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Calculations for the electronic transport in molecular nanostructures Gotthard Seifert Institut für Physikalische Chemie und Elektrochemie Technische Universität Dresden

Greens-Function Method Calculation of Transport Properties in molecular Systems Green‘s Function G(E) S,H – Overlap- and Hamilton Matrices Model: Molecule (M) and two contacts (α, β) Calculation of H and S matrices Aldo di Carlo!

LCAO Ansatz Atomic Orbitals - AO Slater Type Orbitals - STO

Hamilton matrix Overlap matrix Density-Functional based „tight binding“ DF-TB

- electron density - magnetization density Density fluctuations: Total Energy in DFT - E DFT

Expansion of E DFT around n=n 0, μ=0

Approximations: Minimal (valence) basis in LCAO ansatz Neglect of pseudopotential terms in h 0 μν  2-center approximation -Mulliken gross population at j 2nd order approximation in energy

Cancellation of „double counting terms“ E B /eV R/a B U(R jk ) E B - U(R jk ) Li 2 - dimer Short range repulsive energy U(R jk )

Approximation for magnetization density

Energy :

Hamiltonian: : Self Consistent Charge method SCC-DFTB

with Γ α - Spectral functions of the Selfenergy-operators Transmission coefficient T(E)

Electronic Current – I Keldysh formalism Contact scattering functions Scattering function Inelastic processes (e-e, e-p intereaction) Non-equilibrium Green‘s functions

External bias – V Modification of the Hamiltonian matrix elements Calculation of I-V curves

Application ∞ Examples

Nanotubes of Carbon S. Iijima Nature 354 (1991) 56 ~1nm~ μm Single-wall Nanotubes – SWNT‘s

(10,0) zig-zag tube10-10 arm chair tube

Electronic Structure of Nanotubes Band-structure graphene monolayer k  Rolling „Zone folding“

zig-zag tube (n,0) mod(n,3)=0mod(n,3)≠0

arm chair tube (n,n)

Functionalization of Carbon Nanotubes ? Graphite > Lamellar intercalation: > Lamellar covalent: O, F, S Fluorination Li, Na, K, Rb; Cl, Br, I

2C graphite + F 2  2CF sp 2 -C graphite  sp 3 -C Fluorination F F

Carbon Nanotubes fluorination 2C + F 2  2CF 2C+1/2F 2  C 2 F

Decoration pattern – no „frustration“!

C 2 F – fluorine decoration pattern n,0 F Ethylen - like

C 2 F – fluorine decoration pattern Ethylen - like

EFEF Density-of-States 10,0 C 2 F NT 10,0 CNT Large gap

C 2 F – fluorine decoration pattern n,0 F trans-polyacetylen – like helical C C ∞

C 2 F – fluorine decoration pattern Trans-polyacetylen – like helical C C ∞

10,0 C 2 F NT Density-of-States energy/eV Density-of-States small gap

projected Density-of-States

C 2 F – fluorine decoration pattern cis-polyacetylen – like chain CC ∞

Density-of-States 10,0 C 2 F NT no gap

Transmission 10,0 C 2 F NanoTubes cis-polyacetylen – like chain ethylen - like

Transmission as function of coverage C 2 F (10,0) Nanotube cis-polyacetylen – like chain

trans-Polyacetylene

C 2 F (10,10) Nanotube chain (10,10) Nanotube

(9,0) Nanotube

9,0 C 2 F NT ring HOMO –LUMO „aromatic“ π-states

Fluorine Carbon

Outlook/Problems ->Contacts – Molecule interaction -> electron-phonon interaction -> electron-electron interaction? -> non-adiabatic description -> Applications.

Thanks Aldo di Carlo (Rome) Thomas Niehaus (Paderborn) Nitesh Ranjan (Dresden)