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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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

Diamond-like carbon (DLC) is a metastable form of amorphous carbon with significant sp3 bonding. DLC is a semiconductor with a high mechanical hardness, chemical inertness, and optical transparency. This review will describe the deposition methods, deposition mechanisms, characterisation methods, electronic structure, gap states, defects, doping, luminescence, field emission, mechanical properties and some applications of DLCs. The films have widespread applications as protective coatings in areas, such as magnetic storage disks, optical windows and micro-electromechanical devices (MEMs).

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Diamond-like amorphous carbon

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

We study the Anderson transition for three-dimensional (3D) $N\ifmmode\times\else\texttimes\fi{}N\ifmmode\times\else\texttimes\fi{}N$ tightly bound cubic lattices where both real and imaginary parts of on-site energies are independent random variables distributed uniformly between $\ensuremath{-}W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from 0.72 to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at ${W}_{c}=6.0\ifmmode\pm\else\textpm\fi{}0.1$ (in units of nearest-neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.

Anderson transition in three-dimensional systems with non-Hermitian disorder

Electric double-layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of ~100 F/cm(3), nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally measured capacitance values of ~100 F/cm(3) may be understood.

Theory of volumetric capacitance of an electric double-layer supercapacitor.

We consider ion transport through protein ion channels in lipid membranes and water-filled nanopores in silicon films. It is known that, due to the large ratio of dielectric constants of water and the surrounding material, an ion placed inside the channel faces a large electrostatic self-energy barrier. The barrier leads to an exponentially large resistance of the channel. We study reduction of the electrostatic barrier by immobile charges located on the internal walls of the channel. We show that the barrier practically vanishes already at relatively small concentration of wall charges.

Conductance of ion channels and nanopores with charged walls: a toy model.

Electron tunneling experiments are used to probe Coulomb correlation effects in the single-particle density-of-states (DOS) of boron-doped silicon crystals near the critical density of the metal-insulator transition (MIT). At low energies, a DOS measurement distinguishes between insulating and metallic samples with densities 10 to 15 % on either side of the MIT. However, at higher energies the DOS of both insulators and metals show a common behavior, increasing roughly as the square-root of energy. The observed characteristics of the DOS can be understood using a classical treatment of Coulomb interactions combined with a phenomenological scaling ansatz to describe the length-scale dependence of the dielectric constant as the MIT is approached from the insulating side.

https://arxiv.org/pdf/cond-mat/9902169.pdf

Coulomb gap in a doped semiconductor near the metal-insulator transition: Tunneling experiment and scaling ansatz

We study a two-dimensional motion of a charged particle in a weak random potential and a perpendicular magnetic field. The correlation length of the potential is assumed to be much larger than the de Broglie wavelength. Under such conditions, the motion on not too large length scales is described by classical equations of motion. We show that the phase-space averaged diffusion coefficient is given by the Drude-Lorentz formula only at magnetic fields $B$ smaller than certain value ${B}_{c}.$ At larger fields, the chaotic motion is suppressed and the diffusion coefficient becomes exponentially small. In addition, we calculate the quantum-mechanical localization length as a function of $B$ at the minima of ${\ensuremath{\sigma}}_{\mathrm{xx}}.$ At $Bl{B}_{c}$ it is exponentially large but decreases with increasing $B$. At $Bg{B}_{c},$ this decrease becomes very rapid and the localization length ceases to be exponentially large at a field ${B}_{*},$ which is only slightly larger than ${B}_{c}.$ Implications for the crossover from the Shubnikov--de Haas oscillations to the quantum Hall effect are discussed.

http://arxiv.org/pdf/cond-mat/9702121.pdf

Boris I Shklovskii

Papers

Anderson transition in three-dimensional systems with non-Hermitian disorder

Theory of volumetric capacitance of an electric double-layer supercapacitor.

Conductance of ion channels and nanopores with charged walls: a toy model.

Coulomb gap in a doped semiconductor near the metal-insulator transition: Tunneling experiment and scaling ansatz

Suppression of chaotic dynamics and localization of two-dimensional electrons by a weak magnetic field