This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

It is possible to say that zeolites are the most widely used catalysts in industry They are crystalline microporous materials which have become extremely successful as catalysts for oil refining, petrochemistry, and organic synthesis in the production of fine and speciality chemicals, particularly when dealing with molecules having kinetic diameters below 10 A The reason for their success in catalysis is related to the following specific features of these materials:1 (1) They have very high surface area and adsorption capacity (2) The adsorption properties of the zeolites can be controlled, and they can be varied from hydrophobic to hydrophilic type materials (3) Active sites, such as acid sites for instance, can be generated in the framework and their strength and concentration can be tailored for a particular application (4) The sizes of their channels and cavities are in the range typical for many molecules of interest (5-12 A), and the strong electric fields2 existing in those micropores together with an electronic confinement of the guest molecules3 are responsible for a preactivation of the reactants (5) Their intricate channel structure allows the zeolites to present different types of shape selectivity, ie, product, reactant, and transition state, which can be used to direct a given catalytic reaction toward the desired product avoiding undesired side reactions (6) All of these properties of zeolites, which are of paramount importance in catalysis and make them attractive choices for the types of processes listed above, are ultimately dependent on the thermal and hydrothermal stability of these materials In the case of zeolites, they can be activated to produce very stable materials not just resistant to heat and steam but also to chemical attacks Avelino Corma Canos was born in Moncofar, Spain, in 1951 He studied chemistry at the Universidad de Valencia (1967−1973) and received his PhD at the Universidad Complutense de Madrid in 1976 He became director of the Instituto de Tecnologia Quimica (UPV-CSIC) at the Universidad Politecnica de Valencia in 1990 His current research field is zeolites as catalysts, covering aspects of synthesis, characterization and reactivity in acid−base and redox catalysis A Corma has written about 250 articles on these subjects in international journals, three books, and a number of reviews and book chapters He is a member of the Editorial Board of Zeolites, Catalysis Review Science and Engineering, Catalysis Letters, Applied Catalysis, Journal of Molecular Catalysis, Research Trends, CaTTech, and Journal of the Chemical Society, Chemical Communications A Corma is coauthor of 20 patents, five of them being for commercial applications He has been awarded with the Dupont Award on new materials (1995), and the Spanish National Award “Leonardo Torres Quevedo” on Technology Research (1996) 2373 Chem Rev 1997, 97, 2373−2419

From Microporous to Mesoporous Molecular-Sieve Materials and Their Use in Catalysis

Graphene — a recently isolated one-atom-thick layered form of graphite — is a hot topic in the materials science and condensed matter physics communities, where it is proving to be a popular model system for investigation. An experiment involving individual graphene sheets suspended over a microscale scaffold has allowed structure determination using transmission electron microscopy and diffraction, perhaps paving the way towards an answer to the question of why graphene can exist at all. The 'two-dimensional' sheets, it seems, are not flat, but wavy. The undulations are less pronounced in a two-layer system, and disappear in multilayer samples. Learning more about this 'waviness' may reveal what makes these extremely thin carbon membranes so stable. Investigations of individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or in air reveal that the membranes are not perfectly flat, but exhibit an intrinsic waviness, such that the surface normal varies by several degrees, and out-of-plane deformations reach 1 nm. The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.

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The structure of suspended graphene sheets

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Motivated by a freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky 1992). The experimental realization of atom-thin graphene sheets has driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: d --> infinity, D --> 4, and D=d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional membrane embedded in three dimensions, we predict its universal length-scale dependent roughness, elastic moduli exponents, and a universal negative Poisson ratio of -1/3. We also extend these results to short- and long-range correlated random heterogeneity, predicting a variety of glassy wrinkled membrane states. Finally, we also predict and analyze a continuous crumpling transition in a "phantom" elastic sheet. We hope that this detailed presentation of the SCSA theory will be useful for further theoretical developments and corresponding experimental investigations on freely suspended graphene.

Anomalous elasticity, fluctuations and disorder in elastic membranes

We discuss strategies for obtaining deliberately splayed columnar defects in type-II superconductors with some degree of control over the distribution of orientation. These ideas are illustrative, and intended to suggest directions for future experiments. Some experimental problems and technological issues are also considered.

Towards engineering of splayed columnar defects in type-II superconductors

We reconsider the functional renormalization-group (FRG) approach to decaying Burgers turbulence, and extend it to decaying Navier-Stokes and Surface-Quasi-Geostrophic turbulence. The method is based on a renormalized small-time expansion, equivalent to a loop expansion, and naturally produces a dissipative anomaly and a cascade after a finite time. We explicitly calculate and analyze the one-loop FRG equations in the zero- viscosity limit as a function of the dimension. For Burgers they reproduce the FRG equation obtained in the context of random manifolds, extending previous results of one of us. Breakdown of energy conservation due to shocks and the appearance of a direct energy cascade corresponds to failure of dimensional reduction in the context of disordered systems. For Navier-Stokes in three dimensions, the velocity-velocity correlation function acquires a linear dependence on the distance, ζ2 = 1, in the inertial range, instead of Kolmogorov's ζ2 = 2/3; however the possibility remains for corrections at two- or higher-loop order. In two dimensions, we obtain a numerical solution which conserves energy and exhibits an inverse cascade, with explicit analytical results both for large and small distances, in agreement with the scaling proposed by Batchelor. In large dimensions, the one-loop FRG equation for Navier-Stokes converges to that of Burgers.

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Functional renormalization-group approach to decaying turbulence

We study the high-temperature regime within the glass phase of an elastic object with short-ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $\ensuremath{\delta}$-correlated disorder and that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization-group arguments. We discuss experimental consequences such as nonmonotonous behavior with temperature.

Universal high-temperature regime of pinned elastic objects

We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the interface heights at two times $t_1$ and $t_2>t_1$, with droplet initial conditions at $t=0$. In the limit of large times this JPDF is expected to become a universal function of the time ratio $t_2/t_1$, and of the (properly scaled) heights $h(x,t_1)$ and $h(x,t_2)$. Using the replica Bethe ansatz method for the KPZ equation, in [J. Stat. Mech. (2017) 053212] we obtained a formula for the JPDF in the (partial) tail regime where $h(x,t_1)$ is large and positive, subsequently found in excellent agreement with experimental and numerical data [Phys. Rev. Lett. 118, 125701 (2017)]. Here we show that our results are in perfect agreement with Johansson's recent rigorous expression of the full JPDF [arXiv:1802.00729 ], thereby confirming the validity of our methods.

Pierre Le Doussal

Papers

Anomalous elasticity, fluctuations and disorder in elastic membranes

Towards engineering of splayed columnar defects in type-II superconductors

Functional renormalization-group approach to decaying turbulence

Universal high-temperature regime of pinned elastic objects

Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica