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

We consider an elastic manifold of internal dimension d and length L pinned in a N dimensional random potential and confined by an additional parabolic potential of curvature $$\mu $$. We are interested in the mean spectral density $$\rho (\lambda )$$ of the Hessian matrix $${{\mathcal {K}}}$$ at the absolute minimum of the total energy. We use the replica approach to derive the system of equations for $$\rho (\lambda )$$ for a fixed $$L^d$$ in the $$N \rightarrow \infty $$ limit extending $$d=0$$ results of our previous work (Fyodorov et al. in Ann Phys 397:1–64, 2018). A particular attention is devoted to analyzing the limit of extended lattice systems by letting $$L\rightarrow \infty $$. In all cases we show that for a confinement curvature $$\mu $$ exceeding a critical value $$\mu _c$$, the so-called “Larkin mass”, the system is replica-symmetric and the Hessian spectrum is always gapped (from zero). The gap vanishes quadratically at $$\mu \rightarrow \mu _c$$. For $$\mu <\mu _c$$ the replica symmetry breaking (RSB) occurs and the Hessian spectrum is either gapped or extends down to zero, depending on whether RSB is 1-step or full. In the 1-RSB case the gap vanishes in all d as $$(\mu _c-\mu )^4$$ near the transition. In the full RSB case the gap is identically zero. A set of specific landscapes realize the so-called “marginal cases” in $$d=1,2$$ which share both feature of the 1-step and the full RSB solution, and exhibit some scale invariance. We also obtain the average Green function associated to the Hessian and find that at the edge of the spectrum it decays exponentially in the distance within the internal space of the manifold with a length scale equal in all cases to the Larkin length introduced in the theory of pinning.

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Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum

We study a system of N noninteracting spinless fermions in a confining double-well potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size 2L centered around the position of the local maximum, for sufficiently small L. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.

Noninteracting trapped fermions in double-well potentials: Inverted-parabola kernel

the point d = 2, a = 2). Superdiffusive behavior was obtained for gT/gL ≫ 1 and subdiffusive slow dynamics for gT/gL ≪ 1. A line of fixed points was obtained up to order ǫ 2 , with a continuously variable exponent ν, in the case of LR correlations (d > 2, a < 2), parametrized by the ratio gT/gL. The divergence-free case gL = 0 is simpler, since the value of ν is equal to the Flory value νF obtained by purely dimensional arguments, as discussed below. On the other hand, out of equilibrium relaxational (potential) dynamics has recently been studied extensively, in the context of spin glass models [9] as well as particles [10,11] and manifolds [12] in random potentials. Analytical solutions were obtained [9] for the long-time dynamics in mean-field models, showing explicitly their glassy features such as slow (aging) dynamics, and the breakdown of time-translation invariance (TTI) and of fluctuation-dissipation theorems (FDT). Whether these glassy properties of potential dynamics survive to a small non-potential perturbation was recently addressed [13], and it was found that, while the dynamics becomes TTI in most cases, some glassy features survive. Similarly, a glassy state with stationary dissipation was proposed [14] for driven vortex systems. In this paper we thus reconsider the dynamics of a particle (D = 0) in a d-dimensional random force field as well !

Dynamics of particles and manifolds in a quenched random force field

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that al l geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.

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Wetting and minimal surfaces.

We calculate the joint min-max distribution and the Edwards-Anderson's order parameter for the circular model of 1/f -noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

Pierre Le Doussal

Papers

Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum

Noninteracting trapped fermions in double-well potentials: Inverted-parabola kernel

Dynamics of particles and manifolds in a quenched random force field

Wetting and minimal surfaces.

Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model