Pauli Blockade of Tunable Two-Electron Spin and Valley States in Graphene Quantum Dots.

Pauli blockade mechanisms-whereby carrier transport through quantum dots (QD) is blocked due to selection rules even when energetically allowed-are a direct manifestation of the Pauli exclusion principle, as well as a key mechanism for manipulating and reading out spin qubits. The Pauli spin blockade is well established for systems such as GaAs QDs, but is to be further explored for systems with additional degrees of freedom, such as the valley quantum numbers in carbon-based materials or silicon. Here we report experiments on coupled bilayer graphene double quantum dots, in which the spin and valley states are precisely controlled, enabling the observation of the two-electron combined blockade physics. We demonstrate that the doubly occupied single dot switches between two different ground states with gate and magnetic-field tuning, allowing for the switching of selection rules: with a spin-triplet-valley-singlet ground state, valley blockade is observed; and with the spin-singlet-valley-triplet ground state, robust spin blockade is shown.

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots.

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor gv, defined analogously to the spin g-factor gs for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger gv results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Coherent Jetting from a Gate-Defined Channel in Bilayer Graphene.

Graphene has evolved as a platform for quantum transport that can compete with the best and cleanest semiconductor systems. Here, we report on the observation of distinct electronic jets emanating from a narrow split-gate-defined channel in bilayer graphene. We find that these jets, which are visible via their interference patterns, occur predominantly with an angle of 60° between each other. This observation is related to the trigonal warping in the band structure of bilayer graphene, which, in conjunction with electron injection through a constriction, leads to a valley-dependent selection of momenta. This experimental observation of electron jetting has consequences for carrier transport in two-dimensional materials with a trigonally warped band structure in general, as well as for devices relying on ballistic and valley-selective transport.

Real-Time Detection of Single Auger Recombination Events in a Self-Assembled Quantum Dot.

Auger recombination is a nonradiative process, where the recombination energy of an electron-hole pair is transferred to a third charge carrier. It is a common effect in colloidal quantum dots that quenches the radiative emission with an Auger recombination time below nanoseconds. In self-assembled QDs, the Auger recombination has been observed with a much longer recombination time on the order of microseconds. Here, we use two-color laser excitation on the exciton and trion transition in resonance fluorescence on a single self-assembled quantum dot to monitor in real-time single quantum events of the Auger process. Full counting statistics on the random telegraph signal give access to the cumulants and demonstrate the tunability of the Fano factor from a Poissonian to a sub-Poissonian distribution by Auger-mediated electron emission from the dot. Therefore, the Auger process can be used to tune optically the charge carrier occupation of the dot by the incident laser intensity, independently from the electron tunneling from the reservoir by the gate voltage. Our findings are not only highly relevant for the understanding of the Auger process but also demonstrate the perspective of the Auger effect for controlling precisely the charge state in a quantum system by optical means.

Combined Minivalley and Layer Control in Twisted Double Bilayer Graphene.

Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37°. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the carriers, formerly separated by their minivalley character, are mixed by tuning through a Lifshitz transition, where the Fermi surface topology changes. The high degree of control over the minivalley character of the bulk charge transport in twisted double bilayer graphene offers new opportunities for realizing valleytronics devices such as valley valves, filters, and logic gates.

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts.

In multivalley semiconductors, the valley degree of freedom can be potentially used to store, manipulate, and read quantum information, but its control remains challenging. The valleys in bilayer graphene can be addressed by a perpendicular magnetic field which couples by the valley g factor g_{v}. However, control over g_{v} has not been demonstrated yet. We experimentally determine the energy spectrum of a quantum point contact realized by a suitable gate geometry in bilayer graphene. Using finite bias spectroscopy, we measure the energy scales arising from the lateral confinement as well as the Zeeman splitting and find a spin g factor g_{s}∼2. g_{v} can be tuned by a factor of 3 using vertical electric fields, g_{v}∼40-120. The results are quantitatively explained by a calculation considering topological magnetic moment and its dependence on confinement and the vertical displacement field.

Photon Noise Suppression by a Built-in Feedback Loop.

Visionary quantum photonic networks need transform-limited single photons on demand. Resonance fluorescence on a quantum dot provides the access to a solid-state single photon source, where the environment is unfortunately the source of spin and charge noise that leads to fluctuations of the emission frequency and destroys the needed indistinguishability. We demonstrate a built-in stabilization approach for the photon stream, which relies solely on charge carrier dynamics of a two-dimensional hole gas inside a micropillar structure. The hole gas is fed by hole tunneling from field-ionized excitons and influences the energetic position of the excitonic transition by changing the local electric field at the position of the quantum dot. The standard deviation of the photon noise is suppressed by nearly 50% (noise power reduction of 6 dB) and it works in the developed micropillar structure for frequencies up to 1 kHz. This built-in feedback loop represents an easy way for photon noise suppression in large arrays of single photon emitters and promises to reach higher bandwidth by device optimization.

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields.

Crystal fields occur due to a potential difference between chemically different atomic species. In van der Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions, and elastic relaxations, but crystal fields have not received the attention they deserve. Here, we show that the band structure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic band gap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer [Formula: see text] = 0.13 V/nm ≈ [Formula: see text] = 0.12 V/nm. We show both by means of first-principles calculations and low energy models that crystal fields open a band gap in the ground state. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers.

Charge Detection in Gate-Defined Bilayer Graphene Quantum Dots.

We report on charge detection in electrostatically defined quantum dot devices in bilayer graphene using an integrated charge detector. The device is fabricated without any etching and features a graphite back gate, leading to high-quality quantum dots. The charge detector is based on a second quantum dot separated from the first dot by depletion underneath a 150 nm wide gate. We show that Coulomb resonances in the sensing dot are sensitive to individual charging events on the nearby quantum dot. The potential change due to single electron charging causes a steplike change (up to 77%) in the current through the charge detector. Furthermore, the charging states of a quantum dot with tunable tunneling barriers and of coupled quantum dots can be detected.

Large Multidirectional Spin-to-Charge Conversion in Low-Symmetry Semimetal MoTe2 at Room Temperature.

Efficient and versatile spin-to-charge current conversion is crucial for the development of spintronic applications, which strongly rely on the ability to electrically generate and detect spin currents. In this context, the spin Hall effect has been widely studied in heavy metals with strong spin-orbit coupling. While the high crystal symmetry in these materials limits the conversion to the orthogonal configuration, unusual configurations are expected in low-symmetry transition-metal dichalcogenide semimetals, which could add flexibility to the electrical injection and detection of pure spin currents. Here, we report the observation of spin-to-charge conversion in MoTe2 flakes, which are stacked in graphene lateral spin valves. We detect two distinct contributions arising from the conversion of two different spin orientations. In addition to the conventional conversion where the spin polarization is orthogonal to the charge current, we also detect a conversion where the spin polarization and the charge current are parallel. Both contributions, which could arise either from bulk spin Hall effect or surface Edelstein effect, show large efficiencies comparable to the best spin Hall metals and topological insulators. Our finding enables the simultaneous conversion of spin currents with any in-plane spin polarization in one single experimental configuration.

Coupled Quantum Dots in Bilayer Graphene.

Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge, or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile and widely tunable multiquantum dot system. We demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene, we have the possibility to form tunnel barriers using different mechanisms. We can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alternatively, we can use gates to form tunnel barriers, where we can vary the tunnel coupling by more than 2 orders of magnitude tuning between a deeply Coulomb blockaded system and a Fabry-Pérot-like cavity. Demonstrating such tunability is an important step toward graphene-based quantum computation.

Auger Recombination in Self-Assembled Quantum Dots: Quenching and Broadening of the Charged Exciton Transition.

In quantum dots (QDs), the Auger recombination is a nonradiative process in which the electron-hole recombination energy is transferred to an additional carrier. It has been studied mostly in colloidal QDs, where the Auger recombination time is in the picosecond range and efficiently quenches the light emission. In self-assembled QDs, on the other hand, the influence of Auger recombination on the optical properties is in general neglected, assuming that it is masked by other processes such as spin and charge fluctuations. Here, we use time-resolved resonance fluorescence to analyze the Auger recombination and its influence on the optical properties of a single self-assembled QD. From excitation-power-dependent measurements, we find a long Auger recombination time of about 500 ns and a quenching of the trion transition by about 80%. Furthermore, we observe a broadening of the trion transition line width by up to a factor of 2. With a model based on rate equations, we are able to identify the interplay between tunneling and Auger rate as the underlying mechanism for the reduced intensity and the broadening of the line width. This demonstrates that self-assembled QDs can serve as an ideal model system to study how the charge recapture process, given by the band-structure surrounding the confined carriers, influences the Auger process. Our findings are not only relevant for improving the emission properties of colloidal QD-based emitters and dyes, which have recently entered the consumer market, but also of interest for more visionary applications, such as quantum information technologies, based on self-assembled quantum dots.

Kondo effect and spin-orbit coupling in graphene quantum dots.

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin-orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin-orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin-orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin-orbit interaction.

Correlated electron-hole state in twisted double-bilayer graphene.

When twisted to angles near 1°, graphene multilayers provide a window on electron correlation physics. Here, we report the discovery of a correlated electron-hole state in double-bilayer graphene twisted to 2.37°. At this angle, the moiré states retain much of their isolated bilayer character, allowing their bilayer projections to be separately controlled by gates. We use this property to generate an energetic overlap between narrow isolated electron and hole bands with good nesting properties. Our measurements reveal the formation of ordered states with reconstructed Fermi surfaces, consistent with a density-wave state. This state can be tuned without introducing chemical dopants, enabling studies of correlated electron-hole states and their interplay with superconductivity.

The electronic thickness of graphene.

When two dimensional crystals are atomically close, their finite thickness becomes relevant. Using transport measurements, we investigate the electrostatics of two graphene layers, twisted by θ = 22° such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance C m and is therefore suited to extract C m. We explain the large observed value of C m by considering the finite dielectric thickness d g of each graphene layer and determine d g ≈ 2.6 Å. In a second experiment, we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi wavelength λ in each layer, showing that the layers are decoupled. Our findings are reproduced using tight-binding calculations.

Author Correction: Contrast of 83% in reflection measurements on a single quantum dot.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Contrast of 83% in reflection measurements on a single quantum dot.

We report on a high optical contrast between the photon emission from a single self-assembled quantum dot (QD) and the back-scattered excitation laser light. In an optimized semiconductor heterostructure with an epitaxially grown gate, an optically-matched layer structure and a distributed Bragg reflector, a record value of 83% is obtained; with tilted laser excitation even 885%. This enables measurements on a single dot without lock-in technique or suppression of the laser background by cross-polarization. These findings open up the possibility to perform simultaneously time-resolved and polarization-dependent resonant optical spectroscopy on a single quantum dot.