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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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
EDUCATIONAL ACTIVITIES ,[object Object],~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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
APPLIED RESEARCH ,[object Object],[object Object],[object Object],[object Object]
CENTRES OF EXCELLENCE
CENTRES OF EXCELLENCE ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
CENTRES OF EXCELLENCE ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
NETWORKING ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
www.nanolab.rs NanoLab   Theory: Symmetry: Line Groups; Computing: POLSym (DFT, TBA)  Systems: Nano- tubes, rods, wires, springs Experimental: nanotemplates, pyrometry
OUTLINE ,[object Object],[object Object],[object Object],[object Object],[object Object]
Belgrade  S chool  of Q uantum  &   M athematical  P h y sics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],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 ,[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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D02L01 M Damnjanovic

  • 1. FACULTY OF PHYSICS ФАКУЛТЕТ University of Belgrade www.ff.bg.ac.rs
  • 3. 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
  • 4.
  • 5.
  • 7.
  • 8.
  • 10.
  • 11.
  • 12.
  • 13. www.nanolab.rs NanoLab Theory: Symmetry: Line Groups; Computing: POLSym (DFT, TBA) Systems: Nano- tubes, rods, wires, springs Experimental: nanotemplates, pyrometry
  • 14.
  • 15.
  • 16. NanoLab Z. Popović B. Dakić I . Milošević E. Dobardžić Т. Vuković S. Dmitrović B. Nikolić M. Damnjanovic
  • 17. Line Groups March 2010 (to appear)
  • 18. Regular quasi-1D Systems DNA model ZnO nanospring SWCNT
  • 19. 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
  • 20. LG symmetric E(3) orbits PRB 47 (1993) 7805, Polymer 38 (1997) 4445, PRB 76 (2007) 0354391 15 classes: elementary monoperiodic systems
  • 21. Diffraction patterns PRB 76 (2007) 0354391, pss (b) 246 (2009) 2631,
  • 22. 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
  • 23.
  • 24. 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
  • 25. 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 +
  • 26. 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
  • 27. 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
  • 28. 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
  • 29. [email_address] Δ D =(6.88±0.40) Å
  • 30. 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
  • 31.
  • 32. 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
  • 33.

Editor's Notes

  1. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)
  2. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)
  3. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)
  4. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)
  5. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)
  6. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059) kako smestiti jednu swcn u drugu swcn?
  7. JPA 1994-2004 (27 4859, 28 1669, 28 4188, 29 7983, 33 6561, 37 4059)