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

Sinai\'s model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits aging\" with $\\frac{\\ln t}{\\ln t\'}$ scaling and a singularity at $\\ln t =\\ln t\'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and \"persistence\" exponents of 1D reaction-diffusion models with random forces.

https://arxiv.org/pdf/cond-mat/9710270.pdf

Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-Dimensional Random Environments

We study a system of $N$ noninteracting spinless fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the confining trap breaks the translational invariance and introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so-called ``bulk regime''), where the fermions do not feel the curvature of the trap, physical properties of the fermions have traditionally been understood using the local density (or Thomas-Fermi) approximation. However, these approximations drastically fail near the edge where the density vanishes and thermal and quantum fluctuations are thus enhanced. The main goal of this paper is to show that, even near the edge, novel universal properties emerge, independently of the details of the shape of the confining potential. We present a unified framework to investigate both the bulk and the edge properties of the fermions. We show that for large $N$, these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any $n$-point correlation function, including the average density profile, can be expressed as an $n\ifmmode\times\else\texttimes\fi{}n$ determinant whose entry is called the kernel, a central object for such processes. Near the edge, we derive the large-$N$ scaling form of the kernels, parametrized by $d$ and $T$. In $d=1$ and $T=0$, this reduces to the so-called Airy kernel, that appears in the Gaussian unitary ensemble (GUE) of random matrix theory. In $d=1$ and $Tg0$ we show a remarkable connection between our kernel and the one appearing in the ($1+1$)-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently, our result provides a finite-$T$ generalization of the Tracy-Widom distribution, that describes the fluctuations of the position of the rightmost fermion at $T=0$, or those of the largest single-fermion momentum. In $dg1$ and $T\ensuremath{\ge}0$, while the connection to GUE no longer holds, the process is still determinantal whose analysis provides a new class of kernels, generalizing the $1d$ Airy kernel at $T=0$ obtained in random matrix theory. Some of our finite-temperature results should be testable in present-day cold-atom experiments, most notably our detailed predictions for the temperature dependence of the fluctuations near the edge.

Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations

Renormalization of Pinned Elastic Systems

We study elastic systems, such as interfaces or lattices, pinned by quenched disorder To escape triviality as a result of ``dimensional reduction,'' we use the functional renormalization group Difficulties arise in the calculation of the renormalization group functions beyond one-loop order Even worse, observables such as the two-point correlation function exhibit the same problem already at one-loop order These difficulties are due to the nonanalyticity of the renormalized disorder correlator at zero temperature, which is inherent to the physics beyond the Larkin length, characterized by many metastable states As a result, two-loop diagrams, which involve derivatives of the disorder correlator at the nonanalytic point, are naively ``ambiguous'' We examine several routes out of this dilemma, which lead to a unique renormalizable field theory at two-loop order It is also the only theory consistent with the potentiality of the problem The \ensuremath{\beta} function differs from previous work and the one at depinning by novel ``anomalous terms'' For interfaces and random-bond disorder we find a roughness exponent $\ensuremath{\zeta}=020829804\ensuremath{\epsilon}+0006858{\ensuremath{\epsilon}}^{2},$ $\ensuremath{\epsilon}=4\ensuremath{-}d$ For random-field disorder we find $\ensuremath{\zeta}=\ensuremath{\epsilon}/3$ and compute universal amplitudes to order $O({\ensuremath{\epsilon}}^{2})$ For periodic systems we evaluate the universal amplitude of the two-point function We also clarify the dependence of universal amplitudes on the boundary conditions at large scale All predictions are in good agreement with numerical and exact results and are an improvement over one loop Finally we calculate higher correlation functions, which turn out to be equivalent to those at depinning to leading order in \ensuremath{\epsilon}

https://arxiv.org/pdf/cond-mat/0304614.pdf

Functional renormalization group and the field theory of disordered elastic systems

We review how the renormalized force correlator $\ensuremath{\Delta}(u)$, the function computed in the functional renormalization-group (RG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a one-dimensional random-force landscape. The limit of small velocity allows one to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Fr\'echet. For each class we obtain analytically the universal function $\ensuremath{\Delta}(u)$, the corrections to the critical force, and the joint probability distribution of avalanche sizes $s$ and waiting times $w$. We find $P(s)=P(w)$ for all three cases. All results are checked numerically. For a Brownian force landscape, known as the Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model, avalanche distributions and $\ensuremath{\Delta}(u)$ can be computed for any velocity. For two-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor ${\ensuremath{\Delta}}_{ij}(\stackrel{P\vec}{u})$, and to extract the anisotropic scaling exponents ${\ensuremath{\zeta}}_{x}g{\ensuremath{\zeta}}_{y}$. We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered, e.g., in some models of global warming. We give the joint distribution of the time $s$ between two successive records and their difference in value $w$.

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Pierre Le Doussal

Papers

Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-Dimensional Random Environments

Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations

Renormalization of Pinned Elastic Systems

Functional renormalization group and the field theory of disordered elastic systems

Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records.