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

We study ac demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground-state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearest-neighbor correlations.

Energy minimization and ac demagnetization in a nanomagnet array.

Trimetallic catalytic microrotors were fabricated by electrodeposition of cylindrical Au−Ru rods in the pores of anodic alumina membranes, dissolution of the template membrane, and then sequential vapor deposition of Cr, SiO2, Cr, Au, and Pt on one side of each rod. This design provides two force vectors for the catalytic motor, including one perpendicular to the rod axis. The rods rotated rapidly (∼180 rpm) in 15% aqueous H2O2 solution with minimal orbital or translational movement. The rotation was rapid enough to observe qualitatively different interactions between pairs of co- and counter-rotating rods. Counter-rotating rods were able to approach each other closely and underwent frequent tip-to-tip collisions. Co-rotating rods could approach each other only to a distance of ∼0.9 μm. This difference is rationalized on the basis of shear forces generated by the catalytically driven rotation of the rods.

Dynamic interactions between fast microscale rotors.

Squashing brings circumferentially separated areas of a carbon nanotube into close proximity, drastically altering the low-energy electronic properties and (in some cases) reversing standard rules for metallic versus semiconducting behavior. Such a deformation mode, not requiring motion of tube ends, may be useful for devices. Uniaxial stress of a few kbar can reversibly collapse a small-radius tube, inducing a 0.1 eV gap with a very strong pressure dependence, while the collapsed state of a larger tube is stable. The low-energy electronic properties of chiral tubes are surprisingly insensitive to collapse.

Gapping by squashing: metal-insulator and insulator-metal transitions in collapsed carbon nanotubes

We have discovered that silver chloride (AgCl) particles in the presence of UV light and dilute hydrogen peroxide exhibit both single-particle and collective oscillations in their motion which arise due to an oscillatory, reversible conversion of AgCl to silver metal at the particle surface. This system exhibits several of the hallmarks of nonlinear oscillatory reactions, including bistability, reaction waves, and synchronized collective oscillations at high particle concentrations. However, unlike traditional oscillatory reactions that take place among dispersed solute species in solution or near a fixed electrode surface, this system of self-mobile catalytic particles evinces a new dynamical length scale: the interparticle spacing, which appears to control wave propagation. The collective motions of these powered nanoparticles self-organize into clumped oscillators with significant spatiotemporal correlations between clumps. A variant of this system using a regular array of lithographically patterned si...

Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions.

Slow decompression of crystalline benzene in large-volume high-pressure cells has recently achieved synthesis of a novel one-dimensional allotrope of sp3 carbon in which stacked columns of benzene molecules rehybridize into an ordered crystal of nanothreads. The progenitor benzene molecules function as six-valent one-dimensional superatoms with multiple binding sites. Here we enumerate their hexavalent bonding geometries, recognizing that the repeat unit of interatomic connectivity (“topological unit cell”) need not coincide with the crystallographic unit cell, and identify the most energetically favorable cases. A topological unit cell of one or two benzene rings with at least two bonds interconnecting each adjacent pair of rings, accommodates 50 topologically distinct nanothreads, 15 of which are within 80 meV/carbon atom of the most stable member. Optimization of aperiodic helicity reveals the most stable structures to be chiral. We generalize Euler’s rules for ring counting to cover this new form of v...

Paul E. Lammert

Papers

Energy minimization and ac demagnetization in a nanomagnet array.

Dynamic interactions between fast microscale rotors.

Gapping by squashing: metal-insulator and insulator-metal transitions in collapsed carbon nanotubes

Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions.

Systematic Enumeration of sp3 Nanothreads