Quantum dot Josephson junctions in the Kondo regime

In this thesis, we study quantum dots (QD) fabricated from single-wall carbon nanotubes (SWCNT). The SWCNT are connected to source (S) and drain (D) leads by tunnelling contacts whose transparency is characterized by their respective coupling parameters, S and D. The leads consist of a Ti/Al double layer and become superconducting below the critical temperatureTC ~ 1K. By application of an external magnetic field B, we can suppress superconductivity and drive the leads into the normal state.
We measure the electrical transport through these QD systems at temperatures well below 1K. The differential conductivity G in dependency of a bias voltage VSD and a backgate voltage VBG reflects the successive filling of electron states on the QD, revealing whether the occupation is odd or even. For an odd occupation and normal metal leads, the Kondo effect will dominate transport when the coupling of the QD to the leads,  = S + D, is large enough. The associated energy scale is parameterized by the Kondo temperature TK. In the presence of a BCS density of states (DOS) in the leads, a competition sets in between superconductivity and the Kondo effect. Both processes rely on the formation of opposing spin singlet states involving electrons in the leads. For TC > TK, the Kondo effect is suppressed, whereas it persists in the opposite regime, TC < TK. Both regimes have previously been studied in similar samples by electrical transport spectroscopy (PRL 89, 256801 (2002); NJP 9, 124 (2007)).
In chapter III, we report on the discovery of a third regime by studying a QD with highly asymmetrical coupling, S / D ~ 50. With superconducting leads, this asymmetry gives rise to a Kondo effect pinned to one lead only, illustrating the fact that TK dominates over TC at one contact, whereas TC > TK at the other. As a result, we observe a significant enhancement of a particular feature in non-equilibrium transport, the Andreev reflection, in states with this kind of asymmetrical Kondo effect.
In chapter IV, we expand our scope of investigation by comparing Kondo physics to the supercurrent IC that is transported through the QD. We extract the full supercurrent by following a fitting procedure based on the `extended resistively and capacitively shunted junction model' for overdamped Josephson junctions (Nature 439, 953 (2006); Nano Lett. 7, 2441 (2007)). Using VBG to tune T within one odd charge state, we drive the QD from
one regime (TK > TC) to the other (TC > TK). Since IC is very sensitive to the Kondo effect, it acts as a probe for the transition that occurs at the crossing between the two regimes (Nature Nanotech. 1, 53 (2006)). In a second odd charge state with larger , TK is always larger than TC, and consequently no transition is observed.
Chapters V and VI document our efforts to gain more direct control over the Kondo effect by means of topgates (TG). Ideally, such TG would allow us to tune S
and D individually, thus greatly increasing the possibilities for comprehension and manipulation of these complex systems. In chapter VI, we report on a TG dependent Kondo effect in the presence of an effective ferromagnetic field (Science 306, 86 (2004); Nature Physics 4, 373 (2008)). Albeit not based on direct control over S,D, this result has caught our interest and might stimulate further research in the same direction.