d02l01 m damnjanovic
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FACULTY OF PHYSICS
ФАКУЛТЕТ
University of Belgrade
ww
w.ff.bg.ac.rs
EBES2010
Faculty of Physics
BASICS
EBES2010
Faculty of Physics
STUFF73 professors and assistants2 institutes: of physics of meteorology3 building in the central area of Belgrade 9000 m2
14 Labs
150 batchelor ( )+ 20 master + 30 Ph.D. students yearly;
~1000 enrolled altogether
EBES2010
Faculty of Physics
PROGRAMS4 batchelor (4 years) +master (1 year)• Theoretical and experimental physics• Applied and computational physics• Educational Physics• Meteorology
3 Ph. D. : • Physics, • Meteorology,• Biophysics
1 specialistic• Medical physics
EBES2010
Faculty of Physics
EDUCATIONAL ACTIVITIES
Laboratory for design and development of teaching aids prototypes: ~30 types of equipments
~100 textbooks
~ 150 courses (also for foreign students)
Seminars for grammar school pupils and teachers
EBES2010
Faculty of Physics
RESEARCH
EBES2010
Faculty of Physics
BASIC RESEARCH
9 Projects of Serbian Ministry of Science
• Nanoscience, Material science, Condensed matter: 4 projects (35 people)
• Lasers, Plasma, Ionized gasses: 4 projects (30 people)
• Meteorology 1 project (10 people)
EBES2010
Faculty of Physics
APPLIED RESEARCH
• PYROMETRY 7 people, 3 projects, 3 patents
• ECOLOGY •5 people,1 project, 2 patents
EBES2010
Faculty of Physics
CENTRES OF EXCELLENCE
EBES2010
Faculty of Physics
• NanoLab: Nanoscience 12 people, Theory+Experiment Equipment: AF/ST Microscopy Small computing cluster Spectrofluorimeter
CENTRES OF EXCELLENCE
EBES2010
Faculty of Physics
• NanoLab: Nanoscience 12 people, Theory+Experiment Equipment: AF/ST Microscopy Small computing cluster Spectrofluorimeter• SYNGLab: synthesis of nanostructures in gass discharges 3 researchers, Experiment Equipment: vacuum systems, CCD cameras
CENTRES OF EXCELLENCE
EBES2010
Faculty of Physics
• NanoLab:• NanoLabFor: FP6 project (2006-2009, M. Damnjanovic)• Synthesis/properties of carbon nanostructures:
Scopes (Swiss project with Swiss, Hungarian and Armeninan groups, 2010-1012, I. Milosevic) • 5 bilateral projects from 2003 (Slovenia, Germany, France, Greece)
• SYNGLab: • GLADNET: FP6 project (Maria Curie Ph. D. training, 12 members Network, N. Konjevic)
NETWORKING
www.nanolab.rs
NanoLab
Theory: Symmetry: Line Groups;Computing: POLSym (DFT, TBA) Systems: Nano- tubes, rods, wires, springsExperimental: nanotemplates, pyrometry
EBES2010
Faculty of Physics
OUTLINE
• Belgrade School of Quantum & Mathematical Physics• NanoLab• Line groups, general applications & exploiting their
symmetry• SWCNTs: structure = symmetry (El. Bands, Optical spectra,
Phonon dispersions, Raman scattering, Stone-Wales deformation & pentaheptite NTs)
• DWCNTs: interaction = symmetry breaking (Rigid layer modes, Super slippery modes &Telescope effect)
EBES2010
Faculty of Physics
Belgrade School of Quantum & Mathematical Physics
1975 Chair of quantum and mathematical physics
F. Herbut, M. Vujičić
I. Božović, Đ. Šijački, I. Ivanović
M. Damnjanović
I. Milošević
Т. Vuković, B. Nikolić, D. Stojković
E. Dоbаrdžić, S. Dmitrović, V. Stevanović,
B. Dakić, Z. Popović, B. Višić
NanoLab 2000
EBES2010
Faculty of Physics
NanoLab
Z. Popović
B. Dakić
I. MiloševićE. Dobardžić
Т. Vuković
S. Dmitrović
B. Nikolić
M. Damnjanovic
EBES2010
Faculty of Physics
Line Groups
March 2010 (to appear)
EBES2010
Faculty of Physics
Regular quasi-1D Systems
DNA model ZnO nanospring
SWCNT
EBES2010
Faculty of Physics
PRB 25 (1982) 6987
Line groups
Incommensurate
and chiral groups are from the families 1 & 5
ZP=PZ arrangement and monomer symmetry are compatible
L=Z P 13 infinite
families
EBES2010
Faculty of Physics
PRB 47 (1993) 7805, Polymer 38 (1997) 4445, PRB 76 (2007) 0354391
LG symmetric E(3) orbits15
cla
sses
: ele
men
tary
mon
oper
iodi
c sy
stem
s
EBES2010
Faculty of Physics
Diffraction patterns
PRB 76 (2007) 0354391, pss (b) 246 (2009) 2631,
EBES2010
Faculty of Physics
PRB 65 (2002) 045418; JPA 36 (2003) 5707
ENERGIES: bands over BZ, assigned by m and Π.
Time reversal: IBZ=[0, π].
STATES: Symmetry adapted = generalized Bloch
BANDS+ASSIGNATION
EBES2010
Faculty of Physics
PRB 65 (2002) 045418
CONSERVATION LAWS =
SELECTION RULESkfmf Πf | AkmΠ | kimi Πi ≠ 0 if
kf -ki = k & mf -mi =m & Πf ΠiΠ ≠ -1
More details: Clebsch-Gordan coefficients
∙ ∙
EBES2010
Faculty of Physics
PRB 75 (2007) 033404
Nanotubes: layer rolling
For each diperiodic group (layer)and each chiral vectorline group symmetry of the obtained nanotubeis determined
5
Chiral80
13 Achiral 80
SWCNT
EBES2010
Faculty of Physics
SSC 121 (2002) 471; PRB 68 (2003) 045408; 72 (2005) 085426; JPC 16 (2004) L505
(9,0) 285 cm-1
Radial Breathing Mode
(8,2
) 31
0 cm
-1 (6,6
) 27
5 cm
-1Nonradial components: zRBM(D, θ)=(0.197D-1-0.167D-3)cos(3θ)
ω [cm-1] = 2243/D [Ǻ] D characterized by Raman
0A0+
EBES2010
Faculty of Physics
PRB 62 (2000) 6971; 67 (2003) 165418; 69} (2004) 113408
OPTICAL CONDUCTIVITY
Selection rules: ∆k=0, ∆m=0, σv: ΠfΠi ≠ -1,σh, σU: ΠfΠi ≠ 1
Parallel polarization
Identified zeolite grown tubes
Dipole approximation
Different selection rules for ∟ field = Dichroism
EBES2010
Faculty of Physics
PlasmonsRPA calculated dielectric function (transfer q < 1 Ǻ-1)
Armchair: strong π plasmon peak (dispersion in q)
Semiconducting: π plasmon+ nondispersive optical
Fit: q < 0.5 Ǻ-1 Ep~ q, q > 0.5 Ǻ-1 Ep~ q2
PRB 77 (2008) 245415
EBES2010
Faculty of Physics
Pentaheptite SWCNTsStone-Wales defect(bond rotation) 2(5+7)
57-tilings 57-CNTs
57CNTs mostly conductive while 6CNTs mostly semiconductive
Electro-mechanical nanoswitch
Mechanical stretching facilitates 57-transition
PRB 76 (2007) 233414
EBES2010
Faculty of Physics
SWCNT@SWCNT
ΔD=(6.88±0.40) Å
EBES2010
Faculty of Physics
EPJB 34 (2003) 409; NJP 5 (2003) 148; PRB 69 (2004) 153401
Rigid layer modes
LRL(9,0)@(18,0)
0A0- 36 cm-1
TWRL (5,5)@(10,10)
0B0- 46 cm-1
EBES2010
Faculty of Physics
EPJB 25 (2002) 131
Symmetry & interaction
Sum over atoms of walls= groups LW and LW’!
VW’(r)=Σl’v(r,rl’): LW’-invariant
W’ receives LW’ harmonics onlyHarmonics: HM
ω(φ,z) = cos(Mφ + 2πωz)
LWLW’ / LW LW’
W-W’ interaction
V (Φ,Z) =Σll’ v(rl,rl’) l,l’ over atoms
VW(r)=Σlv(rl,r): LW-invariant
W emits LW-harmonics only
Interaction mediated through common harmonics
EBES2010
Faculty of Physics
EPJB 34 (2003) 409; NJP 5 (2003) 148; PRB 69 (2004) 153401
W-W’ INTERACTION
Incommensurate walls: super-slippery Z-sliding: Goldstone
Resonance: W-ringof integer W-W’periods vm = v∞
Low rotational corrugation
EBES2010
Faculty of Physics
CONCLUSIONS
• Theory: Line groups, Quasi1D, Diffraction…• Tools: Symmetry, DFT, POLSym code• Carbon Nanotubes:
– Line group symmetry, single atom in symcell, – most of the properties determined by symmetry:
Conductivity, Optical activity, Plasmons, Raman spectra, Phonons, Plasmons…
– DWNT: almost frictionless degrees of freedom
• Other quasi1D nanostructures (MS2, ZnO,…)
• Layers (graphene, MS2,…)