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

Erratum to "Theoretical investigation of the anomalous equilibrium fractionation of multiple sulfur isotopes during adsorption" [Earth Planet. Sci. Lett. 284 (2009) 88–93]

We develop a method to compute the electron-phonon interaction and the phonon frequencies in doped 3-dimensional semiconductors. The present formalism goes beyond the state-of-the-art description of the Fröhlich-like vertex and of the long-range non-analytical part of the dynamical matrix, taking into account the change of the inverse dielectric function −1(q) in presence of free carriers at finite temperature. The method is computationally fast thanks to the use of interpolation based on maximally localized Wannier functions. We apply our approach to cubic silicon carbide 3C-SiC, where we find that in presence of doping the Fröhlich coupling and the LO-TO splitting are strongly reduced, thereby influencing observable properties such as the electronic lifetime.

Fröhlich electron-phonon interaction and LO-TO splitting in doped semiconductors

U. Gerstmann,1,2 A. P. Seitsonen,1 D. Ceresoli,3 F. Mauri,1 H. J. von Bardeleben,4 J. L. Cantin,4 and J. Garcia Lopez5 1Institut de Minéralogie et de Physique des Milieux Condensés, Université Paris 6, 140 rue de Lourmel, F-75015 Paris, France 2Lehrstuhl für Theoretische Physik, Department für Naturwissenschaften, Universität Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany 3Department of Materials Science and Engineering, Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA 4Institut des Nanosciences de Paris, Université Paris 6, 140 rue de Lourmel, F-75015 Paris, France 5Centro Nacional de Aceleradores, Thomas A. Edison, Isla de La Cartuja, E-41092 Sevilla, Spain Received 8 April 2010; published 17 May 2010

Si[subscript C]C[subscript Si] antisite pairs in SiC identified as paramagnetic defects with strongly anisotropic orbital quenching

Kohn anomalies are distinct features of the phonon dispersion in metallic systems, associated to the presence of a Fermi surface. Graphene is a model system to understand the physical properties of carbon nanotubes. Two Kohn anomalies are present in the phonon dispersion of graphene and their slope is proportional to the square of the electron‐phonon coupling. Kohn anomalies are enhanced in metallic nanotubes due to their reduced dimensionality and absent for semiconducting. The electron‐phonon coupling for nanotubes of arbitrary chirality and diameter can be obtained from graphite.

Francesco Mauri

Papers

Erratum to "Theoretical investigation of the anomalous equilibrium fractionation of multiple sulfur isotopes during adsorption" [Earth Planet. Sci. Lett. 284 (2009) 88–93]

Fröhlich electron-phonon interaction and LO-TO splitting in doped semiconductors

Si[subscript C]C[subscript Si] antisite pairs in SiC identified as paramagnetic defects with strongly anisotropic orbital quenching

Kohn Anomalies and Electron‐Phonon Coupling in Carbon Nanotubes

Phonon softeting and superconductivity in tellurium under pressure