The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a nonGaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower. 72.20.Pa, 73.20.Dx, 05.45+b The electrical conductance of small -characteristic size much smaller than the electron mean free path -confined electron systems (usually denoted as quantum dots) shows distinct fluctuations. These fluctuations display correlations as a function of an external parameter such as shape or magnetic field, which can be described in a statistical manner. The electrons can, in fact, be viewed as billiard balls moving in a classically chaotic system where many random reflections at the system walls occur. Because of the wave-like nature of the electrons, quantum mechanics is needed to describe these systems fully. Chaos in quantum dots has been investigated [1][2][3] in conductance measurements but the analysis turns out to be difficult. So-called short trajectories [4] and weak localization effects [1,5] add up to the signature of chaotic motion. Moreover, current heating of the electrons in the dot appears to be unavoidable in conductance measurements. Electron heating effects in the dot smear out the underlying chaotic statistics and therefore the observed fluctuations exhibit mostly a Gaussian distribution, although theory predicts non-Gaussian distributions when a small number of electron modes is admitted to the dot [6]. Only when dephasing (modelled as extra modes coupling the dot to the environment) is included, Random Matrix Theory (RMT) [1,7] gives a Gaussian distribution. Very recently, Huibers et al. [8] observed small deviations from a Gaussian distribution in conductance measurements. However, other transport properties calculated from these data exhibit again Gaussian distributions in contrast to theoretical predictions.An alternative for the conductance measurements pursued so far (which inherently are accompanied by electron heating inside the dot) is to investigate the thermoelectric properties of a system. Thermopower measurements have already been used to study semiconductor nanostructures like quantum point-contacts [9] and quantum dots in the Coulomb blockade regime [10,11]. The thermopower S measures directly the parametric derivative of the conductance, S ∝ G −1 ∂G/∂X with X = E (energy), and thus yields both similar and additional information on the electron transport processes as can be obtained from conductance measurements. The distribution of parametric derivatives (X = E, B, shape, . . .) of the conductance of a quantum dot is the subject of recent 13]. The probability distribution for the thermopower is again expected to be non-Gaussian for chaotic conductors, exhibiting cusps at zero amplitude and non-exponential tails [13,14].In this paper, we present magneto-thermopower measurements of a statistical en...

Electron and hole Bloch states in bilayer graphene exhibit topological orbital magnetic moments with opposite signs, which allows for tunable valley-polarization in an out-of-plane magnetic field. This property makes electron and hole quantum dots (QDs) in bilayer graphene interesting for valley and spin-valley qubits. Here, we show measurements of the electron–hole crossover in a bilayer graphene QD, demonstrating opposite signs of the magnetic moments associated with the Berry curvature. Using three layers of top gates, we independently control the tunneling barriers while tuning the occupation from the few-hole regime to the few-electron regime, crossing the displacement-field-controlled band gap. The band gap is around 25 meV, while the charging energies of the electron and hole dots are between 3 and 5 meV. The extracted valley g -factor is around 17 and leads to opposite valley polarization for electrons and holes at moderate B -fields. Our measurements agree well with tight-binding calculations for our device.

We present transport measurements through an electrostatically defined bilayer graphene double quantum dot in the single electron regime. With the help of a back gate, two split gates and two finger gates we are able to control the number of charge carriers on two gate-defined quantum dot independently between zero and five. The high tunability of the device meets requirements to make such a device a suitable building block for spin-qubits. In the single electron regime, we determine interdot tunnel rates on the order of 2 GHz. Both, the interdot tunnel coupling, as well as the capacitive interdot coupling increase with dot occupation, leading to the transition to a single quantum dot. Finite bias magneto-spectroscopy measurements allow to resolve the excited state spectra of the first electrons in the double quantum dot; being in agreement with spin and valley conserving interdot tunneling processes.Electrostatically defined quantum dots (QDs) offer a compelling platform for spin-qubit-based quantum computation [1]. For that purpose, QDs in semiconductor heterostructures mainly based on GaAs [2, 3] and silicon [4,5] have been studied intensively. For example, high-fidelity single-qubit [6] and two-qubit [7-9] gate operations have been recently demonstrated for silicon qubit devices. Graphene has been early identified as an alternative attractive material platform for spin-qubits thanks to its low nuclear spin densities, weak hyperfine coupling and weak spinorbit interaction promising long spin decoherence times [10]. Physically etched graphene quantum devices including quantum dots [11,12] and double quantum dots (DQDs) [13,14] have been studied for about a decade. Major achievements include the implementation of charge detection [15,16], the observation of spin-states [12] and the measurement of charge relaxation times [17]. However, the influence of disorder, in particular edge disorder [18,19], prevented a precise control of the number of charge carriers on individual QDs making spin-qubit implementation impossible.The advancements in ultra-clean van der Waals heterostructures and in particular the use of local graphite gates allowed for the development of electrostatically defined bilayer graphene (BLG) quantum point contacts [20-23], quantum dots [24-26] and double quantum dots (DQDs) [27,28]. While single-electron and hole occupation has been demonstrated recently for individual QDs [24], the number of charge carriers in DQDs could not be controlled yet [27,28]. The precise control of the number of charge carriers is, however, a requirement for qubit operations in a semiconductor QD device.Here, we show single electron occupation of a bilayer graphene DQD. The electrostatically defined DQD allows for a high tunability of the electrochemical potential such that we can precisely control the number of electrons on * These authors contributed equally to this work. a Corresponding author: luca.banszerus@rwth-aachen.de each of the QDs independently down to zero. The gate voltages tune the interdot tunnel couplin...

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Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the $$K$$ K and $$K^{\prime}$$ K ′ states below 20 μeV.

We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of six orbital symmetric and ten orbital antisymmetric states. We find that orbital symmetric states are lower in energy and separated by ≈ 0.4-0.8 meV from orbital antisymmetric states. The symmetric multiplet exhibits an additional energy splitting of its six states of ≈ 0.15-0.5 meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that intervalley scattering and "current-current" interaction constants are of the same magnitude in BLG.

We present a highly controllable double quantum dot device based on bilayer graphene. Using a device architecture of interdigitated gate fingers, we can control the interdot tunnel coupling between 1 and 4 GHz and the mutual capacitive coupling between 0.2 and 0.6 meV, independent of the charge occupation of the quantum dots. The charging energy and, hence, the dot size remain nearly unchanged. The tuning range of the tunnel coupling covers the operating regime of typical silicon and GaAs spin qubit devices.

The relaxation time of a single-electron spin is an important parameter for solid-state spin qubits, as it directly limits the lifetime of the encoded information. Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture, while the relaxation dynamics have remained mostly unexplored. Here, we report spin relaxation times (T1) of single-electron states in BLG QDs. Using pulsed-gate spectroscopy, we extract relaxation times exceeding 200 μs at a magnetic field of 1.9 T. The T1 values show a strong dependence on the spin splitting, promising even longer T1 at lower magnetic fields, where our measurements are limited by the signal-to-noise ratio. The relaxation times are more than two orders of magnitude larger than those previously reported for carbon-based QDs, suggesting that graphene is a potentially promising host material for scalable spin qubits.