Transcript Document

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).
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Ring synthesis and pattern formation:
Motavas, Omrane, and Papadopoulos:
Large-Area Patterning of Carbon Nanotube
Ring Arrays,
Langmuir 2009, 25(8), 4655–4658.
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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)
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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.
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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.
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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).
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Recursive Green’s Function Algorithm (RGF)
Example: Green’s function Gd for transport in a nanoring device:
Effective Hamiltonian
:
(3,3) armchair nanotorus
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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.
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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.)
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ScaLAPACK
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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).
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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
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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
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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
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NSF TeraGrid – TeraScale Parallel Simulations
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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.
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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)
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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)
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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)
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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.
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High-performance computing in the state of Florida:
Sunshine Grid Project – SSERCA
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Lab Activity 1: PhET – Interactive Simulations,
U Colorado Boulder
http://phet.colorado.edu/en/simulation/gas-properties
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Lab Activity 2: Software ProjectileX (Praeter Software)
http://www.praetersoftware.com/physics
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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
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Thank You !
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