Jack Deslippe

Excitonic effects on the optical response of graphene and bilayer graphene.

We present first-principles calculations of many-electron effects on the optical response of graphene, bilayer graphene, and graphite employing the GW-Bethe Salpeter equation approach. We find that resonant excitons are formed in these two-dimensional semimetals. The resonant excitons give rise to a prominent peak in the absorption spectrum near 4.5 eV with a different line shape and significantly redshifted peak position from those of an absorption peak arising from interband transitions in an independent quasiparticle picture. In the infrared regime, our calculated optical absorbance per graphene layer is approximately a constant, 2.4%, in agreement with recent experiments; additional low frequency features are found for bilayer graphene because of band structure effects.

BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures☆

Abstract BerkeleyGW is a massively parallel computational package for electron excited-state properties that is based on the many-body perturbation theory employing the ab initio GW and GW plus Bethe–Salpeter equation methodology. It can be used in conjunction with many density-functional theory codes for ground-state properties, including PARATEC , PARSEC , Quantum ESPRESSO , SIESTA , and Octopus . The package can be used to compute the electronic and optical properties of a wide variety of material systems from bulk semiconductors and metals to nanostructured materials and molecules. The package scales to 10 000s of CPUs and can be used to study systems containing up to 100s of atoms. Program summary Program title: BerkeleyGW Catalogue identifier: AELG_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELG_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Open source BSD License. See code for licensing details. No. of lines in distributed program, including test data, etc.: 576 540 No. of bytes in distributed program, including test data, etc.: 110 608 809 Distribution format: tar.gz Programming language: Fortran 90, C, C++, Python, Perl, BASH Computer: Linux/UNIX workstations or clusters Operating system: Tested on a variety of Linux distributions in parallel and serial as well as AIX and Mac OSX RAM: (50–2000) MB per CPU (Highly dependent on system size) Classification: 7.2, 7.3, 16.2, 18 External routines: BLAS, LAPACK, FFTW, ScaLAPACK (optional), MPI (optional). All available under open-source licenses. Nature of problem: The excited state properties of materials involve the addition or subtraction of electrons as well as the optical excitations of electron–hole pairs. The excited particles interact strongly with other electrons in a material system. This interaction affects the electronic energies, wavefunctions and lifetimes. It is well known that ground-state theories, such as standard methods based on density-functional theory, fail to correctly capture this physics. Solution method: We construct and solve the Dysonʼs equation for the quasiparticle energies and wavefunctions within the GW approximation for the electron self-energy. We additionally construct and solve the Bethe–Salpeter equation for the correlated electron–hole (exciton) wavefunctions and excitation energies. Restrictions: The material size is limited in practice by the computational resources available. Materials with up to 500 atoms per periodic cell can be studied on large HPCs. Additional comments: The distribution file for this program is approximately 110 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: 1–1000 minutes (depending greatly on system size and processor number).

Many-body interactions in quasi-freestanding graphene

The Landau–Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron–electron and electron–phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron–electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Tuning Many-Body Interactions in Graphene: The Effects of Doping on Excitons and Carrier Lifetimes

The optical properties of graphene are strongly affected by electron-electron (e-e) and electron-hole (e-h) interactions. Here we tune these many-body interactions through varying the density of free charge carriers. Measurements from the infrared to the ultraviolet reveal significant changes in the optical conductivity of graphene for both electron and hole doping. The shift, broadening, and modification in shape of the saddle-point exciton resonance reflect strong screening of the many-body interactions by the carriers, as well as changes in quasi-particle lifetimes. Ab initio calculations by the GW Bethe-Salpeter equation (GW-BSE), which take into account modification of both the repulsive e-e and the attractive e-h interactions, provide excellent agreement with experiment. Understanding the optical properties and high-energy carrier dynamics of graphene over a wide range of doping is crucial for both fundamental graphene physics and for emerging applications of graphene in photonics.

Applying the Roofline Performance Model to the Intel Xeon Phi Knights Landing Processor

The Roofline Performance Model is a visually intuitive method used to bound the sustained peak floating-point performance of any given arithmetic kernel on any given processor architecture. In the Roofline, performance is nominally measured in floating-point operations per second as a function of arithmetic intensity (operations per byte of data). In this study we determine the Roofline for the Intel Knights Landing (KNL) processor, determining the sustained peak memory bandwidth and floating-point performance for all levels of the memory hierarchy, in all the different KNL cluster modes. We then determine arithmetic intensity and performance for a suite of application kernels being targeted for the KNL based supercomputer Cori, and make comparisons to current Intel Xeon processors. Cori is the National Energy Research Scientific Computing Center’s (NERSC) next generation supercomputer. Scheduled for deployment mid-2016, it will be one of the earliest and largest KNL deployments in the world.

Structure Preserving Parallel Algorithms for Solving the Bethe{Salpeter Eigenvalue Problem

Abstract The Bethe–Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe–Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice. We establish the equivalence between Bethe–Salpeter eigenvalue problems and real Hamiltonian eigenvalue problems. Based on theoretical analysis, structure preserving algorithms for a class of Bethe–Salpeter eigenvalue problems are proposed. We also show that for this class of problems all eigenvalues obtained from the Tamm–Dancoff approximation are overestimated. In order to solve large scale problems of practical interest, we discuss parallel implementations of our algorithms targeting distributed memory systems. Several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms.

GW100: Benchmarking G0W0 for Molecular Systems.

We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.

An Explicit Formula for Optical Oscillator Strength of Excitons in Semiconducting Single-Walled Carbon Nanotubes: Family Behavior

The sensitive structural dependence of the optical properties of single-walled carbon nanotubes, which are dominated by excitons and tunable by changing diameter and chirality, makes them excellent candidates for optical devices. Because of strong many-electron interaction effects, the detailed dependence of the optical oscillator strength f(s) of excitons on nanotube diameter d, chiral angle θ, and electronic subband index P (the so-called family behavior), however, has been unclear. In this study, based on results from an extended Hubbard Hamiltonian with parameters derived from ab initio GW plus Bethe-Salpeter equation (GW-BSE) calculations, we have obtained an explicit formula for the family behavior of the oscillator strengths of excitons in semiconducting single-walled carbon nanotubes (SWCNTs), incorporating environmental screening. The formula explains recent measurements well and is expected to be useful in the understanding and design of possible SWCNT optical and optoelectronic devices.

Effects of self-consistency and plasmon-pole models on G W calculations for closed-shell molecules

We present theoretical calculations of quasiparticle energies in closed-shell molecules using the GW method. We compare three different approaches: a full-frequency