Project Title  Parallel code development in computational nanoscience. 
Summary  Quantum transport on carbon nanostructures including electronphonon coupling for lowenergy 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 Description  BlueWaters / Shodor Petascale Computing Internship Program 2011: Parallel C++ Algorithm Development for Tightbinding Charge Transport Simulation on Carbon Nanorings including ElectronPhonon Coupling The summer project will describe with a simplified model of electronphonon coupling effects on charge transport on a carbon nanotorus for lowenergy phonon modes [12]. Based on an existing objectoriented 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]. Largescale parallel production runs will test the physics of electronphonon 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 twotiered approach. The first level would make use of tightbinding/Green's function methods to address questions about systems for which phonon modes can operate on time scales for which electron transport is quasiadiabatic. The second level involves employing timedependent methods to calculate the influence on transport properties arising from the interplay between phonon modes and charge transport along the curved torus surface. The tightbinding method is a way to model charge transport through a carbon nanostructure [46]. 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. Densityofstates 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 ringtoring 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 objectoriented C++ code. Focus of this year's summer project is the parallelization of exactly this objectoriented 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 electronphonon interaction may be modeled using additional terms in the Hamiltonian matrix [78]. 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 finiteelement 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 continuummodel 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 lowenergy 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 twoweek 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, largescale 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 1014, 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 longterm collaborations with researchers at DoE government labs will be discussed. At the NERSC ACTS 2011 workshop the student would be exposed to details of largescale 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. References 1. Xu, H., Nanotubes: The logical choice for electronics? Nature materials, 2005. 4(9): p. 649650. 2. Du, X., et al., Approaching ballistic transport in suspended graphene. Nature Nanotechnology, 2008. 3(8): p. 491495. 3. L.S. Blackford, L.S. et al., ScaLAPACK Users' Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1997. ScaLAPACK, http://www.netlib.org/scalapack. 4. Encinosa, M. and M. Jack, Elliptical tori in a constant magnetic field. Physica Scripta, 2006. 73: p. 439442. 5. Encinosa, M. and M. Jack, Dipole and solenoidal magnetic moments of electronic surface currents on toroidal nanostructures. Journal of ComputerAided Materials Design, 2007. 14(1): p. 6571. 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, Electronphonon effects in graphene and armchair (10,10) singlewall carbon nanotubes, Physical Review B, 2000, 61(16): p. 1065110664. 8. Suzuura, H. and T. Ando, Phonons and electronphonon 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 manifoldbased continuum finite element approach. Computer Methods in Applied Mechanics and Engineering, 2009. 198(1720): p. 15721584. 10. G. Em Karniadakis and R.M. Kirby II, Parallel Scientific Computing in C++ and MPI, Cambridge University Press, NY (2003). 
Conditions/Qualifications  Undergraduate 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 Date  05/23/2011 
End Date  04/30/2012 
Location  Dr. Mark A. Jack, Associate Professor, and Dr. Mario Encinosa, Associate Professor Florida A&M University Physics Department Theoretical Physics FredHumphries Science Research Center 419 1500 MartinLutherKing Jr. Blvd. Tallahassee, FL 32307 Office: 8505998457 / main office: 8505993470 Email: mark (dot) jack (at) famu (dot) edu 
Interns  Adam Byrd
