Persistent Orbital Degeneracy in Carbon Nanotubes

The quantum-mechanical orbitals in carbon nanotubes are doubly degenerate over a large number of states in the Coulomb blockade regime. We argue that this experimental observation indicates that electrons are reflected without mode mixing at the nanotube-metal contacts. Two electrons occupying a pair of degenerate orbitals (a ``shell'') are found to form a triplet state starting from zero magnetic field. Finally, we observe unexpected low-energy excitations at complete filling of a four-electron shell.Comment: 6 pages, 4 figure

Four-Probe Measurements of Carbon Nanotubes with Narrow Metal Contacts

We find that electrons in single-wall carbon nanotubes may propagate substantial distances (tens of nanometers) under the metal contacts. We perform four-probe transport measurements of the nanotube conductance and observe significant deviations from the standard Kirchhoff's circuit rules. Most noticeably, injecting current between two neighboring contacts on one end of the nanotube, induces a non-zero voltage difference between two contacts on the other end.Comment: 4 pages, 5 figures; submitte

Kondo effect in a carbon nanotube with spin-orbit interaction and valley mixing: A DM-NRG study

We investigate the effects of spin-orbit interaction (SOI) and valley mixing on the transport and dynamical properties of a carbon nanotube (CNT) quantum dot in the Kondo regime. As these perturbations break the pseudo-spin symmetry in the CNT spectrum but preserve time-reversal symmetry, they induce a finite splitting $\Delta$ between formerly degenerate Kramers pairs. Correspondingly, a crossover from the SU(4) to the SU(2)-Kondo effect occurs as the strength of these symmetry breaking parameters is varied. Clear signatures of the crossover are discussed both at the level of the spectral function as well as of the conductance. In particular, we demonstrate numerically and support with scaling arguments, that the Kondo temperature scales inversely with the splitting $\Delta$ in the crossover regime. In presence of a finite magnetic field, time reversal symmetry is also broken. We investigate the effects of both parallel and perpendicular fields (with respect to the tube's axis), and discuss the conditions under which Kondo revivals may be achieved.Comment: 13 pages, 17 figure

Evolution of SU(4) Transport Regimes in Carbon Nanotube Quantum Dots

We study the evolution of conductance regimes in carbon nanotubes with doubly degenerate orbitals (``shells'') by controlling the contact transparency within the same sample. For sufficiently open contacts, Kondo behavior is observed for 1, 2, and 3 electrons in the topmost shell. As the contacts are opened more, the sample enters the ``mixed valence'' regime, where different charge states are strongly hybridized by electron tunneling. Here, the conductance as a function of gate voltage shows pronounced modulations with a period of four electrons, and all single-electron features are washed away at low temperature. We successfully describe this behavior by a simple formula with no fitting parameters. Finally, we find a surprisingly small energy scale that controls the temperature evolution of conductance and the tunneling density of states in the mixed valence regime.Comment: 4 pages + supplementary info. The second part of the original submission is now split off as a separate paper (0709.1288

Two-Stage Kondo Effect and Kondo Box Level Spectroscopy in a Carbon Nanotube

The concept of the "Kondo box" describes a single spin, antiferromagnetically coupled to a quantum dot with a finite level spacing. Here, a Kondo box is formed in a carbon nanotube interacting with a localized electron. We investigate the spins of its first few eigenstates and compare them to a recent theory. In an 'open' Kondo-box, strongly coupled to the leads, we observe a non-monotonic temperature dependence of the nanotube conductance, which results from a competition between the Kondo-box singlet and the 'conventional' Kondo state that couples the nanotube to the leads.Comment: 5 pages, 3 figure

SU(4) and SU(2) Kondo Effects in Carbon Nanotube Quantum Dots

We study the SU(4) Kondo effect in carbon nanotube quantum dots, where doubly degenerate orbitals form 4-electron ``shells''. The SU(4) Kondo behavior is investigated for one, two and three electrons in the topmost shell. While the Kondo state of two electrons is quenched by magnetic field, in case of an odd number of electrons two types of SU(2) Kondo effect may survive. Namely, the spin SU(2) state is realized in the magnetic field parallel to the nanotube (inducing primarily orbital splitting). Application of the perpendicular field (inducing Zeeman splitting) results in the orbital SU(2) Kondo effect.Comment: 5 pages. Some material was previously posted in cond-mat/0608573, v

Resonant Tunneling in a Dissipative Environment

We measure tunneling through a single quantum level in a carbon nanotube quantum dot connected to resistive metal leads. For the electrons tunneling to/from the nanotube, the leads serve as a dissipative environment, which suppresses the tunneling rate. In the regime of sequential tunneling, the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weekly than the conventional 1/T. In the resonant tunneling regime (temperature smaller than the level width), the peak width approaches saturation, while the peak height starts to decrease. Overall, the peak height shows a non-monotonic temperature dependence. We associate this unusual behavior with the transition from the sequential to the resonant tunneling through a single quantum level in a dissipative environment.Comment: 5 pages, 5 figure

Transition between SU(4) and SU(2) Kondo effect

Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consists of two spin degenerate doublets hybridized to a singlet by promotion of an electron to two conduction bands, as a function of the energy separation $\delta$ between both doublets. For $\delta$=0 or very large, the model is equivalent to a one-level SU(N) Anderson model, with N=4 and 2 respectively. We study the evolution of the spectral density for both doublets ($\rho_{1 \sigma}(\omega)$ and $\rho_{2 \sigma}(\omega)$) and their width in the Kondo limit as $\delta$ is varied, using the non-crossing approximation (NCA). As $\delta$ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy $\rho_{2 \sigma}(\omega)$ shifts above the Ferrmi energy. The Kondo temperature $T_K$ (determined by the half width at half maximum of the Kondo peak in density of the doublet of lower energy $\rho_{1 \sigma}(\omega)$) decreases dramatically. The variation of $T_K$ with $\delta$ is reproduced by a simple variational calculation.Comment: 8 pages, 4 figures. Presented at the conference "Frontiers of Condensed Matter Physics", December 201

Universal conductance enhancement and reduction of the two-orbital Kondo effect

We investigate theoretically the linear and nonlinear conductance through a nanostructure with two-fold degenerate single levels, corresponding to the transport through nanostructures such as a carbon nanotube, or double dot systems with capacitive interaction. It is shown that the presence of the interaction asymmetry between orbits/dots affects significantly the profile of the linear conductance at finite temperature, and, of the nonlinear conductance, particularly around half-filling, where the two-particle Kondo effect occurs. Within the range of experimentally feasible parameters, the SU(4) universal behavior is suggested, and comparison with relevant experiments is made.Comment: 10 pages, 16 figure

Noisy Kondo impurities

The anti-ferromagnetic coupling of a magnetic impurity carrying a spin with the conduction electrons spins of a host metal is the basic mechanism responsible for the increase of the resistance of an alloy such as Cu${}_{0.998}$Fe${}_{0.002}$ at low temperature, as originally suggested by Kondo . This coupling has emerged as a very generic property of localized electronic states coupled to a continuum . The possibility to design artificial controllable magnetic impurities in nanoscopic conductors has opened a path to study this many body phenomenon in unusual situations as compared to the initial one and, in particular, in out of equilibrium situations. So far, measurements have focused on the average current. Here, we report on \textit{current fluctuations} (noise) measurements in artificial Kondo impurities made in carbon nanotube devices. We find a striking enhancement of the current noise within the Kondo resonance, in contradiction with simple non-interacting theories. Our findings provide a test bench for one of the most important many-body theories of condensed matter in out of equilibrium situations and shed light on the noise properties of highly conductive molecular devices.Comment: minor differences with published versio