Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

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

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

We demonstrate the key role of phonon occupation in limiting the high-field ballistic transport in metallic carbon nanotubes. In particular, we provide a simple analytic formula for the electron transport scattering length, which we validate by accurate first principles calculations on (6, 6) and (11, 11) nanotubes. The comparison of our results with the scattering lengths fitted from experimental I-V curves indicates the presence of a nonequilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.

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Electron transport and hot phonons in carbon nanotubes.

We present a theory for the {ital ab} {ital initio} computation of NMR chemical shifts ({sigma}) in condensed matter systems, using periodic boundary conditions. Our approach can be applied to periodic systems such as crystals, surfaces, or polymers and, with a supercell technique, to nonperiodic systems such as amorphous materials, liquids, or solids with defects. We have computed the hydrogen {sigma} for a set of free molecules, for an ionic crystal LiH, and for a H-bonded crystal HF, using density functional theory in the local density approximation. The results are in excellent agreement with experimental data. {copyright} {ital 1996 The American Physical Society.}

Ab Initio Theory of NMR Chemical Shifts in Solids and Liquids.

A new complete, representative model for the hydroxylated surface of amorphous silica is presented and characterized by means of periodic DFT calculations. This model accounts for the experimentally encountered ring size distribution, Si-O-Si and O-Si-O angles, silanols density, and distribution (isolated, associated, geminals). Properties such as NMR shifts, dehydrogenation energies, OH vibrational frequencies, and the interaction with water are investigated. The results are compared with former experimental and theoretical results. This new representative model for this complex surface would probably help the investigation of its reactivity toward amino acids or other organic molecules, opening new perspectives in the understanding of the chemistry of amorphous materials.

Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model

We present a first-principles theoretical approach for evaluating the lattice thermal conductivity based on the exact solution of the Boltzmann transport equation. We use the variational principle and the conjugate gradient scheme, which provide us with an algorithm faster than the one previously used in literature and able to always converge to the exact solution [Omini and Sparavigna, Physica B: Condens. Matter 212, 101 (1995)]. Three-phonon normal and umklapp collisions, isotope scattering, and border effects are rigorously treated in the calculation. Good agreement with experimental data for diamond is found. Moreover we show that by growing more enriched diamond samples it is possible to achieve values of thermal conductivity up to three times larger than those commonly observed in isotopically enriched diamond samples with $99.93%$ C${}^{12}$ and $0.07$ C${}^{13}$.

Ab initio variational approach for evaluating lattice thermal conductivity

We present a detailed study of the high-current transport properties of graphene devices patterned in a four-point configuration. The current tends to saturate as the voltage across graphene is increased but never reaches the complete saturation as in metallic nanotubes. Measurements are compared to a model based on the Boltzmann equation, which includes electron-scattering processes due to charged and neutral impurities, and graphene optical phonons. The saturation is incomplete because of the competition between disorder and optical phonon scattering.

Francesco Mauri

Papers

Electron transport and hot phonons in carbon nanotubes.

Ab Initio Theory of NMR Chemical Shifts in Solids and Liquids.

Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model

Ab initio variational approach for evaluating lattice thermal conductivity

Transport properties of graphene in the high-current limit.