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

The behavior of a disordered amorphous thin film of superconducting Indium Oxide has been studied as a function of temperature and magnetic field applied perpendicular to its plane. A superconductor-insulator transition has been observed, though the isotherms do not cross at a single point. The curves of resistance vs. temperature on the putative superconducting side of this transition, where the resistance decreases with decreasing temperature, obey two-dimensional Mott variable-range hopping of vortices over wide ranges of temperature and resistance. To estimate the parameters of hopping, the film is modeled as a granular system and the hopping of vortices is treated in a manner analogous to hopping of charges. The reason the long range interaction between vortices over the range of magnetic fields investigated does not lead to a stronger variation of resistance with temperature than that of two-dimensional Mott variable-range hopping remains unresolved.

Vortex Variable Range Hopping in a Conventional Superconducting Film

Quantum Hall stripe phases near half-integer filling factors $\ensuremath{\nu}\ensuremath{\ge}9/2$ were predicted by Hartree-Fock (HF) theory and confirmed by discoveries of giant resistance anisotropies in high-mobility two-dimensional electron gases. A theory of such anisotropy was proposed by MacDonald and Fisher, although they used parameters whose dependencies on the filling factor, electron density, and mobility remained unspecified. Here, we fill this void by calculating the hard-to-easy resistivity ratio as a function of these three variables. Quantitative comparison with experiment yields very good agreement, which we view as evidence for the ``plain vanilla'' smectic stripe HF phases.

Resistivity anisotropy of quantum Hall stripe phases

We argue that it is the hopping transport that is responsible for broadening of the σxx peaks. Explicit expressions for the width Δν of a peak as a function of the temperature T, current J and frequency ω are found. It is shown that Δν grows with T as (T/T1)κ, where κ is the inverse localization-length exponent. The current J is shown to act like the effective temperature T eff (J) ∝ J 1 2 if T eff (J) T . Broadening of the ohmic ac-conductivity peaks with frequency ω is found to be determined by the effective temperature T eff (ω)∼ h ω.

Conductivity peaks broadening in the quantum Hall regime

Quantum Hall stripe (QHS) phases, predicted by the Hartree-Fock theory, are manifested in GaAs-based two-dimensional electron gases as giant resistance anisotropies. Here, we predict a ``hidden'' QHS phase which exhibits isotropic resistivity whose value, determined by the density of states of QHS, is independent of the Landau index $N$ and is inversely proportional to the Drude conductivity at zero magnetic field. At high enough $N$, this phase yields to an Ando-Unemura/Coleridge-Zawadski-Sachrajda phase in which the resistivity is proportional to $1/N$ and to the ratio of quantum and transport lifetimes. Experimental observation of this border can provide an alternative way to obtain quantum relaxation time.

Isotropically conducting (hidden) quantum Hall stripe phases in a two-dimensional electron gas

It is shown that the voltage dependence of the tunneling conductance between two lightly doped semiconductors, which are separated by a large area tunneling barrier, can reveal the high energy part of the Coulomb gap if the barrier is thick enough. At barrier thickness smaller than the average distance between impurities no Coulomb gap feature can be found. This happens because such tunneling is sensitive to very rare shortest pairs of occupied and empty states localized at opposite sides of the barrier, whose density of states in this limit has no Coulomb gap. Small area tunneling contacts are also discussed. It is shown that the tunneling conductance of a point-like contact exponentially grows with the applied voltage. This dependence does not permit a direct measurement of the Coulomb gap.

Boris I Shklovskii

Papers

Vortex Variable Range Hopping in a Conventional Superconducting Film

Resistivity anisotropy of quantum Hall stripe phases

Conductivity peaks broadening in the quantum Hall regime

Isotropically conducting (hidden) quantum Hall stripe phases in a two-dimensional electron gas

Tunneling between two semiconductors with localized electrons: Can it reveal the Coulomb gap?