Carbon nanotubes (CNTs) are almost ideal one-dimensional conductors. However, potential variation caused likely by charge tarps in the substrate induced backscatering on a length scale of a few 100 nm. There are two strategies to overcome this problem: in one the CNT is suspended and in the other it is placed on another substrate. Of particular interest is h-BN, since this substrate yielded much better charge transport mobilities in graphene when place on h-BN instead on an oxidized Si wafer. We have developed a deterministic approach to place single CNTs suspended over contacts and gate arrays and tested CNT on h-BN. In order to go beyond the state-of-the-art we have started to fabricate three-terminal CNT devices with weak contacts, i.e. tunneling contacts using monolayers of h-BN as barriers. Three weakly coupled contacts on a single section of CNT, a quantum dots, allows to obtain all coupling parameters unambiguously. We are also interested to use grow CNT made from the isotope 13C providing a nuclear spin. Due to strong electron-electron interaction the indirect spin-spin coupling can be strongly enhanced leading to a phase transition to a nuclear spin helix at low temperatures. Consequently, the spin in the conduction band is also polarized providing a „natural“ system to test Majorana fermion physics by coupling the CNT to a superconductor.

(a,b) shows how a single carbon nanotube (CNT) can be placed in a deterministic way over a pair of source/drain contacts and a series of gate electrodes. The CNT was grown on a fork and stamped over the electrodes resulting in clean CNT double quantum dots as seen in the transport measurements in (c-e).

Current challenges are: weakly coupled CNTs to allow for high resolution tunneling spectroscopy, measure the spin-lifetime in 12C and 13C CNTs using spin blockade, coupling CNTs to superconductors and measure Andreev bound state in magnetic field.


Relevant papers:

keyword: CNT


  • Blocking-state influence on shot noise and conductance in quantum dots
    M. -C. Harabula, V. Ranjan, R. Haller, G. Fülöp, and C. Schönenberger.
    Phys. Rev. B, 97:115403, mar 2018. [DOI] arXiv:1801.00286

    Quantum dots (QDs) investigated through electron transport measurements often exhibit varying, state-dependent tunnel couplings to the leads. Under speci c conditions, weakly coupled states can result in a strong suppression of the electrical current and they are correspondingly called blocking states. Using the combination of conductance and shot noise measurements, we investigate blocking states in carbon nanotube (CNT) QDs. We report negative di erential conductance and super- Poissonian noise. The enhanced noise is the signature of electron bunching, which originates from random switches between the strongly and weakly conducting states of the QD. Negative differential conductance appears here when the blocking state is an excited state. In this case, at the threshold voltage where the blocking state becomes populated, the current is reduced. Using a master equation approach, we provide numerical simulations reproducing both the conductance and the shot noise pattern observed in our measurements.


  • Andreev bound states probed in three-terminal quantum dots
    J. Gramich, A. Baumgartner, and C. Schönenberger.
    Phys. Rev. B, 96:195418, nov 2017. [DOI] arXiv:1612.01201

    Andreev bound states (ABSs) are well-de ned many-body quantum states that emerge from the hybridization of individual quantum dot (QD) states with a superconductor and exhibit very rich and fundamental phenomena. We demonstrate several new electron transport phenomena mediated by ABSs that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state (or quantum phase) transition in such S-QD systems can occur. In addition, we ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity excited QD states, a process we call excited state ABS resonances. In the conductance between the two N contacts we find a characteristic pattern of positive and negative differential subgap conductance, which we explain by considering two nonlocal processes, the creation of Cooper pairs in S by electrons from both N terminals, and a novel transport mechanism called resonant ABS tunneling, possible only in multi-terminal QD devices. In the latter process, electrons are transferred via the ABS without effectively creating Cooper pairs in S. The three-terminal geometry also allows spectroscopy experiments with different boundary conditions, for example by leaving S floating. Surprisingly, we find that, depending on the boundary conditions and the device parameters, the experiments either show single-particle Coulomb blockade resonances, ABS characteristics, or both in the same measurements, seemingly contradicting the notion of ABSs replacing the single particle states as eigenstates of the QD. We qualitatively explain these results as originating from the nite time scale required for the coherent oscillations between the superposition states after a single electron tunneling event. These experiments demonstrate that three-terminal experiments on a single complex quantum object can also be useful to investigate charge dynamics otherwise not accessible due to the very high frequencies.

  • Measuring a Quantum Dot with an Impedance-Matching On-Chip Superconducting LC Resonator at Gigahertz Frequencies
    M. -C. Harabula, T. Hasler, G. Fülöp, M. Jung, V. Ranjan, and C. Schönenberger.
    Phys. Rev. Appl., 8:54006, nov 2017. [DOI] arXiv:1707.09061

    We report on the realization of a bonded-bridge on-chip superconducting coil and its use in impedance matching a highly ohmic quantum dot (QD) to a 3-GHz measurement setup. The coil, modeled as a lumped-element LC resonator, is more compact and has a wider bandwidth than resonators based on coplanar transmission lines (e.g., λ/4 impedance transformers and stub tuners), at potentially better signal-to-noise ratios. Specifically, for measurements of radiation emitted by the device, such as shot noise, the 50 × larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is 3 times higher than that of the one previously reported, a wire-bonded coil. As a proof of principle, we fabricate an LC circuit that achieves impedance matching to an approximately 15 kOhm load and validate it with a load defined by a carbon nanotube QD, whose shot noise we measure in the Coulomb-blockade regime.


  • Full characterization of a carbon nanotube parallel double quantum dot
    G. Abulizi, A. Baumgartner, and C. Schönenberger.
    Physica Status Solidi B, 253(12):2428-2432, aug 2016. [DOI] arXiv:1605.02300v1

    We have measured the differential conductance of a parallel carbon nanotube (CNT) double quantum dot (DQD) with strong inter-dot capacitance and inter-dot tunnel coupling. Nominally, the device consists of a single CNT with two contacts. However, we identify two sets of Coulomb blockade (CB) diamonds that do not block transport individually, which suggests that two quantum dots (QDs) are contacted in parallel. We find strong and periodic anti-crossings in the gate and bias dependence, which are only possible if the QDs have similar characteristics. We discuss qualitatively the level spectrum and the involved transport processes in this device and extract the DQD coupling parameters. These results lead us to believe that clean and undoped QDs are formed parallel to the CNT axis, possibly on the outer and inner shells of a multi-wall CNT, or in a double-stranded CNT bundle.

  • Subgap resonant quasiparticle transport in normal-superconductor quantum dot devices
    J. Gramich, A. Baumgartner, and C. Schönenberger.
    Applied Physics Letters, 108(17):172604, apr 2016. [DOI] arXiv:1601.00672

    We report thermally activated transport resonances for biases below the superconducting energy gap in a carbon nanotube quantum dot (QD) device with a superconducting Pb and a normal metal contact. These resonances are due to the superconductor’s finite quasi-particle population at elevated temperatures and can only be observed when the QD life-time broadening is considerably smaller than the gap. This condition is fulfilled in our QD devices with optimized Pd/Pb/In multi-layer contacts, which result in reproducibly large and “clean” superconducting transport gaps with a strong conductance suppression for subgap biases. We show that these gaps close monotonically with increasing magnetic field and temperature. The accurate description of the subgap resonances by a simple resonant tunneling model illustrates the ideal characteristics of the reported Pb contacts and gives an alternative access to the tunnel coupling strengths in a QD.

  • Cooper-Paare tunneln durch einen Quantenpunkt
    Andreas Baumgartner, Jörg Gramich, and Christian Schönenberger.
    Physik in unserer Zeit, 47(2):62-63, mar 2016. [DOI]

    Elektronische Bauteile aus Supraleitern und Quantenpunkten zeigen eine Vielzahl von neuen und fundamentalen physikalischen Eigenschaften und stellen neue quantentechnologische Anwendungen in Aussicht. Kuerzlich ist es gelungen, den wohl grundlegendsten Transportprozess in einer solchen Struktur in Experimenten zu identifizieren, naemlich den direkten Transport von Elektronen aus einem Supraleiter durch einen Quantenpunkt, das sogenannte Andreev-Tunneln. Das Verstaendnis dieses Prozesses liefert die Grundlage fuer zukuenftige Anwendungen, die quantenmechanische Phaenomene in elektronischen Bauteilen ausnutzen werden.


  • Magnetic Field Tuning and Quantum Interference in a Cooper Pair Splitter
    G. Fülöp, F. Domínguez, S. d’Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygard, C. Schönenberger, Levy A. Yeyati, Csonka S. -. in cooperation with the Csonka(Budapest), and Levi Yeyati group (Madrid).
    Physical Review Letters, 115(22):227003, nov 2015. [DOI] arXiv:1507.01036

    Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three – site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency.

  • Resonant and Inelastic Andreev Tunneling Observed on a Carbon Nanotube Quantum Dot
    J. Gramich, A. Baumgartner, and C. Schönenberger.
    Physical Review Letters, 115(21):216801, nov 2015. [DOI] arXiv:1507.00526

    We report the observation of two fundamental sub-gap transport processes through a quantum dot (QD) with a superconducting contact. The device consists of a carbon nanotube contacted by a Nb superconducting and a normal metal contact. First, we find a single resonance with position, shape and amplitude consistent with the theoretically predicted resonant Andreev tunneling (AT) through a single QD level. Second, we observe a series of discrete replicas of resonant AT at a separation of ∼145μeV, with a gate, bias and temperature dependence characteristic for boson-assisted, inelastic AT, in which energy is exchanged between a bosonic bath and the electrons. The magnetic field dependence of the replica’s amplitudes and energies suggest that two different bosons couple to the tunnel process.

  • Shot Noise of a Quantum Dot Measured with Gigahertz Impedance Matching
    T. Hasler, M. Jung, V. Ranjan, G. Puebla-Hellmann, A. Wallraff, and C. Schönenberger.
    Physical Review Applied, 4(5):54002, nov 2015. [DOI] arXiv:1507.04884.pdf

    The demand for a fast high-frequency read-out of high-impedance devices, such as quantum dots, necessitates impedance matching. Here we use a resonant impedance-matching circuit (a stub tuner) realized by on-chip superconducting transmission lines to measure the electronic shot noise of a carbonnanotube quantum dot at a frequency close to 3 GHz in an efficient way. As compared to wideband detection without impedance matching, the signal-to-noise ratio can be enhanced by as much as a factor of 800 for a device with an impedance of 100 kOmega. The advantage of the stub resonator concept is the ease with which the response of the circuit can be predicted, designed, and fabricated. We further demonstrate that all relevant matching circuit parameters can reliably be deduced from power-reflectance measurements and then used to predict the power-transmission function from the device through the circuit. The shot noise of the carbon-nanotube quantum dot in the Coulomb blockade regime shows an oscillating suppression below the Schottky value of 2eI, as well as an enhancement in specific regions

  • Fork stamping of pristine carbon nanotubes onto ferromagnetic contacts for spin-valve devices
    J. Gramich, A. Baumgartner, M. Muoth, C. Hierold, and C. Schönenberger.
    physica status solidi (b), 252(11):2496-2502, jul 2015. [DOI] arXiv:1504.05693

    We present a fabrication scheme called ‘fork stamping’ optimized for the dry transfer of individual pristine carbon nanotubes (CNTs) onto ferromagnetic contact electrodes fabricated by standard lithography. We demonstrate the detailed recipes for a residue-free device fabrication and in-situ current annealing on suspended CNT spin-valve devices with ferromagnetic Permalloy (Py) contacts and report preliminary transport characterization and magnetoresistance experiments at cryogenic temperatures. This scheme can directly be used to implement more complex device structures, including multiple gates or superconducting contacts.

  • Clean carbon nanotubes coupled to superconducting impedance-matching circuits
    V. Ranjan, G. Puebla-Hellmann, M. Jung, T. Hasler, A. Nunnenkamp, M. Muoth, C. Hierold, A. Wallraff, and C. Schönenberger.
    Nature Communications, 6:7165, may 2015. [DOI] arXiv:1505.04681

    Coupling carbon nanotube devices to microwave circuits offers a significant increase in bandwidth and signal-to-noise ratio. These facilitate fast non-invasive readouts important for quantum information processing, shot noise and correlation measurements. However, creation of a device that unites a low-disorder nanotube with a low-loss microwave resonator has so far remained a challenge, due to fabrication incompatibility of one with the other. Employing a mechanical transfer method, we successfully couple a nanotube to a gigahertz superconducting matching circuit and thereby retain pristine transport characteristics such as the control over formation of, and coupling strengths between, the quantum dots. Resonance response to changes in conductance and susceptance further enables quantitative parameter extraction. The achieved near matching is a step forward promising high-bandwidth noise correlation measurements on high impedance devices such as quantum dot circuits.


  • Carbon nanotube quantum dots on hexagonal boron nitride
    A. Baumgartner, G. Abulizi, K. Watanabe, T. Taniguchi, J. Gramich, and C. Schönenberger.
    Appl. Phys. Lett., 105:23111, jun 2014. [DOI] arXiv:1406.0897

    We report the fabrication details and low-temperature characteristics of the first carbon nanotube (CNT) quantum dots on flakes of hexagonal boron nitride (hBN) as substrate. We demonstrate that CNTs can be grown on hBN by standard chemical vapor deposition and that standard scanning electron microscopy imaging and lithography can be employed to fabricate nanoelectronic structures when using optimized parameters. This proof of concept paves the way to more complex devices on hBN, with more predictable and reproducible characteristics and electronic stability.

  • Optimized fabrication and characterization of carbon nanotube spin valves
    J. Samm, J. Gramich, A. Baumgartner, M. Weiss, and C. Schönenberger.
    J. Appl. Phys., 115:174309, may 2014. [DOI] arXiv:1312.0159

    We report an improved fabrication scheme for carbon based nanospintronic devices and demonstrate the necessity for a careful data analysis to investigate the fundamental physical mechanisms leading to magnetoresistance. The processing with a low-density polymer and an optimised recipe allows us to improve the electrical, magnetic, and structural quality of ferromagnetic Permalloy contacts on lateral carbon nanotube (CNT) quantum dot spin valve devices, with comparable results for thermal and sputter deposition of the material. We show that spintronic nanostructures require an extended data analysis, since the magnetization can affect all characteristic parameters of the conductance features and lead to seemingly anomalous spin transport. In addition, we report measurements on CNT quantum dot spin valves that seem not to be compatible with the orthodox theories for spin transport in such structures.

  • Nonlocal spectroscopy of Andreev bound states
    J. Schindele, A. Baumgartner, R. Maurand, M. Weiss, and C. Schönenberger.
    Phys. Rev. B, 89:45422, jan 2014. [DOI] arXiv:1311.0659

    We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes u and v.


  • Ultraclean Single, Double, and Triple Carbon Nanotube Quantum Dots with Recessed Re Bottom Gates
    M. Jung, J. Schindele, S. Nau, M. Weiss, A. Baumgartner, and C. Schönenberger.
    Nano Lett., 13:4522-4526, 2013. [DOI]

    We demonstrate that ultraclean single, double, and triple quantum dots (QDs) can be formed reliably in a carbon nanotube (CNT) by a straightforward fabrication technique. The QDs are electrostatically defined in the CNT by closely spaced metallic bottom gates deposited in trenches in SiO2 by sputter deposition of Re. The carbon nanotubes are then grown by chemical vapor deposition (CVD) across the trenches and contacted using conventional resist-based electron beam lithography. Unlike in previous work, the devices exhibit reproducibly the characteristics of ultraclean QDs behavior even after the subsequent electron beam lithography and chemical processing steps. We specifically demonstrate the high quality using CNT devices with two narrow bottom gates and one global back gate. Tunable by the gate voltages, the device can be operated in four different regimes: (i) fully p-type with ballistic transport between the outermost contacts (over a length of 700 nm), (ii) clean n-type single QD behavior where a QD can be induced by either the left or the right bottom gate, (iii) n-type double QD, and (iv) triple bipolar QD where the middle QD has opposite doping (p-type). Our simple fabrication scheme opens up a route to more complex devices based on ultraclean CNTs, since it allows for postgrowth processing.


  • Near-Unity Cooper Pair Splitting Efficiency
    J. Schindele, A. Baumgartner, and C. Schönenberger.
    Phys. Rev. Lett., 109(15):157002, oct 2012. [DOI] arXiv:1204.5777

    The two electrons of a Cooper pair in a conventional superconductor form a spin singlet and therefore a maximally entangled state. Recently, it was demonstrated that the two particles can be extracted from the superconductor into two spatially separated contacts via two quantum dots in a process called Cooper pair plitting (CPS). Competing transport processes, however, limit the efficiency of this process. Here we demonstrate efficiencies up to 90 percent, significantly larger than required to demonstrate interactiondominated CPS, and on the right order to test Bell�s inequality with electrons. We compare the CPS currents through both quantum dots, for which large apparent discrepancies are possible. The latter we explain intuitively and in a semiclassical master equation model. Large efficiencies are required to detect electron entanglement and for prospective electronics-based quantum information technologies.


  • Gate-tunable split Kondo effect in a carbon nanotube quantum dot
    A. Eichler, M. Weiss, and C. Schönenberger.
    Nanotechnology, 22(26):265204, may 2011. [DOI] arXiv:1008.5103

    We show a detailed investigation of the split Kondo effect in a carbon nanotube quantum dot with multiple gate electrodes. Two conductance peaks, observed at finite bias in nonlinear transport measurements, are found to approach each other 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. We think that our observations can be understood in terms of a two-impurity Kondo effect with two spins coupled antiferromagnetically. The exchange coupling between the two spins can be influenced by a local gate, and the non-recovery of the Kondo resonance for certain gate configurations is explained by the existence of a small antisymmetric contribution to the exchange interaction between the two spins


  • Permalloy-based carbon nanotube spin-valve
    H. Aurich, A. Baumgartner, F. Freitag, A. Eichler, J. Trbovic, and C. Schönenberger.
    App. Phys. Lett, 97:153116, oct 2010. [DOI] arXiv:1009.1960

    In this paper we demonstrate that permalloy (Py), a widely used Ni/Fe alloy, forms contacts to carbon nanotubes (CNTs) that meet the requirements for the injection and detection of spin-polarized currents in carbon-based spintronic devices. We establish the material quality and magnetization properties of Py strips in the shape of suitable electrical contacts and find a sharp magnetization switching tunable by geometry in the anisotropic magnetoresistance (AMR) of a single strip at cryogenic temperatures. In addition, we show that Py contacts couple strongly to CNTs, comparable to Pd contacts, thereby forming CNT quantum dots at low temperatures. These results form the basis for a Py-based CNT spin-valve exhibiting very sharp resistance switchings in the tunneling magnetoresistance, which directly correspond to the magnetization reversals in the individual contacts observed in AMR experiments.

  • Hybrid superconductor – quantum dot devices
    De S. Franceschi, L. Kouwenhoven, C. Schönenberger, and W. Wernsdorfer.
    Nature Nanotechnology (invited), 5:703-711, sep 2010. [DOI]

    Advances in nanofabrication techniques have made it possible to make devices in which superconducting electrodes are connected to non-superconducting nanostructures such as quantum dots. The properties of these hybrid devices result from a combination of a macroscopic quantum phenomenon involving large numbers of electrons (superconductivity) and the ability to control single electrons, offered by quantum dots. Here we review research into electron transport and other fundamental processes that have been studied in these devices. We also describe potential applications, such as a transistor in which the direction of a supercurrent can be reversed by adding just one electron to a quantum dot.


  • Tuning the Josephson current in carbon nanotubes with the Kondo effect
    A. Eichler, R. Deblock, M. Weiss, C. Schönenberger, H. Bouchiat, C. Karrasch, and V. Meden.
    Phys. Rev. B, 79:161407(R), apr 2009. [DOI] arXiv:0810.1671

    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 V_BG. Whereas it is largely suppressed at the center of the ridge, it shows a sharp increase at a finite value of V_BG. This increase can be attributed to a doublet-singlet transition of the spin state of the nanotube island leading to a π 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.


  • Large oscillating non-local voltage in multiterminal single-wall carbon nanotube devices
    G. Gunnarsson, J. Trbovic, and C. Schönenberger.
    Phys. Rev. B (rapid), 77:201405, may 2008. [DOI] arXiv:0710.0365

    We report on the observation of a nonlocal voltage in a ballistic (quasi)-one-dimensional conductor, realized by a single-wall carbon nanotube with four contacts. The contacts divide the tube into three quantum dots, which we control by the back-gate voltage Vg . We measure a large oscillating nonlocal voltage Vnl as a function of Vg . Though a resistor model that includes the impedance of the voltmeter can account for a nonlocal voltage including change of sign, it fails to describe the magnitude properly. The large amplitude of Vnl is due to quantum interference effects and can be understood within the scattering approach of electron transport.


  • Mapping electron delocalization by charge transport spectroscopy in an artificial molecule
    M. R. Gräber, M. Weiss, D. Keller, S. Oberholzer, and C. Schönenberger.
    Annalen der Physik, 16(10-11):672-677, oct 2007. [DOI] arXiv:0705.3962

    In this letter we present an experimental realization of the quantum mechanics textbook example of two interacting electronic quantum states that hybridize forming a molecular state. In our particular realization, the quantum states themselves are fabricated as quantum dots in a molecule, a carbon nanotube. For sufficient quantum-mechanical interaction (tunnel coupling) between the two quantum states, the molecular wavefunction is a superposition of the two isolated (dot) wavefunctions. As a result, the electron becomes delocalized and a covalent bond forms. In this work, we show that electrical transport can be used as a sensitive probe to measure the relative weight of the two components in the superposition state as a function of the gate-voltages. For the field of carbon nanotube double quantum dots, the findings represent an additional step towards the engineering of quantum states.

  • Even-Odd Effect in Andreev Transport through a Carbon Nanotube Quantum Dot
    A. Eichler, M. Weiss, S. Oberholzer, C. Schönenberger, Levy A. Yeyati, J. C. Cuevas, and A. Martin-Rodero.
    Phys. Rev. Lett., 99:126602, sep 2007. [DOI] arXiv:0703082

    We have measured the current($I$)-voltage($V$) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance $dI/dV$ due to the Kondo resonance is observed in the normal state, this feature around zero bias voltage is absent in the super\-conducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the $dI/dV$ sub-gap structure caused by Andreev reflection. The first-order Andreev peak appearing around $V=\Delta/e$ is markedly enhanced in gate-voltage regions, in which the charge state of the quantum dot is odd. This enhancement is explained by a `hidden’ Kondo resonance, pinned to one contact only. A comparison with a single-impurity Anderson model, which is solved numerically in a slave-boson mean\-field approach, yields good agreement with the experiment.


  • Defining and Controlling Double Quantum Dots in Single-Wall Carbon Nanotubes
    M. R. Gräber, M. Weiss, S. Oberholzer, and C. Schönenberger.
    Semicond. Sci. Technol., 21:S64-S68, oct 2006. [DOI] arXiv:0605220

    We report the experimental realization of double quantum dots in single-walled carbon nanotubes. The device consists of a nanotube with source and drain contact, and three additional top-gate electrodes in between. We show that, by energizing these top gates, it is possible to locally gate a nanotube, to create a barrier, or to tune the chemical potential of a part of the nanotube. At low temperatures, we find (for three different devices) that in certain ranges of top-gate voltages our device acts as a double quantum dot, evidenced by the typical honeycomb charge stability pattern.

  • Nanospintronics with Carbon Nanotubes
    A. Cottet, T. Kontos, S. Sahoo, H. T. Man, M. -S. Choi, W. Belzig, C. Bruder, A. F. Morpurgo, and C. Scönenberger.
    Semicond. Sci. Technol., 21:S78-S95, oct 2006. [DOI] arXiv:0703472

    One of the actual challenges of spintronics is the realization of a spin transistor allowing control of spin transport through an electrostatic gate. In this paper, we report on different experiments which demonstrate gate control of spin transport in a carbon nanotube connected to ferromagnetic leads. We also discuss some theoretical approaches which can be used to analyse spin transport in these systems. We emphasize the roles of the gate-tunable quasi-bound states inside the nanotube and the coherent spin-dependent scattering at the interfaces between the nanotube and its ferromagnetic contacts.

  • Charge and Spin Transport in Carbon Nanotubes
    C. Schönenberger.
    Semicond. Sci. Technol., 21:S1-S9, oct 2006. [DOI]

    The basic science in quantum transport of nano-scaled ‘devices’ is largely based on the availability of suitable model systems. Nanostructures built from conventional metals are typically in the diffusive transport regime. Semiconductors, as the starting material for nanodevices, are different. Because of the low carrier density and therefore reduced screening, the Fermi energy can be tuned by electrostatic gates. Quantum dots which can be filled sequentially with electrons one by one have been realized in this material system (for a review see Kouwenhoven et al (2001 Rep. Prog. Phys. 64 701)). Today, researchers have also started to explore the new possibilities provided by molecules (see, for example, Selzer and Allara (2006 Ann. Rev. Phys. Chem. 57 593), Cuniberti et al (2006 Lecture Notes in Physics vol 680), McCreery (2004 Chem. Mater. 16 4477)). A rather simple prototype ‘molecule’ is a carbon nanotube (CNT) (for recent reviews, see Anantram and Leonard (2006 Rep. Prog. Phys. 69 507), Dresselhaus et al (2001 Topics in Applied Physics vol 80), Ebbesen (1996 Phys. Today 49 26)). Charge and spin transport in CNTs have attracted a lot of attention in recent years. There are several reasons for this excitement: CNTs are almost ideal quantum-ballistic wires. Large electric field effects have been observed in semiconducting CNTs, potentially of interest for applications in electronics. Because a CNT is an all-surface conductor, the electrical properties are highly sensitive to the environment, which can be exploited in sensing applications. Finally, a wealth of new physics is currently appearing in experiments in which CNT-hybrid devices are used, which employ a combination of normal metal, superconducting and ferromagnetic contacts.

  • Molecular States in Carbon Nanotube Double Quantum Dots
    M. R. Gräber, W. A. Coish, C. Hoffmann, M. Weiss, J. Furer, S. Oberholzer, D. Loss, and C. Schönenberger.
    Phys. Rev. B, 74:75427, aug 2006. [DOI] arXiv:0603367

    We report electrical transport measurements through a semiconducting single-walled carbon nanotube with three additional top gates. At low temperatures the system acts as a double quantum dot with large interdot tunnel coupling allowing for the observation of tunnel-coupled molecular states extending over the whole double-dot system. We precisely extract the tunnel coupling and identify the molecular states by the sequential-tunneling line shape of the resonances in differential conductance.

  • Controlling spin in an electronic interferometer with spin-active interfaces
    A. Cottet, T. Kontos, W. Belzig, C. Schönenberger, and C. Bruder.
    Europhys. Lett., 74:320-326, mar 2006. [DOI] arXiv:0512176

    We consider electronic current transport through a ballistic one-dimensional quantum wire connected to two ferromagnetic leads. We study the effects of the spin-dependence of interfacial phase shifts (SDIPS) acquired by electrons upon scattering at the boundaries of the wire. The SDIPS produces a spin-splitting of the wire resonant energies which is tunable with the gate voltage and the angle between the ferromagnetic polarizations. This property could be used for manipulating spins. In particular, it leads to a giant magnetoresistance effect with a sign tunable with the gate voltage and the magnetic field applied to the wire.


  • Electric field control of spin transport
    S. Sahoo, T. Kontos, J. Furer, C. Hoffmann, M. Gräber, A. Cottet, and C. Schönenberger.
    Nature Physics, 1:99-102, nov 2005. [DOI] arXiv:0511078

    Spintronics aims to develop electronic devices whose resistance is controlled by the spin of the charge carriers that flow through them1, 2, 3. This approach is illustrated by the operation of the most basic spintronic device, the spin valve4, 5, 6, which can be formed if two ferromagnetic electrodes are separated by a thin tunnelling barrier. In most cases, its resistance is greater when the two electrodes are magnetized in opposite directions than when they are magnetized in the same direction7, 8. The relative difference in resistance, the so-called magnetoresistance, is then positive. However, if the transport of carriers inside the device is spin- or energy-dependent3, the opposite can occur and the magnetoresistance is negative9. The next step is to construct an analogous device to a field-effect transistor by using this effect to control spin transport and magnetoresistance with a voltage applied to a gate10, 11. In practice though, implementing such a device has proved difficult. Here, we report on a pronounced gate-field-controlled magnetoresistance response in carbon nanotubes connected by ferromagnetic leads. Both the magnitude and the sign of the magnetoresistance in the resulting devices can be tuned in a predictable manner. This opens an important route to the realization of multifunctional spintronic devices.

  • Electrical spin injection in multi-wall carbon nanotubes with transparent ferromagnetic contacts
    S. Sahoo, T. Kontos, C. Schönenberger, and C. Sürgers.
    Appl. Phys. Lett., 86:112109, mar 2005. [DOI] arXiv:0411623

    We report on electrical spin injection measurements on multiwall carbon nanotubes (MWNTs). We use a ferromagnetic alloy Pd1−xNixPd1−xNix with x≈0.7x≈0.7 which allows us to obtain devices with resistances as low as 5.6kΩ5.6kΩ at 300 K. The yield of device resistances below 100kΩ100kΩ, at 300 K, is around 50%. We measure at 2 K a hysteretic magneto-resistance due to the magnetization reversal of the ferromagnetic leads. The relative difference between the resistance in the antiparallel (AP)(AP) orientation and the parallel (P)(P) orientation is about 2%.


  • Kondo effect in carbon nanotubes at half-filling
    B. Babić, T. Kontos, and C. Schönenberger.
    Phys. Rev. B, 70:235419, dec 2004. [DOI] arXiv:0407193

    {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 chemical vapor deposition, at filling N = 1

  • Observation of Fano-Resonances in Single-Wall Carbon Nanotubes
    B. Babić and C. Schönenberger.
    Phys. Rev. B, 70:195408, nov 2004. [DOI] arXiv:0406571

    We have explored the low-temperature linear and nonlinear electrical conductance G of metallic carbon nanotubes (CNT’s), which were grown by the chemical-vapor deposition method. The high transparency of the contacts allows to study these two-terminal devices in the high conductance regime. We observe the expected four-fold shell pattern together with Kondo physics at intermediate transparency Gless than or similar to2e(2)/h and a transition to the open regime in which the maximum conductance is doubled and bound by G(max)=4e(2)/h. In the high-G regime, at the transition from a quantum dot to a weak link, the CNT levels are strongly broadened. Nonetheless, sharp resonances appear superimposed on the background which varies slowly with gate voltage. The resonances are identified by their lineshape as Fano resonances. The origin of Fano resonances is discussed along the modeling.

  • Conductance properties of nanotubes coupled to superconducting leads: signatures of Andreev states dynamics
    E. Vecino, M. R. Buitelaar, A. Martı́n-Rodero, C. Schönenberger, and Levy A. Yeyati.
    Solid-State Communications 131, 625 (2004), 131:625-630, sep 2004. [DOI] arXiv:0406240

    We present a combined experimental and theoretical analysis of the low bias conductance properties of carbon nanotubes coupled to superconducting leads. In the Kondo regime, the conductance exhibits a zero bias peak which can be several times larger than the unitary limit in the normal case. This zero bias peak can be understood by analyzing the dynamics of the subgap Andreev states under an applied bias voltage. It is shown that the existence of a linear regime is linked to the presence of a finite relaxation rate within the system. The theory provides a good fitting of the experimental results.

  • Quantum dot coupled to a normal and a superconducting lead
    M. R. Gräber, T. Nussbaumer, W. Belzig, and C. Schönenberger.
    Nanotechnology, 15:S479-S482, may 2004. [DOI]

    We report on electrical transport measurements in a carbon nanotube quantum dot coupled to a normal and a superconducting lead. Depending on the ratio of Kondo temperature T-K and superconducting gap Delta, the zero bias conductance resonance either is split into two side-peaks or persists. We also compare our data with a simple model of a resonant level-superconductor interface.


  • Sensitivity of single multiwalled carbon nanotubes to the environment
    M. Krüger, I. Widmer, T. Nussbaumer, M. Buitelaar, and C. Schönenberger.
    New Journal of Physics, 5:138.1-138.11, oct 2003. [DOI]

    We report on electrical resistance measurements of single multiwalled carbon nanotubes (MWNTs) in different environments (ambient air, H2, O2 and the electrolytes LiClO4, KCl, KMnO4 and H3PO3). The gate dependence is studied using back-gating, electrochemical gating and gates evaporated directly onto the nanotubes (NTs). MWNTs at room temperature are p-doped. Upon changing the environment a change of the doping state of the MWNTs is inferred from the linear resistance. The effect of the environment on the contacts is negligible in our experiments. The p-doping is proposed to originate from the specific adsorption of an oriented dipole layer of water on the nanotube, which is affected by the kind of ions.

  • Intrinsic thermal vibrations of suspended doubly clamped singe-wall carbon nanotubes
    B. Babić, J. Furer, S. Sahoo, S. Farhangfar, and C. Schönenberger.
    Nano Letters, 3:1577, sep 2003. [DOI]

    We report the observation of thermally driven mechanical vibrations of suspended doubly clamped carbon nanotubes, grown by chemical vapor deposition (CVD). Several experimental procedures are used to suspend carbon nanotubes. The vibration is observed as a blurring in images taken with a scanning electron microscope. The measured vibration amplitudes are compared with a model based on linear continuum mechanics.

  • Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot
    M. R. Buitelaar, W. Belzig, T. Nussbaumer, B. Babić, B. Bruder, and C. Schönenberger.
    Phys. Rev. Lett., 91:57005, Aug 2003. [DOI] arXiv:0304233

    We report resonant multiple Andreev reflections in a multiwall carbon nanotube quantum dot coupled to superconducting leads. The position and magnitude of the subharmonic gap structure is found to depend strongly on the level positions of the single-electron states which are adjusted with a gate electrode. We discuss a theoretical model of the device and compare the calculated differential conductance with the experimental data.

  • Ambipolar field-effect transistor on as-grown single-wall carbon nanotube
    B. Babić, M. Iqbal, and C. Schönenberger.
    Nanotechnology, 14:327-331, jan 2003. [DOI]

    We use a simultaneous flow of ethylene and hydrogen gases to grow single-wall carbon nanotubes by chemical vapour deposition. Strong coupling to the gate is inferred from transport measurements for both metallic and semiconducting tubes. At low temperatures, our samples act as single-electron transistors where the transport mechanism is mainly governed by Coulomb blockade. The measurements reveal very rich quantized energy level spectra spanning from the valence to the conduction band. The Coulomb diamonds have similar addition energies on both sides of the semiconducting gap. Signatures of the subband population have been observed at intermediate temperature.


  • Quantum Dot in the Kondo Regime Coupled to Superconductors
    M. R. Buitelaar, T. Nussbaumer, and C. Schönenberger.
    Phys. Rev. Lett., 89(25):256801, dec 2002. [DOI] arXiv:0209048

    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.

  • Multi-wall carbon nanotubes as quantum dots
    M. R. Buitelaar, A. Bachtold, T. Nussbaumer, M. Iqbal, and C. Schönenberger.
    Phys. Rev. Lett., 88(15):156801, apr 2002. [DOI] arXiv:0110074

    We have measured the differential conductance dI/dV of individual multi-wall carbon nanotubes (MWNT) of different lengths. A cross-over from wire-like (long tubes) to dot-like (short tubes) behavior is observed. dI/dV is dominated by random conductance fluctuations (UCF) in long MWNT devices (L=2…7 μm), while Coulomb blockade and energy level quantization are observed in short ones (L=300 nm). The electron levels of short MWNT dots are nearly four-fold degenerate (including spin) and their evolution in magnetic field (Zeeman splitting) agrees with a g-factor of 2. In zero magnetic field the sequential filling of states evolves with spin S according to S=0 -> 1/2 -> 0… In addition, a Kondo enhancement of the conductance is observed when the number of electrons on the tube is odd.


  • Suppression of tunneling into multi-walled carbon nanotubes
    M. Bachtold, M. de Jonge, K. Grove-Rasmussen, P. L. McEuen, M. Buitelaar, and C.~Schönenberger.
    Phys. Rev. Lett., 87(16):166801, oct 2001. [DOI] arXiv:0012262

    We have studied tunneling of electrons into multi-wall carbon nanotubes. Nanotube/electrode interfaces with low transparency as well as nanotube/nanotube junctions created with atomic force microscope manipulation have been used. The tunneling conductance goes to zero as the temperature and bias are reduced, and the functional form is consistent with a power law suppression of tunneling as a function of energy. The exponent depends upon sample geometry. The relationship between these results and theories for tunneling into ballistic and disordered metals is discussed.

  • Electrochemical carbon nanotube field-effect transistor
    M. Krüger, M. Buitelaar, T. Nussbaumer, C.~Schönenberger, and L. Forró.
    App. Phys. Lett., 78(9):1291-1293, feb 2001. [DOI] arXiv:0009171

    We explore the electric-field effect of carbon nanotubes (NTs) in electrolytes. Due to the large gate capacitance, Fermi energy (EF)(EF) shifts of order ±1 V can be induced, enabling to tune NTs from p to n-type. Consequently, large resistance changes are measured. At zero gate voltage, the NTs are hole-doped in air with |EF|≈0.3–0.5 eV,|EF|≈0.3–0.5 eV, corresponding to a doping level of ≈10 13 cm−2.≈10 13 cm−2. Hole-doping increases in the electrolyte.

  • Carbon nanotubes, materials for the future
    L. Forró and C.~Schönenberger.
    Europhysics news, 32(3):86-90, May/June 2001.


  • Interference and interactions in multiwall nanotubes
    C.~Strunk, A.~Bachtold, T.~Nussbaumer, and C.~Schönenberger.
    Physica B, 280(1-4):384-385, sep 2000. [DOI]

    We report equilibrium electric resistance R and tunneling spectroscopy (dI/dV)measurements obtained on single multi-wall nanotubes contacted by four metallic Au fingers from above. At low temperature quantum interference phenomena dominate the magnetoresistance. The phase-coherence (lφ)and elastic-scattering lengths (le)are deduced. Because le is of order of the circumference of the nanotubes, transport is quasi-ballistic. This result is supported by a dI/dV spectrum which is in good agreement with the density of states (DOS) due to the one-dimensional subbands expected for a perfect single-wall tube. As a function of temperature T the resistance increases on decreasing T and saturates at ≈1–10 Kfor all measured nanotubes. R(T) cannot be related to the energy-dependent DOS of graphene but is mainly caused by interaction and interference effects. On a relatively small voltage scale of the order ≈10 meV, a pseudogap is observed in dI/dV which agrees with Luttinger-liquid theories for nanotubes. Because we have used quantum diffusion based on Fermi-liquid as well as Luttinger-liquid theory in trying to understand our results, a large fraction of this paper is devoted to a careful discussion of all our results.

  • Physics of Multiwall-Carbon Nanotubes
    C. Schönenberger and L. Forró.
    Physics World, 13(6):37-41, June 2000.


  • Interference and Interaction in multi-wall carbon nanotubes
    C. Schönenberger, A. Bachtold, C. Strunk, J. -P. Salvetat, and L. Forró.
    Appl. Phys. A, 69:283-295, sep 1999. [DOI]

    We report equilibrium electric resistance R and tunneling spectroscopy (dI/dV)measurements obtained on single multi-wall nanotubes contacted by four metallic Au fingers from above. At low temperature quantum interference phenomena dominate the magnetoresistance. The phase-coherence (lφ)and elastic-scattering lengths (le)are deduced. Because le is of order of the circumference of the nanotubes, transport is quasi-ballistic. This result is supported by a dI/dV spectrum which is in good agreement with the density of states (DOS) due to the one-dimensional subbands expected for a perfect single-wall tube. As a function of temperature T the resistance increases on decreasing T and saturates at ≈1–10 Kfor all measured nanotubes. R(T) cannot be related to the energy-dependent DOS of graphene but is mainly caused by interaction and interference effects. On a relatively small voltage scale of the order ≈10 meV, a pseudogap is observed in dI/dV which agrees with Luttinger-liquid theories for nanotubes. Because we have used quantum diffusion based on Fermi-liquid as well as Luttinger-liquid theory in trying to understand our results, a large fraction of this paper is devoted to a careful discussion of all our results.

  • Aharonov-Bohm Oscillations in Carbon Nanotubes
    A. Bachtold, C. Strunk, J. -P. Salvetat, J. -M. Bonard, L. Forró, T. Nussbaumer, and C. Schönenberger.
    Nature, 397:673, feb 1999. [DOI]

    When electrons pass through a cylindrical electrical conductor aligned in a magnetic field, their wave-like nature manifests itself as a periodic oscillation in the electrical resistance as a function of the enclosed magnetic flux1. This phenomenon reflects the dependence of the phase of the electron wave on the magnetic field, known as the Aharonov–Bohm effect2, which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. Such oscillations have been observed in micrometre-sized thin-walled metallic cylinders3, 4, 5 and lithographically fabricated rings6, 7, 8. Carbon nanotubes9, 10 are composed of individual graphene sheets rolled into seamless hollow cylinders with diameters ranging from 1 nm to about 20 nm. They are able to act as conducting molecular wires11, 12, 13, 14, 15, 16, 17, 18, making them ideally suited for the investigation of quantum interference at the single-molecule level caused by the Aharonov–Bohm effect. Here we report magnetoresistance measurements on individual multi-walled nanotubes, which display pronounced resistance oscillations as a function of magnetic flux.We find that the oscillations are in good agreement with theoretical predictions for the Aharonov–Bohm effect in a hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. In some nanotubes we also observe shorter-period oscillations, which might result from anisotropic electron currents caused by defects in the nanotube lattice.


  • Contacting Carbon-Nanotubes selectively with Low-Ohmic Contacts for Four-Probe Electric Measurements
    A. Bachtold, J. -P. Salvetat, J. -M. Bonard, M. Henny, C. Terrier, C. Strunk, L. Forró, and C. Schönenberger.
    Appl. Phys. Lett., 73:274-276, jul 1998. [DOI]

    Contact resistances of multiwalled nanotubes deposited on gold contact fingers are very large. We show that the contact resistances decrease by orders of magnitudes when the contact areas are selectively exposed to the electron beam in a scanning electron microscope. The focused electron beam enables the selection of one particular nanotube for electrical measurement in a four-terminal configuration, even if a loose network of nanotubes is deposited on the gold electrodes. For all measured nanotubes, resistance values lie in a narrow range of 0.35–2.6 kΩ at room temperature.