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

We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.

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Electronic transport in two-dimensional graphene

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

The reported thermal conductivity (κ) of suspended graphene, 3000 to 5000 watts per meter per kelvin, exceeds that of diamond and graphite. Thus, graphene can be useful in solving heat dissipation problems such as those in nanoelectronics. However, contact with a substrate could affect the thermal transport properties of graphene. Here, we show experimentally that κ of monolayer graphene exfoliated on a silicon dioxide support is still as high as about 600 watts per meter per kelvin near room temperature, exceeding those of metals such as copper. It is lower than that of suspended graphene because of phonons leaking across the graphene-support interface and strong interface-scattering of flexural modes, which make a large contribution to κ in suspended graphene according to a theoretical calculation.

http://science.sciencemag.org/content/sci/328/5975/213.full.pdf

Two-Dimensional Phonon Transport in Supported Graphene

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Using scanning tunneling microscopy in an ultrahigh vacuum and atomic force microscopy, we investigate the corrugation of graphene flakes deposited by exfoliation on a Si/SiO 2 (300 nm) surface. While the corrugation on SiO 2 is long range with a correlation length of about 25 nm, some of the graphene monolayers exhibit an additional corrugation with a preferential wavelength of about 15 nm. A detailed analysis shows that the long-range corrugation of the substrate is also visible on graphene, but with a reduced amplitude, leading to the conclusion that the graphene is partly freely suspended between hills of the substrate. Thus, the intrinsic rippling observed previously on artificially suspended graphene can exist as well, if graphene is deposited on SiO 2 .

/pdf/intrinsic-and-extrinsic-corrugation-of-monolayer-graphene-ktjwlq7uww.pdf

Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO 2

We report on a method for the fabrication of graphene on a silicon dioxide substrate by solid-state dissolution of an overlying stack of a silicon carbide and a nickel thin film. The carbon dissolves in the nickel by rapid thermal annealing. Upon cooling, the carbon segregates to the nickel surface forming a graphene layer over the entire nickel surface. By wet etching of the nickel layer, the graphene layer was allowed to settle on the original substrate. Scanning tunneling microscopy (STM) as well as Raman spectroscopy has been performed for characterization of the layers. Further insight into the morphology of the layers has been gained by Raman mapping indicating micrometer-size graphene grains. Devices for electrical measurement have been manufactured exhibiting a modulation of the transfer current by backgate electric fields. The presented approach allows for mass fabrication of polycrystalline graphene without transfer steps while using only CMOS compatible process steps.

Synthesis of Graphene on Silicon Dioxide by a Solid Carbon Source

The truly two-dimensional material graphene is an ideal candidate for nanoelectromechanics due to its large strength and mobility. Here we show that graphene flakes provide natural nanomembranes of diameter down to 3 nm within its intrinsic rippling. The membranes can be lifted either reversibly or hysteretically by the tip of a scanning tunneling microscope. The clamped-membrane model including van-der-Waals and dielectric forces explains the results quantitatively. AC-fields oscillate the membranes, which might lead to a completely novel approach to controlled quantized oscillations or single atom mass detection.

Bistability and oscillatory motion of natural nanomembranes appearing within monolayer graphene on silicon dioxide.

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene $K$ point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moir\'e potential and a 10% penetration of an Ir surface resonance into the graphene layer.

Wave-Function Mapping of Graphene Quantum Dots with Soft Confinement

The recently found material graphene is a truly two-dimensional crystal and exhibits, in addition, an extreme mechanical strength. This in combination with the high electron mobility favours graphene for electromechanical investigations down to the quantum limit. Here, we show that a monolayer of graphene on SiO2 provides natural, ultra-small membranes of diameters down to 3 nm, which are caused by the intrinsic rippling of the material. Some of these nano-membranes can be switched hysteretically between two vertical positions using the electric field of the tip of a scanning tunnelling microscope (STM). They can also be forced to oscillatory motion by a low frequency ac-field. Using the mechanical constants determined previously, we estimate a high resonance frequency up to 0.4 THz. This might be favorable for quantum-electromechanics and is prospective for single atom mass spectrometers.

V. Geringer

Papers

Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO 2

Synthesis of Graphene on Silicon Dioxide by a Solid Carbon Source

Bistability and oscillatory motion of natural nanomembranes appearing within monolayer graphene on silicon dioxide.

Wave-Function Mapping of Graphene Quantum Dots with Soft Confinement

Bistability and oscillatory motion of natural nano-membranes appearing within monolayer graphene on silicon dioxide