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

Publisher's Note: Electronic structure of heavily doped graphene: The role of foreign atom states [Phys. Rev. B 76 , 161406 (2007)]

Within density-functional theory we compute the orbital magnetization for periodic systems evaluating a recently discovered Berry-phase formula. For the ferromagnetic metals Fe, Co, and Ni we explicitly calculate the contribution of the interstitial regions neglected so far in literature. We also use the orbital magnetization to compute the electron paramagnetic resonance $g$ tensor in paramagnetic systems. Here the method can also be applied in cases where linear-response theory fails, e.g., radicals and defects with an orbital-degenerate ground state or those containing heavy atoms.

First-principles theory of orbital magnetization

In this work we elucidate the microscopic origin of the dominant radiation induced I-II spectra in p-type doped 4H-SiC. By calculating the electronic g-tensor from first principles in the framework of density functional theory, basal antisite pairs Si(C)C(Si)(+) are shown to give rise to the characteristic anisotropic g-tensors found in the electron paramagnetic resonance (EPR) measurements. Additional central hyperfine (hf) splittings of about 100 MHz due to the Si(C) antisite nuclei are predicted theoretically and also resolved experimentally. We have, thus, identified antisite pairs as a dominant defect in electron and proton irradiated p-type doped 4H-SiC.

Si(C)C(Si) Antisite Pairs as Dominant Irradiation Induced Defects in p-type 4H-SiC

Atomic vibrations are partially screened by electrons. In a metal this screening can change rapidly for vibrations associated to certain points of the Brillouin zone, entirely determined by the shape of the Fermi surface. The consequent anomalous behaviour of the phonon dispersion is called Kohn anomaly. Graphite is a semimetal. Nanotubes can be metals or semiconductors. We demonstrate that two Kohn anomalies are present in the phonon dispersion of graphite and that their slope is proportional to the square of the electron-phonon coupling. Metallic nanotubes have much stronger anomalies than graphite, due to their reduced dimensionality. Semiconducting nanotubes have no Kohn anomalies.

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Kohn Anomalies in Graphite and Nanotubes

There has been a lot of excitement around the observation of superconductivity in twisted bilayer graphene, associated to flat bands close to the Fermi level. Such correlated electronic states also occur in multilayer rhombohedral stacked graphene (RG), which has been receiving increasing attention in the last years. In both natural and artificial samples however, multilayer stacked Bernal graphene (BG) occurs more frequently, making it desirable to determine what is their relative stability and under which conditions RG might be favored. Here, we study the energetics of BG and RG in bulk and also multilayer stacked graphene using first-principles calculations. It is shown that the electronic temperature, not accounted for in previous studies, plays a crucial role in determining which phase is preferred. We also show that the low energy states at room temperature consist of BG, RG and mixed BG-RG systems with a particular type of interface. Energies of all stacking sequences (SSs) are calculated for N = 12 layers, and an Ising model is used to fit them, which can be used for larger N as well. In this way, the ordering of low energy SSs can be determined and analyzed in terms of a few parameters. Our work clarifies inconsistent results in the literature, and sets the basis to studying the effect of external factors on the stability of multilayer graphene systems in first principles calculations.

Francesco Mauri

Papers

Publisher's Note: Electronic structure of heavily doped graphene: The role of foreign atom states [Phys. Rev. B 76 , 161406 (2007)]

First-principles theory of orbital magnetization

Si(C)C(Si) Antisite Pairs as Dominant Irradiation Induced Defects in p-type 4H-SiC

Kohn Anomalies in Graphite and Nanotubes

Ab-initio energetics of graphite and multilayer graphene: stability of Bernal versus rhombohedral stacking