Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

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

Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

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Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

Raman spectroscopy of graphene and graphite: Disorder, electron phonon coupling, doping and nonadiabatic effects

Raman spectroscopy is an integral part of graphene research. It is used to determine the number and orientation of layers, the quality and types of edge, and the effects of perturbations, such as electric and magnetic fields, strain, doping, disorder and functional groups. This, in turn, provides insight into all sp(2)-bonded carbon allotropes, because graphene is their fundamental building block. Here we review the state of the art, future directions and open questions in Raman spectroscopy of graphene. We describe essential physical processes whose importance has only recently been recognized, such as the various types of resonance at play, and the role of quantum interference. We update all basic concepts and notations, and propose a terminology that is able to describe any result in literature. We finally highlight the potential of Raman spectroscopy for layered materials other than graphene.

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Raman spectroscopy as a versatile tool for studying the properties of graphene

We present Raman spectroscopy measurements on single- and few-layer graphene flakes. By using a scanning confocal approach, we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double- and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

We report ab initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS2 and WS2. We explore in detail the behavior of the Raman-active modes A1g and E 1 2g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et al., ACS Nano 4, 2695 (2010)], we find that the A1g mode increases in frequency with an increasing number of layers while the E 1g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with a growing number of layers. This decrease in the long-range part overcompensates for the increase of the short-range interaction due to the weak interlayer interaction.

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Phonons in single-layer and few-layer MoS 2 and WS 2

Phonons in single-layer and few-layer MoS2

We present converged ab initio calculations of the optical absorption spectra of single-layer, double-layer, and bulk MoS${}_{2}$. Both the quasiparticle-energy calculations (on the level of the GW approximation ) and the calculation of the absorption spectra (on the level of the Bethe-Salpeter equation) explicitly include spin-orbit coupling, using the full spinorial Kohn-Sham wave functions as input. Without excitonic effects, the absorption spectra would have the form of a step function, corresponding to the joint density of states of a parabolic band dispersion in two dimensions. This profile is deformed by a pronounced bound excitonic peak below the continuum onset. The peak is split by spin-orbit interaction in the case of single-layer and (mostly) by interlayer interaction in the case of double-layer and bulk MoS${}_{2}$. The resulting absorption spectra are thus very similar in the three cases, but the interpretation of the spectra is different. Differences in the spectra can be seen in the shape of the absorption spectra at 3 eV where the spectra of the single and double layers are dominated by a strongly bound exciton.

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Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS 2

We show that the optical absorption spectra of boron nitride (BN) nanotubes are dominated by strongly bound excitons. Our first-principles calculations indicate that the binding energy for the first and dominant excitonic peak depends sensitively on the dimensionality of the system, varying from 0.7 eV in bulk hexagonal BN via 2.1 eV in the single sheet of BN to more than 3 eV in the hypothetical (2, 2) tube. The strongly localized nature of this exciton dictates the fast convergence of its binding energy with increasing tube diameter towards the sheet value. The absolute position of the first excitonic peak is almost independent of the tube radius and system dimensionality. This provides an explanation for the observed "optical gap" constancy for different tubes and bulk hexagonal BN.

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Ludger Wirtz

Papers

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

Phonons in single-layer and few-layer MoS 2 and WS 2

Phonons in single-layer and few-layer MoS2

Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS 2

Excitons in Boron Nitride Nanotubes: Dimensionality Effects