Quantum phase transition in a single-molecule quantum dot

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, can be observed in several strongly correlated materials such as heavy fermion compounds or possibly high-temperature superconductors, and is believed to govern many of their fascinating, yet still unexplained properties. In contrast to these bulk materials with very complex electronic structure, artificial nanoscale devices could offer a new and simpler vista to the comprehension of quantum phase transitions. This long-sought possibility is demonstrated by our work in a fullerene molecular junction, where gate voltage induces a crossing of singlet and triplet spin states at zero magnetic field. Electronic tunneling from metallic contacts into the $\rm{C_{60}}$ quantum dot provides here the necessary many-body correlations to observe a true quantum critical behavior.Comment: 8 pages, 5 figure

Kondo physics in carbon nanotubes

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger-liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically-contacted single-wall nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far higher tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron number (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.Comment: 7 pages, pdf onl

Spectroscopic analysis of finite size effects around a Kondo quantum dot

We consider a simple setup in which a small quantum dot is strongly connected to a finite size box. This box can be either a metallic box or a finite size quantum wire.The formation of the Kondo screening cloud in the box strongly depends on the ratio between the Kondo temperature and the box level spacing. By weakly connecting two metallic reservoirs to the quantum dot, a detailed spectroscopic analysis can be performed. Since the transport channels and the screening channels are almost decoupled, such a setup allows an easier access to the measure of finite-size effects associated with the finite extension of the Kondo cloud.Comment: contribution to Les Houches proceeding, ``Quantum magnetism'' 200

Kondo effect in an integer-spin quantum dot

The Kondo effect is a key many-body phenomenon in condensed matter physics. It concerns the interaction between a localised spin and free electrons. Discovered in metals containing small amounts of magnetic impurities, it is now a fundamental mechanism in a wide class of correlated electron systems. Control over single, localised spins has become relevant also in fabricated structures due to the rapid developments in nano-electronics. Experiments have already demonstrated artificial realisations of isolated magnetic impurities at metallic surfaces, nanometer-scale magnets, controlled transitions between two-electron singlet and triplet states, and a tunable Kondo effect in semiconductor quantum dots. Here, we report an unexpected Kondo effect realised in a few-electron quantum dot containing singlet and triplet spin states whose energy difference can be tuned with a magnetic field. This effect occurs for an even number of electrons at the degeneracy between singlet and triplet states. The characteristic energy scale is found to be much larger than for the ordinary spin-1/2 case.Comment: 12 page

Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states

Many-body correlations and macroscopic quantum behaviors are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo model which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems and can be explored with tunable nanostructures. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum. Here we demonstrate the previously elusive `charge' Kondo effect in a hybrid metal-semiconductor implementation of a single-electron transistor, with a quantum pseudospin-1/2 constituted by two degenerate macroscopic charge states of a metallic island. In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel, thereby providing an unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics. Using a weakly coupled probe, we reveal the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point. Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality.Comment: Letter (5 pages, 4 figures) and Methods (10 pages, 6 figures