D02L01 M Damnjanovic

FACULTY OF PHYSICS ФАКУЛТЕТ University of Belgrade www.ff.bg.ac.rs

BASICS

STUFF 73 professors and assistants 2 institutes: of physics of meteorology 3 building in the central area of Belgrade 9000 m 2 14 Labs 150 batchelor ( )+ 20 master + 30 Ph.D. students yearly; ~100 0 enrolled altogether

PROGRAMS
4 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

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

RESEARCH

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)

APPLIED RESEARCH
PYROMETRY
7 people, 3 projects, 3 patents
ECOLOGY
5 people,1 project, 2 patents

CENTRES OF EXCELLENCE

NanoLab: Nanoscience
12 people, Theory+Experiment
Equipment:
AF/ST Microscopy
Small computing cluster
Spectrofluorimeter

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

NETWORKING
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 )

www.nanolab.rs NanoLab Theory: Symmetry: Line Groups; Computing: POLSym (DFT, TBA) Systems: Nano- tubes, rods, wires, springs Experimental: nanotemplates, pyrometry

OUTLINE
Belgrade S chool of Q uantum & M athematical P h y sics
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)

Belgrade S chool of Q uantum & M athematical P h y sics
Chair of quantum and mathematical physics
F. Herbut , M. Vuji čić
Božović , Đ . Šijački , I . Ivanović
M. Damnjanović
I . Milošević
Т. Vuković , B . Nikolić , D. Stojković
E. D о b а rdžić , S . Dmitrović , V. Stevanović ,
B . Dakić , Z. Popović , B. Vi šić
NanoLab 2000

NanoLab Z. Popović B. Dakić I . Milošević E. Dobardžić Т. Vuković S. Dmitrović B. Nikolić M. Damnjanovic

Line Groups March 2010 (to appear)

Regular quasi-1D Systems DNA model ZnO nanospring SWCNT

Line groups PRB 25 (1982) 6987 Incommensurate and chiral groups are from the families 1 & 5 ZP=PZ arrangement and monomer symmetry are compatible L=Z P 13 infinite families

LG symmetric E(3) orbits PRB 47 (1993) 7805, Polymer 38 (1997) 4445, PRB 76 (2007) 0354391 15 classes: elementary monoperiodic systems

Diffraction patterns PRB 76 (2007) 0354391, pss (b) 246 (2009) 2631,

BANDS+ASSIGNATION 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

CONSERVATION LAWS = SELECTION RULES
k f m f Π f | A kmΠ | k i m i Π i  ≠ 0 if
k f - k i = k & m f - m i = m & Π f Π i Π ≠ -1
PRB 65 (2002) 045418 More details: Clebsch-Gordan coefficients ∙ ∙

Nanotubes: layer rolling PRB 75 (2007) 033404 For each diperiodic group (layer) and each chiral vector line group symmetry of the obtained nanotube is determined SWCNT 5 Chiral 80 13 Achiral 80

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) 310 cm -1 (6,6) 275 cm -1 Nonradial components: z RBM ( D, θ )=(0.197 D -1 -0.167 D -3 )cos(3 θ ) ω [cm -1 ] = 2243/D [Ǻ] D characterized by Raman 0 A 0 +

OPTICAL CONDUCTIVITY PRB 62 (2000) 6971; 67 (2003) 165418; 69} (2004) 113408 Selection rules: ∆k=0, ∆m=0, σ v : Π f Π i ≠ -1, σ h , σ U : Π f Π i ≠ 1 Parallel polarization Identified zeolite grown tubes Dipole approximation Different selection rules for ∟ field = Dichroism

Plasmons RPA calculated dielectric function (transfer q < 1 Ǻ -1 ) Fit: q < 0.5 Ǻ -1 E p ~ q, q > 0.5 Ǻ -1 E p ~ q 2 PRB 77 (2008) 245415 Armchair: strong π plasmon peak (dispersion in q ) Semiconducting: π plasmon+ nondispersive optical

Pentaheptite SWCNTs Stone-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

[email_address] Δ D =(6.88±0.40) Å

Rigid layer modes EPJB 34 (2003) 409; NJP 5 (2003) 148; PRB 69 (2004) 153401 LRL(9,0)@(18,0) 0 A 0 - 36 cm -1 TWRL (5,5)@(10,10) 0 B 0 - 46 cm -1

Symmetry & interaction
Sum over atoms of walls = groups L W and L W’ !
EPJB 25 (2002) 131 V W’ ( r ) = Σ l’ v ( r , r l’ ) : L W’ -invariant W’ receives L W’ harmonics only Harmonics: H M ω (φ,z) = cos (Mφ + 2πωz) L W    L W’ / L W  L W’ W-W’ interaction V ( Φ,Z ) = Σ ll’ v ( r l , r l’ ) l,l’ over atoms V W ( r ) = Σ l v ( r l , r ) : L W - invariant W emits L W -harmonics only Interaction mediated through common harmonics

W-W’ INTERACTION EPJB 34 (2003) 409; NJP 5 (2003) 148; PRB 69 (2004) 153401 Incommensurate walls: super-slippery Z-sliding: Goldstone Resonance: W-ring of integer W-W’ periods v m = v ∞ Low rotational corrugation

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,…)

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D02L01 M Damnjanovic

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