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Project TitleParallel code development in computational nanoscience.
SummaryQuantum transport on carbon nanostructures including electron-phonon coupling for low-energy phonon modes shall be modeled using parallel numerical integration routines in C/C++ on TeraGrid and local computer cluster resources. MPI and parallel linear algebra libraries will be used to calculate electronic transport for system sizes of up to roughly 30,000 atoms.
Job DescriptionBlueWaters / Shodor Petascale Computing Internship Program 2011:

Parallel C++ Algorithm Development for Tightbinding Charge Transport Simulation on Carbon Nanorings including Electron-Phonon Coupling

The summer project will describe with a simplified model of electron-phonon coupling effects on charge transport on a carbon nanotorus for low-energy phonon modes [1-2]. Based on an existing object-oriented C++ code to calculate transport in a nanoring developed in a project in last year's BlueWaters summer internship program, the student now will help to develop a parallel C++ algorithm based on MPI and parallel matrix libraries such as ScaLAPACK, PETSC or Trilinos available on NSF TeraGrid resources [3]. Large-scale parallel production runs will test the physics of electron-phonon interactions for nanoring sizes of several 1,000 to 1,0000 atoms.

Electron transport through carbon nanostructures in the presence of phonons will necessitate a two-tiered approach. The first level would make use of tight-binding/Green's function methods to address questions about systems for which phonon modes can operate on time scales for which electron transport is quasi-adiabatic. The second level involves employing time-dependent methods to calculate the influence on transport properties arising from the interplay between phonon modes and charge transport along the curved torus surface.

The tight-binding method is a way to model charge transport through a carbon nanostructure [4-6]. The Hamiltonian matrix can be derived in a basis set expansion from the Hubbard model. All observables can then be derived from the (retarded / advanced) Green's function Gd(E) of the device region which is computed in a reverse Green's function algorithm. Density-of-states D(E) and transmissivities T(E) for electron transport may be calculated through a nanotorus between two attached metallic leads under a small voltage bias. For a metallic (3,3)-armchair carbon nanoring, for example, the effective Hamiltonian in this case may be described by a 300 x 300 matrix (each matrix element itself being a 12x12 matrix for the local ring-to-ring couplings). This has been compressed due to the original matrix' banded structure to a 3x300 matrix of objects, each object representing a 12x12 matrix that can be individually addressed in a serial object-oriented C++ code. Focus of this year's summer project is the parallelization of exactly this object-oriented code with MPI calls and using routines for fast parallel matrix manipulations provided by tools such as ScaLAPACK, PETSC or Trilinos.

The interaction of electrons with phonons in carbon nanostructure electron transport will be the major science focus of the proposed work to be continued throughout the internship program in the fall of 2011 and spring of 2012. The electron-phonon interaction may be modeled using additional terms in the Hamiltonian matrix [7-8]. The strength of the coupling term will be derived from the lattice deformation accompanying each phonon mode and the occupancy of the phonon modes at the temperature of the system. A research collaborator at the Georgia Institute of Technology has developed a finite-element based code that permits the calculation of phonon frequencies and phonon polarization vectors that can then be directly extracted for each atomic lattice site by properly discretizing the continuum-model description of the ring distortions [9]. For a given vibrational mode, this information will then be read into the electronic transport Hamiltonian in tightbinding approximation for each matrix element. The effect of different low-energy modes of vibrations on electron transport in a nanoring may then be systematically studied. Transmissivities, integrated currents, and magneto- resistance might be sensitive to particular vibrational modes which may be suppressed e.g. through smart choice of a substrate on which the nanodevice setup would rest.

After the student's two-week intensive introduction to parallel computing and multicore processing at the NCSA, he summer project will start with a quick introduction to parallel scientific computing in C++ and MPI. The student will be setup with a student user account at Florida State University's HPC Center (FSU HPC) and with an NSF TeraGrid user account at the Texas Advanced Computing Center (TACC) to practice tutorial examples. The editing, compiling and execution of parallel routines will be practiced for 64 to 512 processor runs on the FSU HPC account, large-scale production runs using up to 1,000 processors are later planned on the TeraGrid. The book by George Em Karniadakis and Robert M. Kirby II, Parallel Scientific Computing in C++ and MPI [10], will act as a quick study guide with available example programs and detailed discussion of matrix algorithms and their parallel implementation with basic MPI commands. The student will have the opportunity to familiarize herself/himself with the relevant chapters on fast linear solvers and Eigensolvers and to try out some of the routines on a laptop or campus workstation. Concerns, problems, optimizations with the coding can be addressed with the staff at FSU HPC and at TACC. The discussion of the physics context of the Hamiltonian matrix description will be developed at the same time with the faculty member.

A conference trip with the student to the SciDAC Conference in Denver, July 10-14, hosted by the Department of Energy's (DoE) SciDAC division is suggested in the final part of the summer project, possibly including a trip of the student to the DoE NERSC ACTS 2011 workshop in Berkeley, CA in August after the summer project phase pending funding. At the SciDAC Conference possible long-term collaborations with researchers at DoE government labs will be discussed. At the NERSC ACTS 2011 workshop the student would be exposed to details of large-scale parallel linear algebra tools such as ScaLAPACK, SuperLU, PETSC etc. to further the student's training as preparation for graduate research in computational physics later.

1. Xu, H., Nanotubes: The logical choice for electronics? Nature materials, 2005. 4(9): p. 649-650.
2. Du, X., et al., Approaching ballistic transport in suspended graphene. Nature Nanotechnology, 2008. 3(8): p. 491-495.
3. L.S. Blackford, L.S. et al., ScaLAPACK Users' Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997. ScaLAPACK,
4. Encinosa, M. and M. Jack, Elliptical tori in a constant magnetic field. Physica Scripta, 2006. 73: p. 439-442.
5. Encinosa, M. and M. Jack, Dipole and solenoidal magnetic moments of electronic surface currents on toroidal nanostructures. Journal of Computer-Aided Materials Design, 2007. 14(1): p. 65-71.
6. Encinosa, M. and M. Jack, Quantum electron transport in toroidal carbon nanotubes with metallic leads. Journal of Molecular Simulations, 2008. 34(1): p. 9ff.
7. Woods, L.M. and G.D. Mahan, Electron-phonon effects in graphene and armchair (10,10) single-wall carbon nanotubes, Physical Review B, 2000, 61(16): p. 10651-10664.
8. Suzuura, H. and T. Ando, Phonons and electron-phonon scattering in carbon nanotubes. Physical Review B, 2002, 65: p. 235412ff.
9. Leamy, M.J. and A. DiCarlo, Phonon spectra prediction in carbon nanotubes using a manifold-based continuum finite element approach. Computer Methods in Applied Mechanics and Engineering, 2009. 198(17-20): p. 1572-1584.
10. G. Em Karniadakis and R.M. Kirby II, Parallel Scientific Computing in C++ and MPI, Cambridge University Press, NY (2003).

Conditions/QualificationsUndergraduate or graduate student.
Necessary qualifications: Quantum mechanics theory (undergraduate level), programming experience (Undergraduate project: Mathematica, Fortran or C/C++; Graduate project: Fortran or C/C++).

Start Date05/23/2011
End Date04/30/2012
LocationDr. Mark A. Jack, Associate Professor, and Dr. Mario Encinosa, Associate Professor
Florida A&M University
Physics Department
Theoretical Physics
Fred-Humphries Science Research Center 419
1500 Martin-Luther-King Jr. Blvd.
Tallahassee, FL 32307
Office: 850-599-8457 / main office: 850-599-3470
Email: mark (dot) jack (at) famu (dot) edu
Adam Byrd