Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

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

The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.

https://science.sciencemag.org/content/sci/287/5453/637.full.pdf

Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load

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

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Hydrodynamics of soft active matter

This corrects the article DOI: 10.1103/PhysRevLett.123.037401.

Erratum: Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions [Phys. Rev. Lett. 123, 037401 (2019)].

A standard approach to propulsion velocities of autophoretic colloids with thin interaction layers uses a reciprocity relation applied to the slip velocity. But the surface flux (chemical, electrical, thermal, etc.), which is the source of the field driving the slip is often more accessible. We show how, under conditions of low Reynolds number and a field obeying the Laplace equation in the outer region, the slip velocity can be bypassed in velocity calculations. In a sense, the actual slip velocity and a normal field proportional to the flux density are equivalent for this type of calculation. Using known results for surface traction induced by rotating or translating an inert particle in a quiescent fluid, we derive simple and explicit integral formulas for translational and rotational velocities of arbitrary spheroidal and slender-body autophoretic colloids.

Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux

The statistical mechanical behavior of quantum gases adsorbed on various surfaces is analyzed. The specific surfaces explored are (a) a finite and an infinite plane, (b) a circular and/or square disk, (c) a sphere, (d) a cylinder, and (e) a cone. The approximation is made that the particles are confined to the close vicinity of the specified surface by a holding potential. As expected, quantum size and statistical effects are large at low temperature, while at high temperature the limiting behavior is that of a classical two-dimensional gas on a flat surface. An application to the surface separation of HD or D2 from H2 is discussed.

Adsorption of Quantum Gases on Curved Surfaces

We analyze the rotational demagnetization of artificial spin ice, a recently realized array of nanoscale single-domain ferromagnetic islands. Demagnetization does not anneal this model system into its anti-ferromagnetic ground state: the moments have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal system has an effective extensive degeneracy and we introduce a formalism that can predict the populations of local states in this ice-like system with no adjustable parameters.

Effective Thermodynamics of Artificial Spin Ice

Typical multiwalled carbon tubes have interlayer incommensuration both azimuthally and axially. Finite size effects then imply that the maximal energetic barrier to interlayer sliding in nanoscale multiwalled carbon nanotubes is, surprisingly, independent of the size of the system. Turning attention from post-synthesis interwall interactions to interwall fluctuations during growth, we note that certain thermal fluctuations during multiwalled nanotube growth and tapering are locked into the final structure. The thermal dispersion in the diameters of tube endcaps reveals that multiwalled nanotubes grow at temperatures much lower than the maximum plasma temperatures for the arc discharge. Finally, considering only noncatastrophic structural distortions (i.e. plastic as opposed to brittle failure under tensile load), the onset of plastic deformation in carbon nanotubes depends very strongly on the wrapping index, as can be understood from a simple model of index-dependent defect-induced lengthing of the tube.

Paul E. Lammert

Papers

Erratum: Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions [Phys. Rev. Lett. 123, 037401 (2019)].

Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux

Adsorption of Quantum Gases on Curved Surfaces

Effective Thermodynamics of Artificial Spin Ice

Sliding, stretching, and tapering: recent structural results for carbon nanotubes