Particle-hole symmetry protects spin-valley blockade in graphene quantum dots.

Particle-hole symmetry plays an important role in the characterization of topological phases in solid-state systems1. It is found, for example, in free-fermion systems at half filling and it is closely related to the notion of antiparticles in relativistic field theories2. In the low-energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation3,4 in which topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries5,6. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase7 while preserving particle-hole symmetry. Here we show that bilayer graphene allows the realization of electron-hole double quantum dots that exhibit near-perfect particle-hole symmetry, in which transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that particle-hole symmetric spin and valley textures lead to a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge and valley-to-charge conversion, which are essential for the operation of spin and valley qubits.

Probing Two-Electron Multiplets in Bilayer Graphene Quantum Dots.

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.

Electron-Hole Crossover in Gate-Controlled Bilayer Graphene Quantum Dots.

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.

Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport.

We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80 µeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe a spin polarized channel of 6e^{2}/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.

Gate-Defined Electron-Hole Double Dots in Bilayer Graphene.

We present gate-controlled single-, double-, and triple-dot operation in electrostatically gapped bilayer graphene. Thanks to the recent advancements in sample fabrication, which include the encapsulation of bilayer graphene in hexagonal boron nitride and the use of graphite gates, it has become possible to electrostatically confine carriers in bilayer graphene and to completely pinch-off current through quantum dot devices. Here, we discuss the operation and characterization of electron-hole double dots. We show a remarkable degree of control of our device, which allows the implementation of two different gate-defined electron-hole double-dot systems with very similar energy scales. In the single-dot regime, we extract excited state energies and investigate their evolution in a parallel magnetic field, which is in agreement with a Zeeman-spin-splitting expected for a g-factor of 2.

Impact of Many-Body Effects on Landau Levels in Graphene.

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity v_{F}. In contrast to the logarithmic divergence of v_{F} at zero magnetic field, we find a piecewise linear scaling of v_{F} as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

Fabrication of comb-drive actuators for straining nanostructured suspended graphene.

We report on the fabrication and characterization of an optimized comb-drive actuator design for strain-dependent transport measurements on suspended graphene. We fabricate devices from highly p-doped silicon using deep reactive ion etching with a chromium mask. Crucially, we implement a gold layer to reduce the device resistance from ≈51.6 kΩ to ≈236 Ω at room temperature in order to allow for strain-dependent transport measurements. The graphene is integrated by mechanically transferring it directly onto the actuator using a polymethylmethacrylate membrane. Importantly, the integrated graphene can be nanostructured afterwards to optimize device functionality. The minimum feature size of the structured suspended graphene is 30 nm, which allows for interesting device concepts such as mechanically-tunable nanoconstrictions. Finally, we characterize the fabricated devices by measuring the Raman spectrum as well as the a mechanical resonance frequency of an integrated graphene sheet for different strain values.

High Quality Factor Graphene-Based Two-Dimensional Heterostructure Mechanical Resonator.

Ultralight mechanical resonators based on low-dimensional materials are well suited as exceptional transducers of minuscule forces or mass changes. However, the low dimensionality also provides a challenge to minimize resistive losses and heating. Here, we report on a novel approach that aims to combine different two-dimensional (2D) materials to tackle this challenge. We fabricated a heterostructure mechanical resonator consisting of few layers of niobium diselenide (NbSe2) encapsulated by two graphene sheets. The hybrid membrane shows high quality factors up to 245,000 at low temperatures, comparable to the best few-layer graphene mechanical resonators. In contrast to few-layer graphene resonators, the device shows reduced electrical losses attributed to the lower resistivity of the NbSe2 layer. The peculiar low-temperature dependence of the intrinsic quality factor points to dissipation over two-level systems which in turn relax over the electronic system. Our high sensitivity readout is enabled by coupling the membrane to a superconducting cavity which allows for the integration of the hybrid mechanical resonator as a sensitive and low loss transducer in future quantum circuits.

Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States.

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.

Limitations to carrier mobility and phase-coherent transport in bilayer graphene.

We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase-coherence times τϕ as well as the inter- and intravalley scattering times τi and τ*, respectively. While τϕ is in qualitative agreement with an electron-electron interaction-mediated dephasing mechanism, electron spin-flip scattering processes are limiting τϕ at low temperatures. The analysis of τi and τ* points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.

Low-frequency noise in individual carbon nanotube field-effect transistors with top, side and back gate configurations: effect of gamma irradiation.

We report on the influence of low gamma irradiation (10(4) Gy) on the noise properties of individual carbon nanotube (CNT) field-effect transistors (FETs) with different gate configurations and two different dielectric layers, SiO2 and Al2O3. Before treatment, strong generation-recombination (GR) noise components are observed. These data are used to identify several charge traps related to dielectric layers of the FETs by determining their activation energy. Investigation of samples with a single SiO2 dielectric layer as well as with two dielectric layers allows us to separate traps for each of the two dielectric layers. We reveal that each charge trap level observed in the side gate operation splits into two levels in top gate operation due to a different potential profile along the CNT channel. After gamma irradiation, only reduced flicker noise is registered in the noise spectra, which indicates a decrease of the number of charge traps. The mobility, which is estimated to be larger than 2 × 10(4) cm(2) V(-1) s(-1) at room temperature, decreases only slightly after radiation treatment, demonstrating high radiation hardness of the CNTs. Finally, we study the influence of Schottky barriers at the metal-nanotube interface on the transport properties of FETs, analyzing the behavior of the flicker noise component.

Graphene-based charge sensors.

We discuss graphene nanoribbon-based charge sensors and focus on their functionality in the presence of external magnetic fields and high frequency pulses applied to a nearby gate electrode. The charge detectors work well with in-plane magnetic fields of up to 7 T and pulse frequencies of up to 20 MHz. By analyzing the step height in the charge detector's current at individual charging events in a nearby quantum dot, we determine the ideal operation conditions with respect to the applied charge detector bias. Average charge sensitivities of 1.3 × 10(-3)e Hz(-1/2) can be achieved. Additionally, we investigate the back action of the charge detector current on the quantum transport through a nearby quantum dot. By varying the charge detector bias from 0 to 4.5 mV, we can increase the Coulomb peak currents measured at the quantum dot by a factor of around 400. Furthermore, we can completely lift the Coulomb blockade in the quantum dot.

Fabrication of coupled graphene-nanotube quantum devices.

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 conductance maxima in the graphene nanoribbon, acting as a well performing charge detector. Moreover, we discuss an electrically coupled graphene-nanotube junction, which exhibits a tunneling barrier with tunneling rates in the low GHz regime. This allows us to observe Coulomb blockade on a carbon nanotube quantum dot with graphene source and drain leads.

Coherent charge oscillations in a bilayer graphene double quantum dot.

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Transport through graphene quantum dots.

We review transport experiments on graphene quantum dots and narrow graphene constrictions. In a quantum dot, electrons are confined in all lateral dimensions, offering the possibility for detailed investigation and controlled manipulation of individual quantum systems. The recently isolated two-dimensional carbon allotrope graphene is an interesting host to study quantum phenomena, due to its novel electronic properties and the expected weak interaction of the electron spin with the material. Graphene quantum dots are fabricated by etching mono-layer flakes into small islands (diameter 60-350 nm) with narrow connections to contacts (width 20-75 nm), serving as tunneling barriers for transport spectroscopy. Electron confinement in graphene quantum dots is observed by measuring Coulomb blockade and transport through excited states, a manifestation of quantum confinement. Measurements in a magnetic field perpendicular to the sample plane allowed to identify the regime with only a few charge carriers in the dot (electron-hole transition), and the crossover to the formation of the graphene specific zero-energy Landau level at high fields. After rotation of the sample into parallel magnetic field orientation, Zeeman spin splitting with a g-factor of g ≈ 2 is measured. The filling sequence of subsequent spin states is similar to what was found in GaAs and related to the non-negligible influence of exchange interactions among the electrons.

Electronic excited states in bilayer graphene double quantum dots.

We report tunneling spectroscopy experiments on a bilayer graphene double quantum dot device that can be tuned by all-graphene lateral gates. The diameter of the two quantum dots are around 50 nm and the constrictions acting as tunneling barriers are 30 nm in width. The double quantum dot features additional energies on the order of 20 meV. Charge stability diagrams allow us to study the tunable interdot coupling energy as well as the spectrum of the electronic excited states on a number of individual triple points over a large energy range. The obtained constant level spacing of 1.75 meV over a wide energy range is in good agreement with the expected single-particle energy spacing in bilayer graphene quantum dots. Finally, we investigate the evolution of the electronic excited states in a parallel magnetic field.

Spin relaxation in a single-electron graphene quantum dot.

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.

Upstream modes and antidots poison graphene quantum Hall effect.

The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antidots along the graphene edges, mediating backscattering towards upstream edge channels, hence triggering topological breakdown. Combined with simulations, our experimental results provide further insights into graphene quantum Hall channels vulnerability. In turn, this may ease future developments towards precise manipulation of topologically protected edge channels hosted in various types of two-dimensional crystals.

Spin-valley coupling in single-electron bilayer graphene quantum dots.

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 [Formula: see text] and [Formula: see text] states below 20 µeV.

Spin states in graphene quantum dots.

We investigate ground and excited state transport through small (d≈70 nm) graphene quantum dots. The successive spin filling of orbital states is detected by measuring the difference between ground-state energies as a function of a magnetic field. For a magnetic field in-plane of the quantum dot the Zeeman splitting of spin states is measured. The results are compatible with a g factor of 2, and we detect a spin-filling sequence for a series of states which is reasonable given the strength of exchange interaction effects expected by comparing Coulomb interaction energy and kinetic energy of charge carriers in graphene.