We investigate the Josephson current in a single wall carbon nanotube connected to superconducting electrodes. We focus on the parameter regime in which transport is dominated by Kondo physics. A sizeable supercurrent is observed for odd number of electrons on the nanotube when the Kondo temperature Tk is sufficiently large compared to the superconducting gap. On the other hand when, in the center of the Kondo ridge, Tk is slightly smaller than the superconducting gap, the supercurrent is found to be extremely sensitive to the gate voltage Vbg. Whereas it is largely suppressed at the center of the ridge, it shows a sharp increase at a finite value of Vbg. This increase can be attributed to a doublet-singlet transition of the spin state of the nanotube island leading to a pi shift in the current phase relation. This transition is very sensitive to the asymmetry of the contacts and is in good agreement with theoretical predictions.
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.
We present low-temperature electron transport measurements on a single-wall carbon nanotube quantum dot exhibiting Kondo resonances at low temperature. Contrary to the usual behavior for the spin-1/2 Kondo effect we find that the temperature dependence of the zero bias conductance is nonmonotonic. In nonlinear transport measurements low-energy splittings of the Kondo resonances are observed at zero magnetic field. We suggest that these anomalies reflect interactions between the nanotube and a magnetic (catalyst) particle. The nanotube device may effectively act as a ferromagnetically contacted…
Understanding the interplay between many-body phenomena and non-equilibrium in systems with entangled spin and orbital degrees of freedom is a central objective in nano-electronics. We demonstrate that the combination of Coulomb interaction, spin-orbit coupling and valley mixing results in a particular selection of the inelastic virtual processes contributing to the Kondo resonance in carbon nanotubes at low temperatures. This effect is dictated by conjugation properties of the underlying carbon nanotube spectrum at zero and finite magnetic field. Our measurements on a clean carbon nanotube ar…
We study electron mechanical coupling in a suspended carbon nanotube (CNT) quantum dot device. Electron spin couples to the flexural vibration mode due to spin-orbit coupling in the electron tunneling processes. In the weak coupling limit, i.e. electron-vibration coupling is much smaller than the electron energy scale, the damping and resonant frequency shift of the CNT resonator can be obtained by calculating the dynamical spin susceptibility. We find that strong spin-flip scattering processes in Kondo regime significantly affect the mechanical motion of the carbon nanotube: Kondo effect indu…
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 in…
The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $ν$ of the order or higher than the frequency associated with the Kondo effect $k_B T_K/h$, with $T_K$ the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for $h ν\approx k_B T_K$ a Kondo effect related singularity at a voltage bias $eV \approx h ν$, and a strong reduction of this singularity for $h ν\approx 3 k_B T_K$, in good agreement with theory. Our experiment co…
Using the transversal vibration resonance of a suspended carbon nanotube as charge detector for its embedded quantum dot, we investigate the case of strong Kondo correlations between a quantum dot and its leads. We demonstrate that even when large Kondo conductance is carried at odd electron number, the charging behaviour remains similar between odd and even quantum dot occupation. While the Kondo conductance is caused by higher order processes, a sequential tunneling only model can describe the time-averaged charge. The gate potentials of maximum current and fastest charge increase display a …
We study magnetoconductance of the small bandgap carbon nanotube quantum dots in the presence of spin-orbit coupling in the strong correlations regime. The finite-U mean field slave boson approach is used to study many-body effects. Different degeneracies are restored in magnetic field and Kondo effects of different symmetries arise including SU(3) effects of different types. Full spin-orbital degeneracy might be recovered for zero field and correspondingly SU(4) Kondo effect sets in. We point out on the possibility of the occurrence of electron-hole Kondo effects in slanting magnetic fields, …
The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. …
We probe the high frequency emission of a carbon nanotube based Josephson junction and compare it to its DC Josephson current. The AC emission is probed by coupling the carbon nanotube to an on-chip detector (a Superconductor-Insulator-Superconductor junction), via a coplanar waveguide resonator. The measurement of the photo-assisted current of the detector gives direct access to the signal emitted by the carbon nanotube. We focus on the gate regions that exhibit Kondo features in the normal state and demonstrate that when the DC supercurrent is enhanced by the Kondo effect, the AC Josephson e…
Using nonequilibrium Green functions and several complementary many-body approximations we calculate shot noise and spin dependent conductance in carbon nanotube semiconducting quantum dot in spin-orbital Kondo regime. We point out on the possibility of reaching giant values of tunnel magnetoresistance in this range and discuss a prospect of its gate control. We also analyze the influence of symmetry breaking perturbations on the shot noise with special emphasis on spin dependent effects. The gate and bias dependencies of noise Fano factors influenced by magnetic field, polarization of electro…
We show a detailed investigation of the split Kondo effect in a carbon nanotube quantum dot with multiple gate electrodes. It is found that the splitting decreases for increasing magnetic field, to result in a recovered zero-bias Kondo resonance at finite magnetic field. Surprisingly, in the same charge state, but under different gate-configurations, the splitting does not disappear for any value of the magnetic field, but we observe an avoided crossing of two high-conductance lines. We think that our observations can be understood in terms of a two-impurity Kondo effect with two spins coupled…
In a single-walled carbon nanotube, we observe the spin-1/2 Kondo effect. The energy of spin-resolved Kondo peaks is proportional to magnetic field at high fields, contrary to recent reports. At lower fields, the energy falls below this linear dependence, in qualitative agreement with theoretical expectations. For even electron occupancy, we observe a spin-1 Kondo effect due to the degeneracy of the triplet ground states. Tuning gate voltage within the same Coulomb diamond drives a transition to a singlet ground state. We also independently tune the energy difference between singlet and triple…
We study the Kondo effect in a single-electron transistor device realized in a single-wall carbon nanotube. The K-K' double orbital degeneracy of a nanotube, which originates from the peculiar two-dimensional band structure of graphene, plays the role of a pseudo-spin. Screening of this pseudo-spin, together with the real spin, can result in an SU(4) Kondo effect at low temperatures. For such an exotic Kondo effect to arise, it is crucial that this orbital quantum number is conserved during tunneling. Experimentally, this conservation is not obvious and some mixing in the orbital channel may o…
High quality single wall carbon nanotube quantum dots have been made showing both metallic and semiconducting behavior. Some of the devices are identified as small band gap semiconducting nanotubes with relatively high broad conductance oscillations for hole transport through the valence band and low conductance Coulomb blockade oscillations for electron transport through the conduction band. The transition between these regimes illustrates that transport evolves from being wave-like transmission known as Fabry-Perot interference to single particle-like tunneling of electrons or holes. In the …
Most of the time, electronic excitations in mesoscopic conductors are well described, around equilibrium, by non-interacting Landau quasi-particles. This allows a good understanding of the transport properties in the linear regime. However, the role of interaction in the non-equilibrium properties beyond this regime has still to be established. A paradigmatic example is the Kondo many body state, which can be realized in a carbon nanotube (CNT) quantum dot for temperatures below the Kondo temperature $T_K$. As CNT possess spin and orbital quantum numbers, it is possible to investigate the twof…
We have reproducibly contacted gated single wall carbon nanotubes (SWCNT) to superconducting leads based on niobium. The devices are identified to belong to two transparency regimes: The Coulomb blockade and the Kondo regime. Clear signature of the superconducting leads is observed in both regimes and in the Kondo regime a narrow zero bias peak interpreted as a proximity induced supercurrent persist in Coulomb blockade diamonds with Kondo resonances.
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 $Δ$ 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…
We demonstrate that curvature-induced spin-orbit (SO) coupling induces a $0-π$ transition in the Josephson current through a carbon nanotube quantum dot coupled to superconducting leads. In the non-interacting regime, the transition can be tuned by applying parallel magnetic field near the critical field where orbital states become degenerate. Moreover, the interplay between charging and SO effects in the Coulomb Blockade and cotunneling regimes leads to a rich phase diagram with well-defined (analytical) boundaries in parameter space. Finally, the 0 phase always prevails in the Kondo regime. …
We report on electrical transport measurements through a carbon nanotube quantum dot coupled to a normal and a superconducting lead. The ratio of Kondo temperature and superconducting gap $T_{K}/Δ$ is identified to govern the transport properties of the system. In the case of $T_{K}<Δ$ the conductance resonance splits into two resonances at $\pm Δ$. For the opposite scenario $T_{K}>Δ$ the conductance resonance persists, however the conductance is not enhanced compared to the normal state due to a relative asymmetry of the lead-dot couplings. Within this limit the data is in agreement with a si…
Recently, Coulomb blockade physics was observed at room temperature in a carbon nanotube single-electron transistor (H. W. Ch. Postma, et. al., Science 293, 76 (2001)). In this work, we suggest that these devices may be promising for studying the Kondo effect. In particular, they could allow for a detailed investigation of the 2-channel Kondo fixed point. Moreover, fabricating a similar device in a short nanotube could be promising for studying the effect of a magnetic impurity in an ultrasmall metallic grain. Experimental signatures of the Kondo effect in these systems is discussed.
Transition metal impurities will yield zero bias anomalies in the conductance of well contacted metallic carbon nanotubes, but Kondo temperatures and geometry dependences have not been anticipated so far. Applying the density functional plus numerical renormalization group approach of Lucignano \textit{et al.} to Co and Fe impurities in (4,4) and (8,8) nanotubes, we discover a huge difference of behaviour between outside versus inside adsorption of the impurity. The predicted Kondo temperatures and zero bias anomalies, tiny outside the nanotube, turn large and strongly radius dependent inside,…
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) K…
In a single state of a quantum dot the Kondo effect arises due to the spin-degeneracy, which is present if the dot is occupied with one electron (N = 1). The eigenstates of a carbon nanotube quantum dot possess an additional orbital degeneracy leading to a four-fold shell pattern. This additional degeneracy increases the possibility for the Kondo effect to appear. We revisit the Kondo problem in metallic carbon nanotubes by linear and non-linear transport measurement in this regime, in which the four-fold pattern is present. We have analyzed the ground state of CNTs, which were grown by chemic…
We investigate theoretically the non-equilibrium transport properties of carbon nanotube quantum dots. Owing to the two-dimensional band structure of graphene, a double orbital degeneracy plays the role of a pseudo-spin, which is entangled with the spin. Quantum fluctuations between these four degrees of freedom result in an SU(4) Kondo effect at low temperatures. This exotic Kondo effect manifests as a four-peak splitting in the non-linear conductance when an axial magnetic field is applied.
The out-of-equilibrium electron transport of carbon nanotube semiconducting quantum dot placed in a magnetic field is studied in the Kondo regime by means of the non-equilibrium Green functions. The equation of motion method is used. For parallel magnetic field the Kondo peak splits in four peaks, following the simultaneous splitting of the orbital and spin states. For perpendicular field orientation the triple peak structure of density of states is observed with the central peak corresponding to orbital Kondo effect and the satellites reflecting the spin and spin-orbital fluctuations.
Spin polarized transport through a quantum dot coupled to ferromagnetic electrodes with noncollinear magnetizations is discussed in terms of nonequilibrium Green functions formalism in the finite-U slave boson mean field approximation. The difference of orientations of the magnetizations of electrodes opens off-diagonal spin-orbital transmission and apart from spin currents of longitudinal polarization also spin-flip currents appear. We also study equilibrium pure spin current at zero bias and discuss its dependence on magnetization orientation, spin-orbit coupling strength and gate voltage. I…
We investigate a tunable two-impurity Kondo system in a strongly correlated carbon nanotube double quantum dot, accessing the full range of charge regimes. In the regime where both dots contain an unpaired electron, the system approaches the two-impurity Kondo model. At zero magnetic field the interdot coupling disrupts the Kondo physics and a local singlet state arises, but we are able to tune the crossover to a Kondo screened phase by application of a magnetic field. All results show good agreement with a numerical renormalization group study of the device.
We investigate the supercurrent through a quantum dot for the whole range of couplings using the numerical renormalization group method. We find that the Josephson current switches abruptly from a $π$- to a 0-phase as the coupling increases. At intermediate couplings the total spin in the ground state depends on the phase difference between the two superconductors. Our numerical results can explain the crossover in the conductance observed experimentally by Buitelaar \textit{et al.} [Phys. Rev. Lett. \textbf{89}, 256 801 (2002)].
The linear response transport properties of carbon nanotube quantum dot in the strongly correlated regime are discussed. The finite-U mean field slave boson approach is used to study many-body effects. Magnetic field can rebuilt Kondo correlations, which are destroyed by the effect of spin-orbit interaction or valley mixing. Apart from the field induced revivals of SU(2) Kondo effects of different types: spin, valley or spin-valley, also more exotic phenomena appear, such as SU(3) Kondo effect. Threefold degeneracy occurs due to the effective intervalley exchange induced by short-range part of…
We report on cotunneling spectroscopy magnetoconductance measurements of multi-hole ultraclean carbon nanotube quantum dots in the SU(4) Kondo regime with strong spin-orbit coupling. Successive shells show a gradual weakening of the Kondo effect with respect to the spin-orbital splittings, leading to an evolution from SU(4) to SU(2) symmetry with a suppressed conductance at half shell filling. The extracted energy level spectrum, overally consistent with negligible disorder in the nanotube, shows in the half filled case large renormalizations due to Coulombian effects.
By introducing a normal self-energy to incorporate the effects of magnetic impurities, Kondo effects in single-walled metallic carbon nanotubes are investigated within the Anderson model and Landauer formula. Magnetic impurities induce Kondo resonance and bring a valley of conductance unction near the Fermi level. The conductance of the nanotube increases with the temperature in the low temperature range. Thermoelectric power induced by magnetic impurities is gotten from Mott relation, and the calculations indicate its dependence on the temperature could interpret the experiment well.
Motivated by recent experimental observation of spin-orbit coupling in carbon nanotube quantum dots [F. Kuemmeth \textsl{et al.}, Nature (London) {\bf 452}, 448 (2008)], we investigate in detail its influence on the Kondo effect. The spin-orbit coupling intrinsically lifts out the fourfold degeneracy of a single electron in the dot, thereby breaking the SU(4) symmetry and splitting the Kondo resonance even at zero magnetic field. When the field is applied, the Kondo resonance further splits and exhibits fine multipeak structures resulting from the interplay of spin-orbit coupling and Zeeman ef…
Numerical calculations simulate transport experiments in carbon nanotube quantum dots (P. Jarillo-Herrero et al., Nature 434, 484 (2005)), where a strongly enhanced Kondo temperature T_K ~ 8K was associated with the SU(4) symmetry of the Hamiltonian at quarter-filling for an orbitally double-degenerate single-occupied electronic shell. Our results clearly suggest that the Kondo conductance measured for an adjacent shell with T_K ~ 16K, interpreted as a singlet-triplet Kondo effect, can be associated instead to an SU(4) Kondo effect at half-filling. Besides presenting spin-charge Kondo screenin…
Many-body entanglement is at the heart of the Kondo effect, which has its hallmark in quantum dots as a zero-bias conductance peak at low temperatures. It signals the emergence of a conducting singlet state formed by a localized dot degree of freedom and conduction electrons. Carbon nanotubes offer the possibility to study the emergence of the Kondo entanglement by tuning many-body correlations with a gate voltage. Here we quantitatively show an undiscovered side of Kondo correlations, which counterintuitively tend to block conduction channels: inelastic cotunneling lines in the magnetospectru…
We have contacted single wall carbon nanotubes grown by chemical vapor deposition to superconducting Ti/Al/Ti electrodes. The device, we here report on is in the Kondo regime exhibiting a four-fold shell structure, where a clear signature of the superconducting electrodes is observed below the critical temperature. Multiple Andreev reflections are revealed by sub-gap structure and a narrow peak in the differential conductance around zero bias is seen depending on the shell filling. We interpret the peak as a proximity induced supercurrent and examine its interplay with Kondo resonances.
We study a carbon nanotube quantum dot embedded into a SQUID loop in order to investigate the competition of strong electron correlations with proximity effect. Depending whether local pairing or local magnetism prevails, a superconducting quantum dot will respectively exhibit positive or negative supercurrent, referred to as a 0 or $π$ Josephson junction. In the regime of strong Coulomb blockade, the 0 to $π$ transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at larger tunneling amplitude the Kondo effect develops for an odd …
In this work, we use three different numerical techniques to study the charge transport properties of a system in the two-level SU(2) (2LSU2) regime, obtained from an SU(4) model Hamiltonian by introducing orbital mixing of the degenerate orbitals via coupling to the leads. SU(4) Kondo physics has been experimentally observed, and studied in detail, in Carbon Nanotube Quantum Dots. Adopting a two molecular orbital basis, the Hamiltonian is recast into a form where one of the molecular orbitals decouples from the charge reservoir, although still interacting capacitively with the other molecular…
We propose carbon nanotubes (CNTs) with magnetic impurities as a versatile platform to achieve unconventional Kondo physics, where the CNT bath is gapped by the spin-orbit interaction and surface curvature. While the strong-coupling phase is inaccessible for the special case of half-filled impurities in neutral armchair CNTs, the system in general can undergo quantum phase transitions to the Kondo ground state. The resultant position-specific phase diagrams are investigated upon variation of the CNT radius, chirality, and carrier doping, revealing several striking features, e.g., the existence…
We investigate the influence of spin-orbit coupling on the Kondo effects in carbon nanotube quantum dots, using the numerical renormalization group technique. A sufficiently large spin-orbit coupling is shown to destroy the SU(4) Kondo effects at zero magnetic field, leaving only two SU(2) Kondo effects in the one- and three-electron Coulomb blockade valleys. On applying a finite magnetic field, two additional, spin-orbit induced SU(2) Kondo effects arise in the three- and two-electron valleys. Using physically realistic model parameters, we calculate the differential conductance over a range …
We study Majorana devices featuring a competition between superconductivity and multi-channel Kondo physics. Our proposal extends previous work on single-channel Kondo systems to a topologically nontrivial setting of non-Fermi liquid type, where topological superconductor wires (with gap $Δ$) represent leads tunnel-coupled to a Coulomb-blockaded Majorana box. On the box, a spin degree of freedom with Kondo temperature $T_K$ is nonlocally defined in terms of Majorana states. For $Δ\gg T_K$, the destruction of Kondo screening by superconductivity implies a $4π$-periodic Josephson current-phase r…
In a quantum dot hybrid superconducting junction, the behavior of the supercurrent is dominated by Coulomb blockade physics, which determines the magnetic state of the dot. In particular, in a single level quantum dot singly occupied, the sign of the supercurrent can be reversed, giving rise to a pi-junction. This 0-pi transition, corresponding to a singlet-doublet transition, is then driven by the gate voltage or by the superconducting phase in the case of strong competition between the superconducting proximity effect and Kondo correlations. In a two-level quantum dot, such as a clean carbon…
We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that when the coupling of the spin is of the order of the superconducting gap two almost degenerate subgap states are formed. By computing the Berry phase that is associated with the superconducting phase rotations in this model, we prove that these subgap states are characterized by a different charge and demonstrate that the switching between these states has the same effect as quasiparticle poisoning (unpoisoning) of the island. We also …
The dc Josephson effect is investigated in a single-walled metallic carbon nanotube connected to two superconducting leads. In particular, by using the Luttinger liquid theory, we analyze the effects of the electron-electron interaction on the supercurrent. We find that in the long junction limit the strong electronic correlations of the nanotube, together with its peculiar band structure, induce oscillations in the critical current as a function of the junction length and/or the nanotube electron filling. These oscillations represent a signature of the Luttinger liquid physics of the nanotube…
We present the theory of the Josephson effect in nanotube dots where an SU(4) symmetry can be realized. We find a remarkably rich phase diagram that significantly differs from the SU(2) case. In particular, π-junction behavior is largely suppressed. We analytically obtain the Josephson current in various parameter regions: (i) in the Kondo regime, covering the full crossover from SU(4) to SU(2), (ii) for weak tunnel couplings, and (iii) for large BCS gap. The transition between these regions is studied numerically.
Carbon nanotube (CNT) Josephson junctions in the open quantum dot limit exhibit superconducting switching currents which can be controlled with a gate electrode. Shapiro voltage steps can be observed under radiofrequency current excitations, with a damping of the phase dynamics that strongly depends on the gate voltage. These measurements are described by a standard RCSJ model showing that the switching currents from the superconducting to the normal state are close to the critical current of the junction. The effective dynamical capacitance of the nanotube junction is found to be strongly gat…
We investigate electronic transport in Josephson junctions formed by single-walled carbon nanotubes coupled to superconducting electrodes. We observe enhanced zero-bias conductance (up to 10e^2/h) and pronounced sub-harmonic gap structures in differential conductance, which arise from the multiple Andreev reflections at superconductor/nanotube interfaces. The voltage-current characteristics of these junctions display abrupt switching from the supercurrent branch to resistive branch, with a gate-tunable switching current ranging from 50 pA to 2.3 nA. The finite resistance observed on the superc…
The effect of magnetic impurities on the ballistic conductance of nanocontacts is, as suggested in recent work, amenable to ab initio study \cite{naturemat}. Our method proceeds via a conventional density functional calculation of spin and symmetry dependent electron scattering phase shifts, followed by the subsequent numerical renormalization group solution of Anderson models -- whose ingredients and parameters are chosen so as to reproduce these phase shifts. We apply this method to investigate the Kondo zero bias anomalies that would be caused in the ballistic conductance of perfect metalli…
Progress in the fabrication of nanometer-scale electronic devices is opening new opportunities to uncover the deepest aspects of the Kondo effect, one of the paradigmatic phenomena in the physics of strongly correlated electrons. Artificial single-impurity Kondo systems have been realized in various nanostructures, including semiconductor quantum dots, carbon nanotubes and individual molecules. The Kondo effect is usually regarded as a spin-related phenomenon, namely the coherent exchange of the spin between a localized state and a Fermi sea of electrons. In principle, however, the role of the…
We discuss the change of the Kondo effect in the Josephson junction formed by the indirect coupling between a one-dimensional \emph{DIII}-class topological and s-wave superconductors via a quantum dot. By performing the Schrieffer-Wolff transformation, we find that the single-electron occupation in the quantum dot induces various correlation modes, such as the Kondo and singlet-triplet correlations between the quantum dot and the $s$-wave superconductor and the spin exchange correlation between the dot and Majorana doublet. Moreover, it plays a nontrivial role in modifying the Josephson effect…
We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant And…
By coupling on chip a carbon nanotube to a quantum noise detector, a superconductor-insulator-superconductor junction, via a resonant circuit, we measure the emission noise of a carbon nanotube quantum dot in the Kondo regime. The signature of the Kondo effect in the current noise is measured for different ratios of the Kondo temperature over the measured frequency and for different asymmetries of the coupling to the contacts, and compared to finite frequency quantum noise calculations. Our results point towards the existence of a high frequency cut-off of the electronic emission noise associa…
We study the Kondo effect in a CNT(left lead)-CNT(QD)-CNT(right lead) structure. Here CNT is a single-wall metallic carbon nanotube, for which 1) the valence and conduction bands of electrons with zero orbital angular momentum ($m=0$) coalesc at the two valley points ${\bf{K}}$ and ${\bf{K}}'$ of the first Brillouin zone and 2) the energy spectrum of electrons with $m \ne 0$ has a gap whose size is proportional to $|m|$. Following adsorption of hydrogen atoms and application of an appropriately designed gate potential, electron energy levels in the CNT(QD) are tunable to have: 1) two-fold spin…
We investigate transport of Cooper pairs through a double quantum dot (DQD) in the Kondo regime and coupled to superconducting leads. Within the non-perturbative slave boson mean-field theory we evaluate the Josephson current for two different configurations, the DQD coupled in parallel and in series to the leads. We find striking differences between these configurations in the supercurrent as a function of the ratio t/Γ, where t is the interdot coupling and Γis the coupling to the leads: the critical current I_c decreases monotonously with t/Γfor the parallel configuration whereas I_c exhibit…
The Kondo effect and superconductivity are both prime examples of many-body phenomena. Here we report transport measurements on a carbon nanotube quantum dot coupled to superconducting leads that show a delicate interplay between both effects. We demonstrate that the superconductivity of the leads does not destroy the Kondo correlations on the quantum dot when the Kondo temperature, which varies for different single-electron states, exceeds the superconducting gap energy.
We measure the non-dissipative supercurrent in a single InAs self-assembled quantum dot (QD) coupled to superconducting leads. The QD occupation is both tuned by a back-gate electrode and lateral side-gate. The geometry of the side-gate allows tuning of the QD-lead tunnel coupling in a region of constant electron number with appropriate orbital state. Using the side-gate effect we study the competition between Kondo correlations and superconducting pairing on the QD, observing a decrease in the supercurrent when the Kondo temperature is reduced below the superconducting energy gap in qualitati…
Dissipation is ubiquitous in quantum systems, and its interplay with fluctuations is critical to maintaining quantum coherence. We experimentally investigate the dissipation dynamics in single-walled carbon nanotubes coupled to superconductors. The voltage-current characteristics display gate-tunable hysteresis, with sizes that perfectly correlate with the normal state resistance RN, indicating the junction undergoes a periodic modulation between underdamped and overdamped regimes. Surprisingly, when a device's Fermi-level is tuned through a local conductance minimum, we observe a gate-control…
