Carbon Nanotube Double Quantum Dot Research Articles

Resonator-induced quantum phase transitions in a hybrid Josephson junction

We investigate the Josephson current through a suspended carbon nanotube double quantum dot which, at sufficiently low temperatures, is characterized by the ground state of the electronic subsystem. Depending on parameters like a magnetic field or the inter-dot coupling, the ground state can either be a current-carrying singlet or doublet, or a blockaded triplet state. Since the electron-vibration interaction has been demonstrated to be electrostatically tuneable, we study in particular its effect on the current-phase relation. We show that the coupling to the vibration mode can lift the current-suppressing triplet blockade by inducing a quantum phase transition to a ground state of a different total spin. Our key finding is the development of a triple point in the Josephson current parameterized by the resonator coupling and the Josephson phase. The quantum phase transitions around the triple point are directly accessible through the critical current and resilient to moderately finite temperatures. The proposed setup makes the mechanical degree of freedom part of a superconducting hybrid device which is interesting for ultra-sensitive displacement detectors.

Nanotube double quantum dot spin transducer for scalable quantum information processing

One of the key challenges for the implementation of scalable quantum information processing is the design of scalable architectures that support coherent interaction and entanglement generation between distant quantum systems. We propose a nanotube double quantum dot spin transducer that allows to achieve steady-state entanglement between nitrogen-vacancy center spins in diamond with spatial separations up to micrometers. The distant spin entanglement further enables us to design a scalable architecture for solid-state quantum information processing based on a hybrid platform consisting of nitrogen-vacancy centers and carbon-nanotube double quantum dots.

Nanoscale Magnetic Resonance Spectroscopy Using a Carbon Nanotube Double Quantum Dot

Quantum sensing exploits fundamental features of quantum mechanics and quantum control to realise sensing devices with potential applications in a broad range of scientific fields ranging from basic science to applied technology. The ultimate goal are devices that combine unprecedented sensitivity with excellent spatial resolution. Here, we propose a new platform for all-electric nanoscale quantum sensing based on a carbon nanotube double quantum dot. Our analysis demonstrates that the platform can achieve sensitivities that allow for the implementation of single-molecule magnetic resonance spectroscopy and therefore opens a promising route towards integrated on-chip quantum sensing devices.

Spin-valley resolved photon-assisted tunneling in carbon nanotube double quantum dots

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 Pauli blocked PAT can be used for resolution of the transitions that involve spin-flip or intervalley transitions without the spin-valley conserving background signal.

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube.

The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via the leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.

Vibrational effects in charge transport through a molecular double quantum dot

Recent progress in the field of molecular electronics has revealed the fundamental importance of the coupling between the electronic degrees of freedom and specific vibrational modes. Considering the examples of a molecular dimer and a carbon nanotube double quantum dot, we here theoretically investigate transport through a two-site system that is strongly coupled to a single vibrational mode. Using a quantum master equation approach, we demonstrate that, depending on the relative positions of the two dots, electron-phonon interactions can lead to negative differential conductance and suppression of the current through the system. We also discuss the experimental relevance of the presented results and possible implementations of the studied system.

Full characterization of a carbon nanotube parallel double quantum dot

AbstractWe 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 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.

Photon-assisted tunneling and charge dephasing in a carbon nanotube double quantum dot

We report microwave-driven photon-assisted tunneling in a suspended carbon nanotube double quantum dot. From the resonant linewidth at a temperature of 13 mK, the charge dephasing time is determined to be 280 +- 30 ps. The linewidth is independent of driving frequency, but increases with increasing temperature. The moderate temperature dependence is inconsistent with expectations from electron-phonon coupling alone, but consistent with charge noise arising in the device. The extracted level of charge noise is comparable with that expected from previous measurements of a valley-spin qubit, where it was hypothesized to be the main cause of qubit decoherence. Our results suggest a possible route towards improved valley-spin qubits.

Interdot Coulomb correlation effects and spin-orbit coupling in two carbon nanotube quantum dots

Transport properties of the two-level Kondo effect involving spin, orbital, and pseudospin degrees of freedom are examined in a parallel carbon nanotube double quantum dot with a sufficient interdot Coulomb interaction and small interdot tunneling. The interdot Coulomb correlation effects are taken into account, and it plays an important role in forming bonding and antibonding states. Attached to ferromagnetic leads, the Kondo effect is observed at the interdot Coulomb blockade region with degeneracy of spin, orbital, and pseudospin degrees of freedom. A crossover from a two-level Kondo state involving the fivefold degeneracy of the double quantum dots to an SU(4) spin-orbit Kondo state and to an SU(2) spin-Kondo effect is demonstrated. At finite magnetic field, the splitting of the spin, orbital, and pseudospin Kondo resonance can be restored. For finite intradot Coulomb interaction U, there is a competition between the single-dot Kondo effect and the antiferromagnetic exchange coupling JAFM, resulting in the suppression of the Kondo resonance. Moreover, both the JAFM and the Zeeman interactions compete, leading to need a much higher value of the magnetic field to compensate for the Kondo splitting.

Tunable Kondo Physics in a Carbon Nanotube Double Quantum Dot

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.

Quantized charge pumping through a carbon nanotube double quantum dot

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.

Measuring the Complex Admittance of a Carbon Nanotube Double Quantum Dot

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. In addition to being of fundamental interest, our results present an important step forward towards noninvasive charge and spin state readout in carbon nanotube quantum dots.

Dephasing and hyperfine interaction in carbon nanotube double quantum dots: The clean limit

We consider theoretically ${}^{13}$C-hyperfine interaction induced dephasing in carbon nanotubes double quantum dots with curvature induced spin-orbit coupling. For two electrons initially occupying a single dot, we calculate the average return probability after separation into the two dots, which have random nuclear-spin configurations. We focus on the long time saturation value of the return probability, $P_\infty$. Because of the valley degree of freedom, the analysis is more complex than in, for example, GaAs quantum dots, which have two distinct $P_\infty$ values depending on the magnetic field. Here the prepared state and the measured state is non-unique because two electrons in the same dot are allowed in six different states. Moreover, for one electron in each dot sixteen states exist and therefore are available for being mixed by the hyperfine field. The return probability experiment is found to be strongly dependent on the prepared state, on the external magnetic field---both Zeeman and orbital effects - and on the spin-orbit splitting. The lowest saturation value, being $P_\infty$=1/3, occurs at zero magnetic field for nanotubes with spin-orbit coupling and the initial state being the groundstate, this situation is equivalent to double dots without the valley degree of freedom. In total, we report nine dynamically different situations that give $P_\infty$=1/3, 3/8, 2/5, 1/2 and for valley anti-symmetric prepared states in an axial magnetic field, $P_\infty$=1. When the groundstate is prepared the ratio between the spin-orbit splitting and the Zeeman energy due to a perpendicular magnetic field can tune the effective hyperfine field continuously from being three dimensional to two dimensional giving saturation values from $P_\infty$=1/3 to 3/8.

Transport Spectroscopy of an Impurity Spin in a Carbon Nanotube Double Quantum Dot

We make use of spin selection rules to investigate the electron spin system of a carbon nanotube double quantum dot. Measurements of the electron transport as a function of the magnetic field and energy detuning between the quantum dots reveal an intricate pattern of the spin state evolution. We demonstrate that the complete set of measurements can be understood by taking into account the interplay between spin-orbit interaction and a single impurity spin coupled to the double dot. The detection and tunability of this coupling are important for quantum manipulation in carbon nanotubes.

Double quantum dots in carbon nanotubes

We study the two-electron eigenspectrum of a carbon-nanotube double quantum dot with spin-orbit coupling. Exact calculation are combined with a simple model to provide an intuitive and accurate description of single-particle and interaction effects. For symmetric dots and weak magnetic fields, the two-electron ground state is antisymmetric in the spin-valley degree of freedom and is not a pure spin-singlet state. When double occupation of one dot is favored by increasing the detuning between the dots, the Coulomb interaction causes strong correlation effects realized by higher orbital-level mixing. Changes in the double-dot configuration affect the relative strength of the electron-electron interactions and can lead to different ground state transitions. In particular, they can favor a ferromagnetic ground state both in spin and valley degrees of freedom. The strong suppression of the energy gap can cause the disappearance of the Pauli blockade in transport experiments and thereby can also limit the stability of spin-qubits in quantum information proposals. Our analysis is generalized to an array of coupled dots which is expected to exhibit rich many-body behavior.

Pauli spin blockade in carbon nanotube double quantum dots

We report Pauli spin blockade in a carbon nanotube double quantum dot defined by tunnel barriers at the contacts and a structural defect in the nanotube. We observe a pronounced current suppression for negative source-drain bias voltages, which is investigated for both symmetric and asymmetric coupling of the quantum dots to the leads. The measured differential conductance agrees well with a theoretical model of a double quantum dot system in the spin-blockade regime, which allows us to estimate the occupation probabilities of the relevant singlet and triplet states. This work shows that effective spin-to-charge conversion in nanotube quantum dots is feasible and opens the possibility of single-spin readout in a material that is not limited by hyperfine interaction with nuclear spins.

Singlet–triplet physics and shell filling in carbon nanotube double quantum dots

Carbon nanotube double quantum dots, whose shell-like electronic structure is reminiscent of that of a simple molecule, provide a useful system to study the interaction of just a few electrons at a time.

Mapping electron delocalization by charge transport spectroscopy in an artificial molecule*

AbstractIn 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.

Quantum dots in carbon nanotubes

In this overview paper, we present low-temperature electronic transport measurements of carbon nanotube quantum dots with a back gate. In a semiconducting tube, charge carriers could be completely depleted. The addition energy and the excitation spectrum have been studied as a function of the number of charges (electrons or holes), one by one. We observe electron–hole symmetry, which is a direct consequence of the symmetric band structure of the nanotube. The excitation spectrum for metallic nanotubes exhibits four-fold shell filling and is completely described by an extended constant-interaction model. Furthermore, nanotubes with a four-fold shell structure are investigated in a parallel magnetic field. The magnetic field induces a large splitting between the two orbital states of each shell, demonstrating their opposite magnetic moment and determining transitions in the spin and orbital configuration of the quantum dot ground state. Also, a small coupling is found between orbitals with opposite magnetic moments leading to anti-crossing behaviour at zero field. Current–voltage characteristics of suspended carbon nanotube quantum dots show an additional series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Finally, we report on a fully tunable carbon nanotube double quantum dot. We perform inelastic transport spectroscopy via the excited states in the double quantum dot, a necessary step towards the implementation of new microwave-based experiments for quantum information technology.

Excited State Spectroscopy in Carbon Nanotube Double Quantum Dots

We report on low-temperature measurements in a fully tunable carbon nanotube double quantum dot. A new fabrication technique has been used for the top-gates in order to avoid covering the whole nanotube with an oxide layer as in previous experiments. The top-gates allow us to form single dots and control the coupling between them, and we observe 4-fold shell filling. We perform inelastic transport spectroscopy via the excited states in the double quantum dot, a necessary step toward the implementation of new microwave-based experiments.