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

Environmental noise can cause an exponential reduction in the mean time to extinction (MTE) of an isolated population. We study this effect on an example of a stochastic birth-death process with rates modulated by a colored (that is, correlated) Gaussian noise. A path integral formulation yields a transparent way of evaluating the MTE and finding the optimal realization of the environmental noise that determines the most probable path to extinction. The population-size dependence of the MTE changes from exponential in the absence of the environmental noise to a power law for a short-correlated noise and to no dependence for long-correlated noise. We also establish the validity domains of the white-noise limit and adiabatic limit.

How colored environmental noise affects population extinction.

Complexation of a polyelectrolyte with an oppositely charged spherical macroion is studied for both salt-free and salty solutions. When a polyelectrolyte winds around the macroion, its turns repel each other and form an almost equidistant solenoid. It is shown that this repulsive correlations of turns lead to the charge inversion: more polyelectrolyte winds around the macroion than it is necessary to neutralize it. The charge inversion becomes stronger with increasing concentration of salt and can exceed 100%. Monte-Carlo simulation results agree with our analytical theory.

Overcharging of a macroion by an oppositely charged polyelectrolyte

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.

Density of states and conductivity of a granular metal or an array of quantum dots

The problem of simultaneous diffusion and recombination of electron-hole pairs, photoexcited in noncrystalline semiconductors at low temperatures, is reduced to a universal mathematical problem whose solution does not depend on the density-of-states function. We derive a general geminate-recombination function which at low light intensities describes the distribution of radiative recombination times. The low-temperature photoconductivity is found to depend only weakly on material parameters and agrees with experiments on hydrogenated amorphous silicon.

Electronic transport and recombination in amorphous semiconductors at low temperatures.

We study the effect of impurities on the ground state and the low-temperature Ohmic dc transport in a one-dimensional chain and quasi-one-dimensional systems of many parallel chains. We assume that strong interactions impose a short-range periodicity of the electron positions. The long-range order of such an electron crystal (or equivalently, a ${4k}_{F}$ charge-density wave) is destroyed by impurities, which act as strong pinning centers. We show that a three-dimensional array of chains behaves differently at large and at small impurity concentrations N. At large N, impurities divide the chains into metallic rods. Additions or removal of electrons from such rods correspond to charge excitations whose density of states exhibits a quadratic Coulomb gap. At low temperatures the conductivity is due to the variable-range hopping of electrons between the rods. It obeys the Efros-Shklovskii (ES) law, $\ensuremath{-}\mathrm{ln}\ensuremath{\sigma}\ensuremath{\sim}{(T}_{\mathrm{ES}}{/T)}^{1/2}.$ ${T}_{\mathrm{ES}}$ decreases as N decreases, which leads to an exponential growth of $\ensuremath{\sigma}.$ When N is small, the metallic-rod (also known as ``interrupted-strand'') picture of the ground state survives only in the form of rare clusters of atypically short rods. They are the source of low-energy charge excitations. In the bulk of the crystal the charge excitations are gapped and the electron crystal is pinned collectively. A strongly anisotropic screening of the Coulomb potential produces an unconventional linear in energy Coulomb gap and an unusual law of the variable-range hopping conductivity $\ensuremath{-}\mathrm{ln}\ensuremath{\sigma}\ensuremath{\sim}{(T}_{1}{/T)}^{2/5}.$ The parameter ${T}_{1}$ remains constant over a finite range of impurity concentrations. At smaller N the $2/5$ law is replaced by the Mott law, $\ensuremath{-}\mathrm{ln}\ensuremath{\sigma}\ensuremath{\sim}{(T}_{M}{/T)}^{1/4}.$ In the Mott regime the conductivity gets suppressed as N goes down. Thus, the overall dependence of $\ensuremath{\sigma}$ on N is nonmonotonic. In the case of a single chain, the metallic-rod picture applies at all N. The low-temperature conductivity obeys the ES law, with log corrections, and decreases exponentially with N. Our theory provides a qualitative explanation for the transport properties of organic charge-density wave compounds of TCNQ family.

https://arxiv.org/pdf/cond-mat/0307299.pdf

Boris I Shklovskii

Papers

How colored environmental noise affects population extinction.

Overcharging of a macroion by an oppositely charged polyelectrolyte

Density of states and conductivity of a granular metal or an array of quantum dots

Electronic transport and recombination in amorphous semiconductors at low temperatures.

Variable-range hopping in quasi-one-dimensional electron crystals