Spectrum and transport properties of interacting carbon nanotubes

URN to cite this document:: urn:nbn:de:bvb:355-opus-9253

Mayrhofer, Leonhard

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Date of publication of this fulltext: 01 Feb 2008 16:20

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Abstract (English)

Abstract (English)

With this thesis we provide a thorough examination of the electronic and transport properties of interacting metallic single-walled carbon nanotubes (SWNTs) in the low energy regime, corresponding to excitation energies in the range of about 1 eV around the charge neutrality point. We have been able to reveal the nature of the eigenstates and of the spectrum of metallic SWNTs away from half-filling. A theory for weakly coupled SWNT quantum dots and spin valves is derived. Our guideline is to base our examinations on a solid microscopic fundament, i.e., all of our calculations start from a basic microscopic model or theory. The validity of necessary approximations is checked carefully for the relevant regimes.

The first part of the thesis is dedicated to explore the electronic properties of interacting electrons in metallic SWNTs. Before tackling this task, a review on noninteracting electrons in SWNTs is presented. Special emphasis is put on the proper treatment of finite size effects by imposing open boundary conditions. The low energy eigenstates of the noninteracting system form the framework for the further discussion where the Coulomb interaction between the electrons is included.
Interactions change qualitatively the properties of fermions in one dimension (1D) compared to the noninteracting case. A successful description of interacting 1D systems is provided by the Luttinger liquid theory based on the bosonization formalism. Experimental works on the ground state properties of metallic SWNTs have found exchange effects which are not in accordance with the Luttinger liquid predictions. Our investigations aim at identifying the microscopic origin of the deviations from Luttinger liquid theory in SWNTs. For this purpose we derive the effectively 1D interaction on the basis of the noninteracting electrons. It turns out that the total Hamiltonian contains apart from the standard Luttinger contribution additional short ranged interactions due to the substructure of the SWNT honeycomb lattice. Those short ranged terms lead to non-forward scattering processes of the pseudo spin degree of freedom and thus to the mixing of different fermionic configurations. Away from half-filling the eigenstates and the spectrum of metallic SWNTs are calculated by expressing the total Hamiltonian in a truncated eigenbasis of the Luttinger Hamiltonian and by the subsequent diagonalization of the obtained matrix. Qualitative and quantitative agreement with the experimentally observed exchange effects has been established. Additionally, we make further predictions concerning the effects of the short ranged interactions not observed in experiments so far. Of special relevance is our finding of a spin 1 triplet groundstate of the 4m+2 charge states in the case of a small band mismatch. It proves - for a realistic system - that the Lieb-Mattis theorem, forbidding groundstates with spin larger than 1/2 in 1D Hubbard models with next neighbour hopping, cannot be applied to 1D systems with an additional degree of freedom for which non-forward scattering is allowed. Concerning the excitation spectrum, we find a partial lifting of the huge degeneracies and a spoiling of the spin-charge separation. At half-filling our diagonalization procedure fails to give exact results due to a very strong coupling of the eigenstates of the Luttinger Hamiltonian via short ranged umklapp interaction processes which are only of relevance near half-filling.

In the second part we examine the transport properties of SWNT quantum dots and spin valves. An introduction to general aspects of quantum dot physics is presented.
A transport theory for generic weakly coupled quantum dots is developed by generalizing the Pauli master equation to systems with degenerate eigenstates. In order to ensure invariance of the results under unitary transformations in the Hilbert spaces of the degenerate states, our approach keeps explicitly coherences between degenerate states in the reduced density matrix of the dot.

Translation of the abstract (German)

Die vorliegende Arbeit stellt eine sorgfältige Untersuchung der elektronischen Eigenschaften und der Transporteigenschaften wechselwirkender Elektronen in metallischen Kohlenstoffnanoröhren (KNR) dar. Das Spektrum und die Eigenzustände metallischer KNR werden für das Niederenergieregime berechnet.
Darüberhinaus wird eine Theorie für unpolarisierte und spinpolarisierte KNR-Quantenpunkte entwickelt.

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