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.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

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.

/pdf/the-structure-of-suspended-graphene-sheets-1hs19mwg5z.pdf

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 propose a simple ansatz that relates the diffusion propagator for the molecules of a fluid confined in a porous medium to the pore-space structure factor. Theoretical arguments and numerical simulations show that it works well for both periodic and disordered geometries. The ansatz allows us to deconvolve structural data from momentum dependent pulsed field gradient spin-echo data. © 1992 The American Physical Society.

Diffusion propagator as a probe of the structure of porous media

The effect of weak impurity disorder on flux lattices at equilibrium is studied quantitatively in the absence of free dislocations using both the Gaussian variational method and the renormalization group. Our results for the mean-square relative displacements B\ifmmode \tilde{}\else \~{}\fi{}(x)=〈u(x)-u(0)${\mathrm{〉}}^{2}$\ifmmode\bar\else\textasciimacron\fi{} clarify the nature of the crossovers with distance. We find three regimes: (i) a short distance regime (``Larkin regime'') whre elasticity holds, (ii) an intermediate reigme (``random manifold'') where vortices are pinned independently, and (iii) a large distance, quasiordered regime where the periodicity of the lattice becomes important. In the last regime we find universal logarithmic growth of displacements for 2d4: B\ifmmode \tilde{}\else \~{}\fi{}(x)\ensuremath{\sim}${\mathit{A}}_{\mathit{d}}$ln\ensuremath{\Vert}x\ensuremath{\Vert} and persistence of algebraic quasi-long-range translational order. The functional renormalization group to O(\ensuremath{\epsilon}=4-d) and the variational method, when they can be compared, agree within 10% on the value of ${\mathit{A}}_{\mathit{d}}$. In d=3 we compute the function describing the crossover between the three reigmes. We discuss the observable signature of this crossover in decoration experiments and in neutron-diffraction experiments on flux lattices. Qualitative arguments are given suggesting the existence for weak disorder in d=3 of a ``Bragg glass'' phase without free dislocations and with algebraically divergent Bragg peaks. In d=1+1 both the variational method and the Cardy-Ostlund renormalization group predict a glassy state below the same transition temperature T=${\mathit{T}}_{\mathit{c}}$, but with different B\ifmmode \tilde{}\else \~{}\fi{}(x) behaviors. Applications to d=2+0 systems and experiments on magnetic bubbles are discussed.

Elastic theory of flux lattices in the presence of weak disorder.

Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive f. We derive functional renormalization-group equations which allow us to describe in detail the properties of the slowly moving states in both cases. Since they hold at finite velocity v, they allow us to remedy some shortcomings of the previous approaches to zero-temperature depinning. In particular, they enable us to derive the depinning law directly from the equation of motion, with no artificial prescription or additional physical assumptions, such as a scaling relation among the exponents. Our approach provides a controlled framework to establish under which conditions the depinning regime is universal. It explicitly demonstrates that the random potential seen by a moving extended system evolves at large scale to a random field and yields a self-contained picture for the size of the avalanches associated with the deterministic motion. At finite temperature $Tg0$ we find that the effective barriers grow with length scale as the energy differences between neighboring metastable states, and demonstrate the resulting activated creep law $v\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{\mathrm{Cf}}^{\ensuremath{-}\ensuremath{\mu}}/T)$ where the exponent \ensuremath{\mu} is obtained in a $\ensuremath{\epsilon}=4\ensuremath{-}D$ expansion $(D$ is the internal dimension of the interface). Our approach also provides quantitatively an interesting scenario for creep motion as it allows us to identify several intermediate length scales. In particular, we unveil a ``depinninglike'' regime at scales larger than the activation scale, with avalanches spreading from the thermal nucleus scale up to the much larger correlation length ${R}_{V}.$ We predict that ${R}_{V}\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\sigma}}{f}^{\ensuremath{-}\ensuremath{\lambda}}$ diverges at small drive and temperature with exponents $\ensuremath{\sigma},\ensuremath{\lambda}$ that we determine.

Creep and depinning in disordered media

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.

Free-energy distribution of the directed polymer at high temperature

We provide the first exact calculation of the height distribution at arbitrary time t of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer with one end fixed, one free, and the Bethe ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e., KPZ height) distribution to the Gaussian orthogonal ensemble Tracy-Widom distribution at large time.

Pierre Le Doussal

Papers

Diffusion propagator as a probe of the structure of porous media

Elastic theory of flux lattices in the presence of weak disorder.

Creep and depinning in disordered media

Free-energy distribution of the directed polymer at high temperature

Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions.