Ground state and dynamical properties of the finite Kondo lattice model and transport through carbon based nanodevices

The first topic of this thesis is the study of many-body effects in an one-dimensional strongly correlated electronic system - the Kondo lattice model. This system is tackled numerically by means of the density matrix renormalization group, since analytic method, i.e., perturbation the- ory fail due to competing coupling constants. The Kondo lattice model consists of a conduction band of electrons which couple via a spin exchange coupling to a localized spin lattice. We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. We compute the dispersion relation of the quasiparticles, their lifetimes, and the Z factor. The exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron are well known. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum. Further- more, we study the effects of the Coulomb interaction on the phase diagram, the static magnetic susceptibility and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest neighbor Coulomb interaction drives, depending on the elec- tron filling, either a paramagnetic or ferromagnetic order. Furthermore, we calculate electron quasiparticle life times, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate. In the second topic of this thesis, we numerically calculate the electron transport through carbon nanotube based quantum dot devices. We use a master equation’s approach in first order of the tunneling rate to the leads and an extended constant interaction model to model the carbon nanotube system. This work has been done in collaboration with two experimental groups and we compare their respective experimentally obtained data to our numerical calculations. In both collaborations striking similarity between the numerical data and the experimental data is found. In the first collaboration transport through a carbon nanotube peapod, i.e, a carbon nanotube filled with fullerenes, has been measured. We identify a small hybridization between a fullerene molecule and the surrounding carbon nanotube to be of crucial importance for the understanding of the transport data. In the second collaboration, electron transport through a carbon nanotube rope, i.e., a bundle of carbon nanotubes has been measured. Also here, hybridization between the different nanotubes plays a crucial role. Furthermore, an external magnetic field is applied, which enables the identification of specific spin states of the compound quantum dot system. This might be important for future applications of such devices in spin-dependent electronics

Spin-dependent electronic hybridization in a rope of carbon nanotubes

We demonstrate single electron addition to different strands of a carbon nanotube rope. Anticrossings of anomalous conductance peaks occur in quantum transport measurements through the parallel quantum dots forming on the individual strands. We determine the magnitude and the sign of the hybridization as well as the Coulomb interaction between the carbon nanotube quantum dots, finding that the bonding states dominate the transport. In a magnetic field the hybridization is shown to be selectively suppressed due to spin effects.Comment: 4 pages, 4 figure

Quasiparticles in the Kondo lattice model at partial fillings of the conduction band

We study the spectral properties of the one-dimensional Kondo lattice model as function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phase. Using the density-matrix renormalization group method, we compute the dispersion relation of the quasiparticles, their lifetimes, and the Z-factor. As a main result, we provide evidence for the existence of the spinpolaron at partial band fillings. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phase and depends strongly on the quasimomentum.Comment: 9 pages, 9 figure

Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model

We study the effects of the Coulomb interaction in the one-dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility, and electron spin relaxation.We show that onsite Coulomb interaction supports ferromagnetic order and nearest-neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or a ferromagnetic order. Furthermore, we calculate electron quasiparticle lifetimes, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate

Transport via coupled states in a C60 peapod quantum dot

We have measured systematic repetitions of avoided crossings in low temperature three-terminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The well-defined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube.Comment: 6 pages, 3 figure

Parallel carbon nanotube quantum dots and their interactions

We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate the inter-dot coupling and show a route to distinguish between various side dots. By comparing the experimental data with master equation calculations, we identify conditions for the tunneling rates that are required in order to observe different manifestations of the inter-dot coupling in the transport spectra