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,…)