallic contacts. Furthermore, we are able to drive the contact resistivity to as little as 6.6 Ω μm2 by tuning the relative orientation of the graphite and graphene crystals. We find that the contact resistivity exhibits a 60° periodicity corresponding to crystal symmetry with additional sharp decreases around 22° and 39°, which are among the commensurate angles of twisted bilayer graphene.

Coulomb drag between parallel quantum wells provides a uniquely sensitive measurement of electron correlations since the drag response depends on interactions only. Recently it has been demonstrated that a new regime of strong interactions can be accessed for devices consisting of two monlolayer graphene (MLG) crystals, separated by few layer hexagonal boron-nitride. Here we report measurement of Coulomb drag in a double bilayer graphene (BLG) stucture, where the interaction potential is anticipated to be yet further enhanced compared to MLG. At low temperatures and intermediate densities a new drag response with inverse sign is observed, distinct from the momentum and energy drag mechanisms previously reported in double MLG. We demonstrate that by varying the device aspect ratio the negative drag component can be suppressed and a response showing excellent agreement with the density and temperature dependance predicted for momentum drag in double BLG is found. Our results pave the way for pursuit of emergent phases in strongly interacting bilayers, such as the exciton condensate.

Using Raman spectroscopy, we study the environmental sensitivity of mechanically exfoliated and electrically floating single-layer graphene transferred onto a hexagonal boron nitride (h-BN) substrate, in comparison with graphene deposited on a SiO(2) substrate. In order to understand and isolate the substrate effect on graphene electrical properties, we model and correct for Raman optical interference in the substrates. As-deposited and unannealed graphene shows a large I(2D)/I(G) ratio on both substrates, indicating extremely high quality, close to that of graphene suspended in vacuum. Thermal annealing strongly activates subsequent environmental sensitivity on the SiO(2) substrate; such activation is reduced but not eliminated on the h-BN substrate. In contrast, in a h-BN/graphene/h-BN sandwich structure, with graphene protected on both sides, graphene remains pristine despite thermal processing. Raman data provide a deeper understanding of the previously observed improved graphene electrical conductivity on h-BN substrates. In the sandwich structure, the graphene 2D Raman feature has a higher frequency and narrower line width than in pristine suspended graphene, implying that the local h-BN environment modestly yet measurably changes graphene electron and phonon dispersions.

The two dimensional charge carriers in monolayer and bilayer graphene are described by massless and massive chiral Dirac Hamiltonians, respectively. These two-dimensional materials are predicted to exhibit a wide range of behavior, etc. However, graphene devices on a typical three-dimensional insulating substrates such as SiO2 are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. We have developed a novel technique for substrate engineering of graphene devices using layered dielectric materials to build graphene based vertical heterostructures. We employ hBN, an insulating isomorph of graphite, as a substrate and gate dielectric for graphene electronics. In this review, we describe the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal hBN substrates, using a mechanical transfer process. Graphene devices on hBN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO2. We use the enhanced mobility of electrons in hBN supported graphene to investigate the effects of electronic interactions. We find that interactions drive spontaneous breaking of the emergent SU(4) symmetry of the graphene Landau levels, leading to a variety of non-trivial integer and fractional quantum Hall states. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.

We investigate current saturation at short channel lengths in graphene field-effect transistors (GFETs). Saturation is necessary to achieve low-output conductance required for device power gain. Dual-channel pulsed current-voltage measurements are performed to eliminate the significant effects of trapped charge in the gate dielectric, a problem common to all oxide-based dielectric films on graphene. With pulsed measurements, graphene transistors with channel lengths as small as 130 nm achieve output conductance as low as 0.3 mS/μm in saturation. The transconductance of the devices is independent of channel length, consistent with a velocity saturation model of high-field transport. Saturation velocities have a density dependence consistent with diffusive transport limited by optical phonon emission.

We present an investigation into the manipulation of nuclear spins near the ν = 1 quantum Hall state of GaAs/AlGaAs using optical pumping methods. For this, we have built a custom-designed polarization controller which allows for arbitrary polarizations of near-infrared laser light to be transmitted through fiber optics onto the sample. Using resistive readout, it is demonstrated that different polarizations of light induce specific changes in the transport properties in the first Landau level of the GaAs/AlGaAs quantum well.

This article discusses the design and application of a simple eye-safe monitoring assembly of thin film deposition and its advantages over the existent eye protection filters. This assembly prevents users from being exposed to the radiation field caused by lasers or incandescent objects during thin film deposition. Its design is simple, the device being reliable and easy to operate.

In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200 meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.

While chemical vapor deposition (CVD) promises a scalable method to produce large-area graphene, CVD-grown graphene has heretofore exhibited inferior electronic properties in comparison with exfoliated samples. Here we test the electrical transport properties of CVD-grown graphene in which two important sources of disorder, namely grain boundaries and processing-induced contamination, are substantially reduced. We grow CVD graphene with grain sizes up to 250 μm to abate grain boundaries, and we transfer graphene utilizing a novel, dry-transfer method to minimize chemical contamination. We fabricate devices on both silicon dioxide and hexagonal boron nitride (h-BN) dielectrics to probe the effects of substrate-induced disorder. On both substrate types, the large-grain CVD graphene samples are comparable in quality to the best reported exfoliated samples, as determined by low-temperature electrical transport and magnetotransport measurements. Small-grain samples exhibit much greater variation in quality and inferior performance by multiple measures, even in samples exhibiting high field-effect mobility. These results confirm the possibility of achieving high-performance graphene devices based on a scalable synthesis process.

Jorge M. Garcia...et al., The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h‐BN) flakes is demonstrated. Formation of single‐layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic‐force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h‐BN substrates. The growth is governed by the high mobility of the carbon atoms on the h‐BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms., This work is supported by ONR (N000140610138 and Graphene MURI), AFOSR (FA9550‐11‐1‐ 0010), EFRC Center for Re‐Defining Photovoltaic Efficiency through Molecule Scale Control (award DE‐SC0001085), NSF (CHE‐0641523), NYSTAR, CSIC‐PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP‐1503), Numancia 2 (S2009/ENE‐1477)) and Spanish MEC (ENE2009‐14481‐C02‐02, TEC2011‐29120‐C05‐04, MAT2011‐26534).

In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can spontaneously break this symmetry, manifesting as additional integer quantum Hall plateaus outside the normal sequence. Here we report the observation of a large number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using temperature-dependent tilted field magnetotransport. The large measured activation gaps confirm the Coulomb origin of the broken symmetry states, but the order is strongly dependent on LL index. In the high energy LLs, the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets with Skyrmionic excitations at half filling, whereas in the `relativistic' zero energy LL, lattice scale anisotropies drive the system to a spin unpolarized state, likely a charge- or spin-density wave., Comment: Supplementary information available at http://pico.phys.columbia.edu

High-frequency performance of graphene field-effect transistors (GFETs) with boron-nitride gate dielectrics is investigated. Devices show saturating IV characteristics and f max values as high as 34 GHz at 600-nm channel length. Bias dependence of f T and f max and the effect of the ambipolar channel on transconductance and output resistance are also examined.

Graphene field-effect transistors are fabricated utilizing single-crystal hexagonal boron nitride (h-BN), an insulating isomorph of graphene, as the gate dielectric. The devices exhibit mobility values exceeding 10,000 cm2/V-sec and current saturation down to 500 nm channel lengths with intrinsic transconductance values above 400 mS/mm. The work demonstrates the favorable properties of using h-BN as a gate dielectric for graphene FETs., Comment: 4 pages, 8 figures

Graphene devices on standard SiO2 substrates are highly disordered, exhibiting characteristics far inferior to the expected intrinsic properties of graphene[1-12]. While suspending graphene above the substrate yields substantial improvement in device quality[13,14], this geometry imposes severe limitations on device architecture and functionality. Realization of suspended-like sample quality in a substrate supported geometry is essential to the future progress of graphene technology. In this Letter, we report the fabrication and characterization of high quality exfoliated mono- and bilayer graphene (MLG and BLG) devices on single crystal hexagonal boron nitride (h-BN) substrates, by a mechanical transfer process. Variable-temperature magnetotransport measurements demonstrate that graphene devices on h-BN exhibit enhanced mobility, reduced carrier inhomogeneity, and reduced intrinsic doping in comparison with SiO2-supported devices. The ability to assemble crystalline layered materials in a controlled way sets the stage for new advancements in graphene electronics and enables realization of more complex graphene heterostructres., 20 pages (includes supplementary info), 7 figures

We report observation of the fractional quantum Hall effect (FQHE) in high mobility multi-terminal graphene devices, fabricated on a single crystal boron nitride substrate. We observe an unexpected hierarchy in the emergent FQHE states that may be explained by strongly interacting composite Fermions with full SU(4) symmetric underlying degrees of freedom. The FQHE gaps are measured from temperature dependent transport to be up 10 times larger than in any other semiconductor system. The remarkable strength and unusual hierarcy of the FQHE described here provides a unique opportunity to probe correlated behavior in the presence of expanded quantum degrees of freedom., Comment: 5 pages, 3 figures

Application of extreme magnetic fields to a low-disorder 2D electron gas causes its electrons to reorder through an unexpected transition from a 2D to quasi-3D Wigner crystal state.

A fiber-optic-based polarization control system that uses a backreflection measurement scheme at low temperatures has been developed. This provides a stringent test of the light polarization state at the output of the fiber, allowing for determination and control of the degree of circular polarization; i.e., it can generate linear, right, or left circular polarization with cryogenic fibers. This polarization controller is paving the way toward the control and manipulation of nuclear spins in semiconductors via the optical Overhauser effect and could be used, for example, for the purpose of quantum information processing with the large nuclear spins of GaAs.