We study the few-electron eigenspectrum of a nanotube quantum dot with spin-orbit coupling. The two-electron phase diagram as a function of the length of the dot and the applied parallel magnetic field shows clear signatures of both spin-orbit coupling and electron-electron interaction. Below a certain critical length, ground state transitions are correctly predicted by a single-particle picture and are mainly independent of the length of the dot despite the presence of strong correlations. However, for longer quantum dots the critical magnetic field strongly decreases with increasing length, which is a pure interaction effect. In fact, the new ground state is spin- and valley-polarized, which implies a strong occupation of higher longitudinal modes.
We will study the competitive effect between the transport of a quantum dot adsorbed to a ballistic channel and laterally coupled to a single-walled carbon nanotube (SWNT). We will use the tight-binding approach to analytically write the SWNT Green function and the quantum dot will be solved by the atomic method for U very large. We will present curves of the electronic density of states for some different sizes of nanotubes. The results for the conductance curves will be presented as a function of Ef and for different values of n and hopping between the nanotube and the quantum dot.
We have characterized a new Magnetic Force Microscopy (MFM) probe based on an iron filled carbon nanotube (FeCNT) using MFM imaging on permalloy (Py) disks saturated in a high magnetic field perpendicular to the disk plane. The experimental data are accurately modeled by describing the FeCNT probe as having a single magnetic monopole at its tip whose effective magnetic charge is determined by the diameter of the iron wire enclosed in the carbon nanotube and its saturation magnetization 4 πM_s ~ 2.2 x 10^4 G. A magnetic monopole probe enables quantitative measurements of the magnetic field grad…
We perform scanning gate microscopy on individual suspended carbon nanotube quantum dots. The size and position of the quantum dots can be visually identified from the concentric high conductance rings. For the ultra clean devices used in this study, two new effects are clearly identified. Electrostatic screening creates non-overlapping multiple sets of Coulomb rings from a single quantum dot. In double quantum dots, by changing the tip voltage, the interactions between the quantum dots can be tuned from the weak to strong coupling regime.
We systematically study the coupling of longitudinal modes (shells) in a carbon nanotube quantum dot. Inelastic cotunneling spectroscopy is used to probe the excitation spectrum in parallel, perpendicular and rotating magnetic fields. The data is compared to a theoretical model including coupling between shells, induced by atomically sharp disorder in the nanotube. The calculated excitation spectra show good correspondence with experimental data.
We propose a simple approach to construct a quantum-dot and it's electrodes using chiral metallic single walled carbon nanotube (CM-SWCNT) segments of exactly opposite chiralities $(m,n)$ and $(n,m)$. The degree and energetics of electron confinement crucially depends on the choice of $n$ and $m$, and collinearity of the SWCNT segments constituting the quantum-dot and the electrodes. All the segments can in principle be obtained through simple manipulations of fragments of a single nanotube of chirality either $(m,n)$ or $(n,m)$.
We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate th…
We propose a scheme for coherent rotation of the valley isospin of a single electron confined in a carbon nanotube quantum dot. The scheme exploits the ubiquitous atomic disorder of the nanotube crystal lattice, which induces time-dependent valley mixing as the confined electron is pushed back and forth along the nanotube axis by an applied ac electric field. Using experimentally determined values for the disorder strength we estimate that valley Rabi oscillations with a period on the nanosecond timescale are feasible. The valley resonance effect can be detected in the electric current through…
We demonstrate gate control of the electronic g-tensor in single and double quantum dots formed along a bend in a carbon nanotube. From the dependence of the single-dot excitation spectrum on magnetic field magnitude and direction, we extract spin-orbit coupling, valley coupling, spin and orbital magnetic moments. Gate control of the g-tensor is measured using the splitting of the Kondo peak in conductance as a sensitive probe of Zeeman energy. In the double quantum dot regime, the magnetic field dependence of the position of cotunneling lines in the two dimensional charge stability diagram is…
We report optical studies of quantum dot excitons in individual suspended carbon nanotubes at cryogenic temperatures. Narrow optical linewidths, strongly suppressed spectral wandering, and photoluminescence lifetimes in the range of nanoseconds emerge as key signatures of exciton localization. We infer exciton quantum dot formation with a characteristic length of a few exciton Bohr radii. Localization inhibits exciton diffusion and protects the exciton from dephasing by structural or environmental inhomogeneities as well as from exploring nonradiative quenching sites. In consequence, quantum d…
Quantum dots defined in carbon nanotubes are a platform for both basic scientific studies and research into new device applications. In particular, they have unique properties that make them attractive for studying the coherent properties of single electron spins. To perform such experiments it is necessary to confine a single electron in a quantum dot with highly tunable barriers, but disorder has until now prevented tunable nanotube-based quantum-dot devices from reaching the single-electron regime. Here, we use local gate voltages applied to an ultra-clean suspended nanotube to confine a si…
We investigate the electronic transport through a suspended carbon-nanotube quantum dot. In the presence of a magnetic field perpendicular to the nanotube and a nearby metallic gate, two forces act on the electrons: the Laplace and the electrostatic force. They both induce coupling between the electrons and the mechanical transverse oscillation modes. We find that the difference between the two mechanisms appears in the cotunneling current.
Spin qubits defined in carbon nanotube quantum dots are of considerable interest for encoding and manipulating quantum information because of the long electron spin coherence times expected. However, before carbon nanotubes can find applications in quantum information processing schemes, we need to understand and control the coupling between individual electron spins and the interaction between the electron spins and their environment. Here we make use of spin selection rules to directly measure - and demonstrate control of - the singlet-triplet exchange coupling between two carbon nanotube qu…
We demonstrate single-electron pumping in a gate-defined carbon nanotube double quantum dot. By periodic modulation of the potentials of the two quantum dots we move the system around charge triple points and transport exactly one electron or hole per cycle. We investigate the pumping as a function of the modulation frequency and amplitude and observe good current quantization up to frequencies of 18 MHz where rectification effects cause the mechanism to break down.
We investigate radio-frequency (rf) reflectometry in a tunable carbon nanotube double quantum dot coupled to a resonant circuit. By measuring the in-phase and quadrature components of the reflected rf signal, we are able to determine the complex admittance of the double quantum dot as a function of the energies of the single-electron states. The measurements are found to be in good agreement with a theoretical model of the device in the incoherent limit. Besides being of fundamental interest, our results present an important step forward towards non-invasive charge and spin state readout in ca…
We report transport measurements on a quantum dot in a partly suspended carbon nanotube. Electrostatic tuning allows us to modify and even switch 'on' and 'off' the coupling to the quantized stretching vibration across several charge states. The magnetic-field dependence indicates that only the two-electron spin-triplet excited state couples to the mechanical motion, indicating mechanical coupling to both the valley degree of freedom and the exchange interaction, in contrast to standard models.
Electronic states and vibrons in carbon nanotube quantum dots have in general different location and size. As a consequence, the conventional Anderson-Holstein model, coupling vibrons to the dot total charge only, may no longer be appropriated in general. Here we explicitly address the role of the spatial fluctuations of the electronic density, yielding space-dependent Franck-Condon factors. We discuss the consequent marked effects on transport which are compatible with recent measurements. This picture can be relevant for tunneling experiments in generic nano-electromechanical systems.
We determine the level-shifts induced by cotunneling in a Coulomb blockaded carbon nanotube quantum dot using leading order quasi-degenerate perturbation theory within a single nanotube quartet. It is demonstrated that otherwise degenerate and equally tunnel-coupled $K$ and $K'$ states are mixed by cotunneling and therefore split up in energy except at the particle/hole-symmetric midpoints of the Coulomb diamonds. In the presence of an external magnetic field, we show that cotunneling induces a gate-dependent $g$-factor renormalization, and we outline different scenarios which might be observe…
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.
Controlling spin current and magnetic exchange coupling by applying an electric field and achieving high spin injection efficiency at the same time in a nanostructure coupled to ferromagnetic electrodes have been the outstanding challenges in nanoscale spintronics. A relentless quest is going on to find new low dimensional materials with tunable spin dependent properties to address these challenges. Herein, we predict, from first principles, the transverse electric field induced switching in the sign of exchange coupling and tunnel magnetoresistance in a boron nitride nanotube quantum dot atta…
We present measurements of tunneling magneto-resistance (TMR) in single-wall carbon nanotubes attached to ferromagnetic contacts in the Coulomb blockade regime. Strong variations of the TMR with gate voltage over a range of four conductance resonances, including a peculiar double-dip signature, are observed. The data is compared to calculations in the "dressed second order" (DSO) framework. In this non-perturbative theory, conductance peak positions and linewidths are affected by charge fluctuations incorporating the properties of the carbon nanotube quantum dot and the ferromagnetic leads. Th…
We report on the fabrication and characterization of all-carbon hybrid quantum devices based on graphene and single-walled carbon nanotubes. We discuss both, carbon nanotube quantum dot devices with graphene charge detectors and nanotube quantum dots with graphene leads. The devices are fabricated by chemical vapor deposition growth of carbon nanotubes and subsequent structuring of mechanically exfoliated graphene. We study the detection of individual charging events in the carbon nanotube quantum dot by a nearby graphene nanoribbon and show that they lead to changes of up to 20% of the conduc…
We consider the photon-assisted tunneling (PAT) and the Landau-Zener-Stueckelberg (LZS) interference for double quantum dots induced electrostatically along a semiconducting carbon nanotube. An atomistic tight-binding approach and the time-dependent configuration interaction method are employed for description of the systems of a few confined electrons and holes. We reproduce the patterns of the LZS interference recently observed for the quantum double dots describing transport across hole-localized states. Moreover, we indicate that for charge configurations for which the ground-state is Paul…
Motivated by recent experiments, we investigate the electron-vibron coupling in suspended carbon nanotube quantum dots, starting with the electron-phonon coupling of the underlying graphene layer. We show that the coupling strength depends sensitively on the type of vibron and is strongly sample dependent. The coupling strength becomes particularly strong when inhomogeneity-induced electronic quantum dots are located near regions where the vibronic mode is associated with large strain. Specifically, we find that the longitudinal stretching mode and the radial breathing mode are coupled via the…
Tunneling spectroscopy of a Nb coupled carbon nanotube quantum dot reveals the formation of pairs of Andreev bound states (ABS) within the superconducting gap. A weak replica of the lower ABS is found, which is generated by quasi-particle tunnelling from the ABS to the Al tunnel probe. An inversion of the ABS-dispersion is observed at elevated temperatures, which signals the thermal occupation of the upper ABS. Our experimental findings are well supported by model calculations based on the superconducting Anderson model.
Generating and detecting radiation in the technologically relevant range of the so-called terahertz gap ($0.1 - 10$ THz) is challenging because of a lack of efficient sources and detectors. Quantum dots in carbon nanotubes have shown great potential to build sensitive terahertz detectors usually based on photon-assisted tunnelling. A recently reported mechanism combining resonant quantum dot transitions and tunnelling barriers asymmetries results in a narrow linewidth photocurrent response with a large signal-to-noise ratio under weak THz radiation. That device was sensitive to one frequency, …
We report results on superconducting tunneling spectroscopy of a carbon nanotube quantum dot. Using a three-probe technique that includes a superconducting tunnel probe, we map out changes in conductance due to band structure, excited states, and end-to-end bias. The superconducting probe allows us to observe enhanced spectroscopic features, such as robust signals of both elastic and inelastic co-tunneling. We also see evidence of inelastic scattering processes inside the quantum dot.
We present a theoretical study of the Pauli or spin-valley blockade for double quantum dots in semiconducting carbon nanotubes. In our model we take into account the following characteristic features of carbon nanotubes: (i) fourfold (spin and valley) degeneracy of the quantum dot levels, (ii) the intrinsic spin-orbit interaction which is enhanced by the tube curvature, and (iii) valley-mixing due to short-range disorder, i.e., substitutional atoms, adatoms, etc. We find that the spin-valley blockade can be lifted in the presence of short-range disorder, which induces two independent random (i…
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 provide an atomistic tight-binding description of a few carriers confined in ambipolar (n-p) double quantum dots defined in a semiconducting carbon nanotube. We focus our attention on the charge state of the system in which Pauli blockade of the current flow is observed [F. Pei et al., Nat. Nanotechnol. 7, 630 (2012); E. A. Laird et al., ibid 8, 565 (2013)] with a single excess electron in the n-dot and a single hole in the p-dot. We use the configuration interaction approach to determine the spin-valley structure of the states near the neutrality point and discuss its consequences for the …
We develop a theory of inter-valley Coulomb scattering in semiconducting carbon-nanotube quantum dots, taking into account the effects of curvature and chirality. Starting from the effective-mass description of single-particle states, we study the two-electron system by fully including Coulomb interaction, spin-orbit coupling, and short-range disorder. We find that the energy level splittings associated with inter-valley scattering are nearly independent of the chiral angle and, while smaller than those due to spin-orbit interaction, large enough to be measurable.
We demonstrate experimentally that non-collinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near four-fold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilita…
Hyperfine interaction (HF) is of key importance for the functionality of solid-state quantum information processing, as it affects qubit coherence and enables nuclear-spin quantum memories. In this work, we complete the theory of the basic hyperfine interaction mechanisms (Fermi contact, dipolar, orbital) in carbon nanotube quantum dots by providing a theoretical description of the orbital HF. We find that orbital HF induces an interaction between the nuclear spins of the nanotube lattice and the valley degree of freedom of the electrons confined in the quantum dot. We show that the resulting …
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 suggest 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 an…
We analytically calculate the nuclear-spin interactions of a single electron confined to a carbon nanotube or graphene quantum dot. While the conduction-band states in graphene are p-type, the accordant states in a carbon nanotube are sp-hybridized due to curvature. This leads to an interesting interplay between isotropic and anisotropic hyperfine interactions. By using only analytical methods, we are able to show how the interaction strength depends on important physical parameters, such as curvature and isotope abundances. We show that for the investigated carbon structures, the 13C hyperfin…
