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Electronic structure calculations of potassium intercalated single-walled carbon

nanotubes

Sven Stafström and Anders HanssonDepartment of Physics, IFM

Linköping University

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• Intercalation with alkali metals will transfer charge to the carbon nanotube.• Raman data by Rao et al., Nature 388, 257 (1997)• EELS data by Liu et al., PRB 67, 125403 (2003)

• The charge transfer results in a metallic state and enhancement of conductivity,• Lee et al ., Nature 388, 255 (1997)

• Both DFT and molecular dynamics simulations show that the alkali metal atoms intercalate the hollow sites between adjacent tubes• Miyamoto et al., PRL, 74, 2993 (1995)• Gao et al. PRL, 80, 5556 (1998)

Introduction

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• Geometry optimizations and band structure calculations of K intercalated (4,4) and (7,0) SWCNT’s.

• Ground state geometries: what is the effect of CT on the geometry.

• Heat of formation: which are the most stable K concentrations/ configurations.

• Electronic structure: band structure and density of states: how does CT affect the electronic structure

Synopsis

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• DFT calculations (Vienna ab initio simulation package (VASP)• Cut-off energy 400 eV• Exchange-correlation energy functional: Perdew and Wang (PW91)• Energy convergence <10 eV • Force convergence <10 meV/Å

Methodology

(4,4) C32K1, C32K2, C48K1, C48K2

(7,0) C28K1, C28K2, C56K1, C56K2, C84K1, C84K2

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The zigzag tubes have a more pronounced bond-length alternation pattern than the armchair tubes.

(n,m) Unitcell r (Å) b1 (Å) b2 (Å)

(2,2) C8 1.41 1.386 1.500

(3,3) C12 2.11 1.431 1.443

(5,0) C20 2.08 1.42 1.44

(4,4) C16 2.77 1.427 1.431

(7,0) C28 2.81 1.417 1.434

(5,5) C20 3.44 1.425 1.428

(10,10) C40 6.81 1.422 1.423

Bond-lengths, pristine SWCNT’s

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(7,0) C28K2

(4,4) C32K2

• Charge transfer leads to occupation of orbitals with a net anti-bonding character

• The zigzag tube shows a larger geometry relaxation

Bond lengths, K intercalated systems

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(7,0) C84K1 C84K2 C84K2 (s) C56K1 C56K2 C56K2 (s) C28K1 C28K2 C28K2 (s)

Eh(eV/K-atom) 1.219 1.213 1.366 1.160 1.299 1.589 1.163 1.206 1.268

(4,4) C48K1 C48K2 C48K2 (s) C32K1 C32K2 C32K2 (s)

Eh(eV/K-atom) 0.875 0.907 0.966 0.782 0.814 0.935

• The electron affinity of the (7,0) tube is considerably larger than of the (4,4) tube.

• Maximum heat of formation is obtained for the staggered phase.

Heats of formation

9Band structure, K-intercalated (4,4) SWCNT

10Intertube interactions, (4,4) SWCNT

Pristine K-intercalated, C32K2

The band-widths perpendicular to the (reciprocal) tube axis are slightly reduced upon K-intercalation.

11Density of states, (4,4) SWCNT

The Fermi energy can enter regions of very high density of states.

12Band structure, K-intercalated (7,0) SWCNT

The manifold of dispersive bands above –6 eV makes the (7,0) NT highly electronegative. This explains the higher Heats of formation of the K-intercalated phases as compared to the (4,4) NT.

13Density of states, SWCNT

(4,4)(7,0)

14Conclusions

• Narrow SWCNT’s show two different bond-lengths, the effect is particularly strong for zigzag tubes.

• Upon intercalation with potassium the size of the unit cell perpendicular to the tube axis expands.

• The bond-lengths are also sensitive to K-intercalation, in particular in the case of the zigzag (7,0) SWCNT.

• K-intercalation results in charge transfer and shift in the Fermi energy for both the (4,4) and the (7,0) SWCNT.

• The dispersion perpendicular to the tube axis is slightly reduced as a result of K-intercalation.

• The Fermi energy of the (4,4) tube can be shifted to a region of very high density of states upon K-intercalation.