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.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

The electronic properties of graphene

We show with an {ital ab initio} calculation that electronic surface states have a strong effect on NMR chemical-shift spectra. For the hydrogen-chemisorbed diamond (111) surface, we find that the atomic layers close to the surface experience a variation of the chemical shift, which is proportional to the density of empty surface states. This effect could be used as a direct probe of the surface-state density profile, by measuring experimentally the NMR chemical shift resolved for each atomic layer. {copyright} {ital 1999} {ital The American Physical Society}

Signature of surface states on nmr chemical shifts : a theoretical prediction

We study, theoretically, the impact of Zener tunneling (the generation of electron-hole pairs by the electric field) on the charge-transport properties of graphene in the high-field regime. We model Zener tunneling in a rigorous way, using the quantum master equation for the density matrix. In the presence of Zener tunneling, a steady-state can be reached only by further including an efficient mechanism for the electron thermalization such as electron-electron scattering. We treat the effects of electron-electron relaxation within a simplified model, that assumes an instantaneous separate thermalization of the electrons in the conduction band and of the holes in the valence band. The inclusion of both Zener tunneling and electron-electron relaxation improves the agreement with measurements performed in graphene in the high-field regime at low doping.

https://iopscience.iop.org/article/10.1088/0953-8984/27/16/164205/pdf

High-field transport in graphene: the impact of Zener tunneling

https://link.aps.org/pdf/10.1103/PhysRevB.96.159904

Erratum: Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations [Phys. Rev. B 94 , 085415 (2016)]

In the present study, we used a combination of 17O NMR methods at a high magnetic field with first-principles calculations in order to characterize the oxygen sites in a series of hydroxylated sodium phosphate compounds, namely the hydrogen pyrophosphate Na2H2P2O7 and the hydrogen orthophosphates NaH2PO4, NaH2PO4·H2O and NaH2PO4·2H2O. The chemical shifts and quadrupolar parameters of these compounds were interpreted in terms of local and semi-local environment, i.e., the chemical composition of the immediate surroundings and the nature of the bonds, e.g. hydrogen bonding. The magnitude of the quadrupolar interaction and its asymmetry were revealed to be a precise indicator of the local structure in sodium hydrogen phosphates. Our 17O NMR experimental and computing approach allowed for identification and quantification of the different crystalline phases involved in the weathering mechanism of a sodium phosphate glass, even in small amount.

New insights into oxygen environments generated during phosphate glass alteration: a combined 17O MAS and MQMAS NMR and first principles calculations study.

Simulating nuclear quantum dynamics in strongly anharmonic materials is an open challenge where state-of-the-art techniques fail. This is relevant in ferroelectrics, charge density waves, and crystals encapsulating light atoms, such as superconductive high-pressure hydrides. Here, the authors develop a theory to compute dynamical properties and predict experimental Raman and IR spectroscopy, neutron scattering, and x-ray scattering of any material, accounting for the nuclear quantum and anharmonic dynamics.The method is efficient and can be applied to systems with hundreds of atoms even when treating electrons $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ within density functional theory.

Francesco Mauri

Papers

Signature of surface states on nmr chemical shifts : a theoretical prediction

High-field transport in graphene: the impact of Zener tunneling

Erratum: Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations [Phys. Rev. B 94 , 085415 (2016)]

New insights into oxygen environments generated during phosphate glass alteration: a combined 17O MAS and MQMAS NMR and first principles calculations study.

Time-dependent self-consistent harmonic approximation: Anharmonic nuclear quantum dynamics and time correlation functions