Quantum Hall effect and Landau level crossing of Dirac fermions in trilayer graphene

We investigate electronic transport in high mobility (\textgreater 100,000 cm$^2$/V$\cdot$s) trilayer graphene devices on hexagonal boron nitride, which enables the observation of Shubnikov-de Haas oscillations and an unconventional quantum Hall effect. The massless and massive characters of the TLG subbands lead to a set of Landau level crossings, whose magnetic field and filling factor coordinates enable the direct determination of the Slonczewski-Weiss-McClure (SWMcC) parameters used to describe the peculiar electronic structure of trilayer graphene. Moreover, at high magnetic fields, the degenerate crossing points split into manifolds indicating the existence of broken-symmetry quantum Hall states.Comment: Supplementary Information at http://jarilloherrero.mit.edu/wp-content/uploads/2011/04/Supplementary_Taychatanapat.pd

Atomically dispersed Pt-N-4 sites as efficient and selective electrocatalysts for the chlorine evolution reaction

Chlorine evolution reaction (CER) is a critical anode reaction in chlor-alkali electrolysis. Although precious metal-based mixed metal oxides (MMOs) have been widely used as CER catalysts, they suffer from the concomitant generation of oxygen during the CER. Herein, we demonstrate that atomically dispersed Pt-N-4 sites doped on a carbon nanotube (Pt-1/CNT) can catalyse the CER with excellent activity and selectivity. The Pt-1/CNT catalyst shows superior CER activity to a Pt nanoparticle-based catalyst and a commercial Ru/Ir-based MMO catalyst. Notably, Pt-1/CNT exhibits near 100% CER selectivity even in acidic media, with low Cl- concentrations (0.1M), as well as in neutral media, whereas the MMO catalyst shows substantially lower CER selectivity. In situ electrochemical X-ray absorption spectroscopy reveals the direct adsorption of Cl- on Pt-N-4 sites during the CER. Density functional theory calculations suggest the PtN4C12 site as the most plausible active site structure for the CER

The nature of localization in graphene under quantum Hall conditions

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.Comment: 18 pages, including 5 figure

Broken symmetry states and divergent resistance in suspended bilayer graphene

Graphene [1] and its bilayer have generated tremendous excitement in the physics community due to their unique electronic properties [2]. The intrinsic physics of these materials, however, is partially masked by disorder, which can arise from various sources such as ripples [3] or charged impurities [4]. Recent improvements in quality have been achieved by suspending graphene flakes [5,6], yielding samples with very high mobilities and little charge inhomogeneity. Here we report the fabrication of suspended bilayer graphene devices with very little disorder. We observe fully developed quantized Hall states at magnetic fields of 0.2 T, as well as broken symmetry states at intermediate filling factors $\nu = 0$, $\pm 1$, $\pm 2$ and $\pm 3$. The devices exhibit extremely high resistance in the $\nu = 0$ state that grows with magnetic field and scales as magnetic field divided by temperature. This resistance is predominantly affected by the perpendicular component of the applied field, indicating that the broken symmetry states arise from many-body interactions.Comment: 23 pages, including 4 figures and supplementary information; accepted to Nature Physic

STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles, resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance. In this letter, we use scanning tunneling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moire patterns in the topographic images. However, contrary to recent predictions, this conformation does not lead to a sizable band gap due to the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron-hole charge fluctuations are reduced by two orders of magnitude as compared to those on silicon oxide. This leads to charge fluctuations which are as small as in suspended graphene, opening up Dirac point physics to more diverse experiments than are possible on freestanding devices.Comment: Nature Materials advance online publication 13/02/201

Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene

We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2)XU(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry.Comment: 35 page

Application of Graphene within Optoelectronic Devices and Transistors

Scientists are always yearning for new and exciting ways to unlock graphene's true potential. However, recent reports suggest this two-dimensional material may harbor some unique properties, making it a viable candidate for use in optoelectronic and semiconducting devices. Whereas on one hand, graphene is highly transparent due to its atomic thickness, the material does exhibit a strong interaction with photons. This has clear advantages over existing materials used in photonic devices such as Indium-based compounds. Moreover, the material can be used to 'trap' light and alter the incident wavelength, forming the basis of the plasmonic devices. We also highlight upon graphene's nonlinear optical response to an applied electric field, and the phenomenon of saturable absorption. Within the context of logical devices, graphene has no discernible band-gap. Therefore, generating one will be of utmost importance. Amongst many others, some existing methods to open this band-gap include chemical doping, deformation of the honeycomb structure, or the use of carbon nanotubes (CNTs). We shall also discuss various designs of transistors, including those which incorporate CNTs, and others which exploit the idea of quantum tunneling. A key advantage of the CNT transistor is that ballistic transport occurs throughout the CNT channel, with short channel effects being minimized. We shall also discuss recent developments of the graphene tunneling transistor, with emphasis being placed upon its operational mechanism. Finally, we provide perspective for incorporating graphene within high frequency devices, which do not require a pre-defined band-gap.Comment: Due to be published in "Current Topics in Applied Spectroscopy and the Science of Nanomaterials" - Springer (Fall 2014). (17 pages, 19 figures

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in ultracold quantum gases -- are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a {\it complex} order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.Comment: 5 pages, 4 figure

Observation of the Fractional Quantum Hall Effect in Graphene

When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields