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

Submitted for the MAR11 Meeting of The American Physical Society Tuning the Kohn Anomaly in the Phonon Dispersion of Graphene by Interaction with the Substrate and by Doping LUDGER WIRTZ, CNRS IEMN, Lille, France, ADRIEN ALLARD, CNRS IEMN, Lille, CLAUDIO ATTACCALITE, CNRS, Institut Neel, Grenoble, MICHELE LAZZERI, CNRS IMPMC, Paris, FRANCESCO MAURI, ANGEL RUBIO, ETSF/Univ. Basque Country, San Sebastian, Spain — The phonon dispersion of graphene displays two strong Kohn Anomalies (kinks) in the highest optical branch (HOB) at the high-symmetry points G and K. The slope of the HOB around K is a measure of the electron-phonon coupling (EPC) and determines the dispersion of the Raman D and 2D lines as a function of the laser energy. We show that the EPC can be strongly modified both due to interaction with a metallic substrate and due to doping. For graphene grown on a Ni(111) surface, a total suppression of the Kohn anomaly occurs: the HOB around K becomes completely flat. This is due to the strong hybridization of the graphene p-bands with the Nickel d-bands which lifts the linear crossing of the p-bands at K. From experimental phonon dispersions one can therefore draw conclusions about the interaction strength between graphene and its different substrates. Furthermore, we present a new way to tune the EPC in graphene through electron/hole doping. We show that for the highest optical branch at K, the EPC is strongly dependent on the doping level. This dependency influences the dispersion of the Raman D and 2D lines and makes it possible to measure the charge state of graphene via resonant Raman spectroscopy. Ludger Wirtz CNRS IEMN, Lille, France Date submitted: 06 Dec 2010 Electronic form version 1.4

http://absimage.aps.org/image/MAR11/MWS_MAR11-2010-020123.pdf

Tuning the Kohn Anomaly in the Phonon Dispersion of Graphene by Interaction with the Substrate and by Doping

We compute, from first-principles, the frequency of the phonons associated to the Raman G-bands in a graphene monolayer and in metallic nanotubes as a function of the charge doping. In both cases, the frequency displays an important measurable shift in the range of doping reached experimentally. As a consequence, Raman spectroscopy can be used as a direct probe of the doping of these systems. Calculations are done using (i) the adiabatic Bom-Oppenheimer approximation and (ii) time-dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. The frequency shift of the G-band in graphene and of the G- in metallic tubes represent remarkable failures of the adiabatic Bom-Oppenheimer approximation.

Breakdown of the adiabatic approximation in a doped graphene monolayer and in metallic carbon nanotubes

We investigate the capability of density functional theory (DFT) to appropriately describe the spin susceptibility, $\chi_s$, and the intervalley electron-phonon coupling in Li$_x$ZrNCl. At low doping, Li$_x$ZrNCl behaves as a 2-dimensional 2-valley electron gas, with parabolic bands. In such a system, $\chi_s$ increases with decreasing doping because of the electron-electron interaction. We show that the DFT with local functionals (LDA/GGA) is not capable of reproducing this behavior. The use of exact exchange in Hartree-Fock (HF) or in DFT hybrid functionals enhances $\chi_s$. HF, B3LYP and PBE0 approaches overestimate $\chi_s$, whereas the range-separated HSE06 functional leads to results similar to those obtained in the Random Phase approximation (RPA) applied to a two valley two spin electron-gas. Within HF, Li$_x$ZrNCl is even unstable towards a ferromagnetic state for $x<0.16$. The intervalley phonons induce an unbalance in the valley occupation that can be viewed as the effect of a pseudo-magnetic field. Thus, similarly to what happens for $\chi_s$, the electron-phonon coupling of intervalley phonons is enhanced by the electron-electron interaction. Only hybrid DFT functionals capture such an enhancement and the HSE06 functional reproduces the RPA results presented in Calandra {\it et al.} Phys. Rev. Lett. {\bf 114}, 077001 (2015).

Enhancement of spin susceptibility and electron-phonon coupling by exchange interaction in Li$_x$ZrNCl at low doping: insight from hybrid functional approaches

Inspired by pulsed laser-assisted thermal relaxation experiments, we simulated the response of a nanometer-size monolayer graphene sample to thermal impulses by means of nonequilibrium molecular dynamics. By following the time evolution of the temperature profile until equilibrium is eventually reached, we obtain a direct estimation of the thermal conductivity of the excited graphene sample. It is shown that the predicted thermal conductivity depends on which vibrational degrees of freedom are in fact excited by the thermal impulse, suggesting that its determination depends, among many other issues, on the actual phonon population generated in the sample. The situation here explored is typically found in experiments or simulations addressing a transient regime of approach to equilibrium.

Predicting the thermal conductivity in a graphene nanoflake from its response to a thermal impulse

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Francesco Mauri

Papers

Tuning the Kohn Anomaly in the Phonon Dispersion of Graphene by Interaction with the Substrate and by Doping

Breakdown of the adiabatic approximation in a doped graphene monolayer and in metallic carbon nanotubes

Enhancement of spin susceptibility and electron-phonon coupling by exchange interaction in Li$_x$ZrNCl at low doping: insight from hybrid functional approaches

Predicting the thermal conductivity in a graphene nanoflake from its response to a thermal impulse

\textit{Ab Initio} Theory of Nuclear Magnetic Resonance Shifts in Metals