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Carbon nanorings, metamaterials, and nanoplasmonics – high-performance computing in physics research and education Mark A. Jack Florida A&M University, Physics Department, FL C-STEM Teacher Preparation Workshop Florida A&M University, Tallahassee, FL – Jun 13, 2011. Toroidal carbon nanotubes P. Avouris (IBM): C. Dekker (TU Delft): Discovery: S. Iijima, Nature 56 (1991). 2 Ring synthesis and pattern formation: Motavas, Omrane, and Papadopoulos: Large-Area Patterning of Carbon Nanotube Ring Arrays, Langmuir 2009, 25(8), 4655–4658. 3 Nanotube Structure (m,n) lattice vector: v = ma1 + na2 Zigzag (9,0) Armchair (5,5) Chiral (10,5) Iijima, Nature 363 (1993) Odom et al., Nature 391 (1998) Dai, Acc. Chem. Res. 35 (2002) 4 Currents in a single nanoring – nanodevice model Right lead w R Left lead Carbon nanotube review: J.C. Charlier et al., Rev. Mod. Phys. 79 (2009). 2a Nanotorus with semi-infinite metallic leads. (3,3) armchair torus. 5 Classical Theory – microscopic model for toroidal moment Toroidal moment generated by microscopic ring currents: d K. Marinov et al., New J. Phys. 9 (2007): a) Singly wound toroid with extra loop (no magn. dipole mom.); b) doubly wound toroid (no magn. di-/quadrupole mom.). 3D array of toroidal solenoids in a medium optical activity Kaelberer et al, Science 330 (2010): Toroidal moment T generated by poloidal currents. 6 Quantum Field Theory: Non-Equilibrium Green’s Function Method (NEGF) Hamiltonian H for electron transport in tight-binding approximation: ballistic transport Example for tightbinding scheme: Single layer graphene Graphene review: A.H. Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009). 7 Recursive Green’s Function Algorithm (RGF) Example: Green’s function Gd for transport in a nanoring device: Effective Hamiltonian : (3,3) armchair nanotorus 8 Algorithm The C atoms can be numbered in consecutive rings in the rolled-up graphene sheet. Including only nearest-neighbor interactions the Hamiltonian matrix has the (mostly) tridiagonal structure shown at the right. 2010 TeraGrid Pathways Project with summer student Leon Durivage (Winona State U.) and NCSI/Shodor Blue Waters Petascale Computing Undergraduate Research Internship Program. 9 Algorithm New object-oriented C++ code: The Hamiltonian matrix H0 can be decomposed locally into the following block structure: The transformation from the tri-diagonal form of the Hamiltonian to the more efficient collapsed form. The C++ code stores each block as an object with its ‘type’. The code can be easily expanded to include e.g. tube distortion, warping etc. (next-to-nearest n. i.) 10 ScaLAPACK 11 Transmission function T(E) Compare different lead angles: 90 and 180 (B = 0). N = 3600 atoms Comparison: Magnitude of T(E) scales to that of 2-dim graphene ring. P. Recher et al., PRB 76, 235404 (2007). 12 Magnetic flux oscillations 90o angle between leads a. Source-drain current ISD as a function of source-drain voltage VSD [eV] (small bias) for different magnetic fields B0. ISD in units of e/h. Chemical potential at left/right lead: = +/- VSD/2. Thermal energy: kBT = 30 meV. 1,2 b. Source-drain current ISD as a function of applied magnetic field B0 [T] (eVSD = 0.05eV, 0.1eV). Torus size: N=1800 atoms 13 FSU Shared-HPC Resources – code development & testing Number of nodes: 404 Dell PowerEdge compute nodes 12 Dell PowerEdge login nodes Number of cores: 3,744 Storage: 156 TB (Panasas) Memory: 8.2 TB Further: Several GPU devices (CUDA, openCL) and SMP machines (132 cores, 550 GB shared memory) Aggregate performance 38 TFLOPS Network: 10 Gbps campus, 10 Gbps FLR connection http://www.hpc.fsu.edu 14 TACC Sun Constellation Linux Cluster: ‘Ranger’ – production runs System Name: Ranger Operating System: Linux Number of Nodes: 3,936 Number of Processing Cores: 62,976 Total Memory: 123 TB Peak Performance: 579.4 TFlops Total Disk: 1.73 PB (shared) 31.4 TB (local) http://www.tacc.utexas.edu/resources/hpc 15 NSF TeraGrid – TeraScale Parallel Simulations 16 Biosensor: Electron transport in functionalized cnts Student Research Project (D. Bryan, 2007): Conductivity of covalently functionalized cnt. CNT with oxygen defect (C-atoms sp2-hybridized). with amino315 acid.(2007) B.R. covalently Goldsmith attached et al., Science a) Density of states D(E) and b) Transmission function T(E). One oxygen defect vertical to tube axis. Hopping parameter: vhop= - 3.1 eV. 17 Metamaterials – carbon nanoring arrays and plasmonics 2010 NSF TeraGrid Pathways Program Idea: Create regular 2-dim lattice of carbon nanorings (armchair, zigzag, chiral). Drive electrical currents with external (coherent) light source. Electromagnetic multipole interference generated from array of ring currents. => Optical activity: negative refractive index, dichroism, birefringence etc. Lattices of ‘chiral molecules’ Wegener and Linden, Physics 2, 3 (2009) Schurig et al., Science 314, 977 (2006) 18 Spintronics – Spin currents driven by microwaves ‘Spin injector’ + ‘spin valve’: Graphene and Spintronics: K. Novoselov et al., Science 306 (2004) B. Trauzettel et al., Nature Phys. 3 (2007) A. Rycerz et al., Nature Phys. 3 (2007) Y.-W. Son et al., Nature 444 (2006); Corr., Nature 446 (2007) 19 SC10 FAMU Group – Physics Eddie Quashie (FAMU) Leon Durivage (Winona State U.) Harsh Jain (FAMU) Jeff Battaglia (FAMU) and Yinka Ogunro (Clark Atlanta U.) MAC XServe Minicluster (Lab Ray O’Neal) 20 SC10 FAMU Student Cluster Competition Group – Computer Science Students: Robert Dunn, Collin Orizu, Tyshun Jones, Neil Greene, Antony Jepson, and Canli Wang. Hardware sponsor: HP Dell. 21 High-performance computing in the state of Florida: Sunshine Grid Project – SSERCA 22 Lab Activity 1: PhET – Interactive Simulations, U Colorado Boulder http://phet.colorado.edu/en/simulation/gas-properties 23 Lab Activity 2: Software ProjectileX (Praeter Software) http://www.praetersoftware.com/physics 24 Acknowledgments Mario Encinosa (collaborator) – Florida A&M University, Physics Leon Durivage (summer student) – Winona State University (MN), BlueWaters Petascale Computing Summer Internship Program Boyan Hristov (Ph.D. student) – Florida A&M University, Physics John Williamson (physics), Jeff Battaglia (physics), Harsh Jain (CIS) Ray O’Neal – Florida A&M University, Physics Tiki Suarez-Brown – Florida A&M University, SBI, Information Systems Jim Wilgenbusch and FSU Department of Scientific Computing Chris Hempel, Bob Garza – Texas Advanced Computing Center (TACC) Scott Lathrop – NCSA, TeraGrid Pathways Program 2010 25 Thank You ! 26