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

Using density functional theory calculations we show that the recently synthesized superhard diamondlike ${\mathrm{BC}}_{5}$ is superconducting with a critical temperature of the same order as that of ${\mathrm{MgB}}_{2}$. The average electron-phonon coupling is $\ensuremath{\lambda}=0.89$, the phonon-frequency logarithmic average is $⟨\ensuremath{\omega}{⟩}_{\mathrm{log}﻿}=67.4\text{ }\text{ }\mathrm{meV}$, and the isotope coefficients are $\ensuremath{\alpha}(\mathrm{C})=0.3$ and $\ensuremath{\alpha}(\mathrm{B})=0.2$. In ${\mathrm{BC}}_{5}$, superconductivity is mostly sustained by concerted vibrations of the B atom and its C neighbors.

High-Tc superconductivity in superhard diamondlike BC5.

The occurrence of nonadiabatic effects in the vibrational properties of metals has been predicted since the 1960s, but hardly confirmed experimentally. We report the first fully ab initio calculations of nonadiabatic frequencies of a number of conventional (hcp Ti and Mg) and layered metals (MgB2, CaC6, and other intercalated graphites). Nonadiabatic effects can be spectacularly large (up to 30% of the phonon frequencies) in both cases, but they can only be experimentally observed in the Raman spectra of layered compounds. In layered metals nonadiabatic effects are crucial to explaining the observed Raman shifts and linewidths. Moreover, we show that those quantities can be used to extract the electron momentum-relaxation time.

Giant nonadiabatic effects in layer metals: raman spectra of intercalated graphite explained.

In this article we unravel the origin of the two-phonon D + D �� peak and its asymmetric line shape by combining experimental data of single-layer graphene with a full twodimensional calculation of the double-resonant Raman process based on fourth-order perturbation theory. We show that the main peak originates from phonons along the K highsymmetry line and that the asymmetry is due to phonons from the two-dimensional Brillouin zone. The analysis of the asymmetric line shape in experiment provides a direct probe of the two-dimensional phonon dispersion. We further show how the D + D �� peak evolves with the number of graphene layers.

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Signature of the two-dimensional phonon dispersion in graphene probed by double-resonant Raman scattering

${\mathrm{K}}_{3}$ picene is a superconducting molecular crystal with a critical temperature of ${T}_{c}=7$ or 18 K, depending on the preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for ${T}_{c}$ 3--8 K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is $\ensuremath{\lambda}=0.73$ and ${\ensuremath{\omega}}_{\mathrm{log}﻿}=18.0\text{ }\text{ }\mathrm{meV}$. Intercalant and intermolecular phonon modes contribute substantially (40%) to $\ensuremath{\lambda}$ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes superconductivity in K-doped picene peculiar and different from that of fullerenes.

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Intercalant and Intermolecular Phonon Assisted Superconductivity in K-Doped Picene

Whether a liquid forms a crystal or a glass on solidification depends on many factors. The finding now that a disordered structure is favoured in B2O3 because the system cannot choose between several crystalline polymorphs of similar energy highlights a link between glass formation and crystallization.

Francesco Mauri

Papers

High-Tc superconductivity in superhard diamondlike BC5.

Giant nonadiabatic effects in layer metals: raman spectra of intercalated graphite explained.

Signature of the two-dimensional phonon dispersion in graphene probed by double-resonant Raman scattering

Intercalant and Intermolecular Phonon Assisted Superconductivity in K-Doped Picene

Hidden polymorphs drive vitrification in B2O3