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

Electron-phonon scattering and anharmonicity are the dominant mechanisms, that enable to describe the equilibrium phonon properties in graphene [1] and Raman scattering is the main tool for their characterization [2]. In the first tens fs after the photoexcitation, an out of equilibrium distribution of (hot) electron is induced with respect to the (cold) phonon bath. Within a few picoseconds, the fast electron-electron and electron-phonon non radiative recombination channels determine the equilibrium between the electronic distribution and the lattice. Therefore, on the laboratory timescale, continuous wave laser sources, commonly used for high resolution spontaneous Raman scattering, examine already equilibrated carrier-phonon distributions.

Phonon anomalies in Graphene induced by highly excited charge carriers

We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the orbitals are not constrained to be orthonormal. Furthermore, by combining this result with a recently introduced Wannier-like representation of the electronic orbitals, we find expressions for the static linear and nonlinear susceptibilities which are much simpler than those obtained by standard perturbative expansions. We test numerically the validity of our approach with a 1D model Hamiltonian.

Localized-orbital computation of linear and nonlinear susceptibilities

Ab initio calculations have been carried out for the three polymorphs of SiAl2O5 in order to study the 17O NMR characteristics of tricoordinated O atoms, O[3], and tetracoordinated O atoms, O[4], that are possibly present in the structure of aluminosilicate glasses. We present δiso, CQ, and η calculations using the density functional theory-based GIPAW method for all silicon, aluminum, and oxygen sites and in particular for the 14 O[3] atoms, which are bonded to three Al or Si atoms in the andalusite, sillimanite, and kyanite polymorphs of SiAl2O5. The O[4] parameters calculated in kyanite are also compared with the corresponding site in α-Al2O3. The calculated values for the 29Si and 27Al isotropic chemical shift values as well as 27Al quadrupolar coupling constants (CQ) and asymmetry parameters (η) are in good agreement with experimental data. Apart from in alumina and in grossite CaAl4O7, 17O NMR parameters have not been measured experimentally yet but the CQ and η values obtained for all sites are con...

Ab initio Calculations of NMR Parameters of Highly Coordinated Oxygen Sites in Aluminosilicates.

Abstract Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity—the former neglects anharmonicity, the latter misses the quantum Bose-Einstein statistics of vibrations—and require atomistic models that are very challenging for first-principles methods. Here, we present a protocol to determine from first principles the thermal conductivity κ ( T ) of glasses above the plateau (i.e., above the temperature-independent region appearing almost without exceptions in the κ ( T ) of all glasses at cryogenic temperatures). The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and accounts comprehensively for the effects of structural disorder, anharmonicity, and Bose-Einstein statistics. We validate this approach in vitreous silica, showing that models containing less than 200 atoms can already reproduce κ ( T ) in the macroscopic limit. We discuss the effects of anharmonicity and the mechanisms determining the trend of κ ( T ) at high temperature, reproducing experiments at temperatures where radiative effects remain negligible. 

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Francesco Mauri

Papers

Phonon anomalies in Graphene induced by highly excited charge carriers

Localized-orbital computation of linear and nonlinear susceptibilities

Ab initio Calculations of NMR Parameters of Highly Coordinated Oxygen Sites in Aluminosilicates.

Thermal conductivity of glasses: first-principles theory and applications