Gate-defined graphene double quantum dot and excited state spectroscopy

Nanoironing van der Waals Heterostructures toward Electrically Controlled Quantum Dots

Assembling two-dimensional van der Waals (vdW)-layered materials into heterostructures is an exciting development that sparked the discovery of rich correlated electronic phenomena. vdW heterostructures also offer possibilities for designer device applications in areas such as optoelectronics, valley- and spintronics, and quantum technology. However, realizing the full potential of these heterostructures requires interfaces with exceptionally low disorder which is challenging to engineer. Here, we show that thermal scanning probes can be used to create pristine interfaces in vdW heterostructures. Our approach is compatible at both the material- and device levels, and monolayer WS2 transistors show up to an order of magnitude improvement in electrical performance from this technique. We also demonstrate vdW heterostructures with low interface disorder enabling the electrical formation and control of quantum dots that can be tuned from macroscopic current flow to the single-electron tunneling regime.

Electronic Quantum Materials Simulated with Artificial Model Lattices

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Single-Electron Double Quantum Dots in Bilayer Graphene

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 dots 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 and are in agreement with spin and valley conserving interdot tunneling processes.

Quantum Dot Formation in Controllably Doped Graphene Nanoribbon

We introduce the controllable doping from hydrogen silsesquioxane (HSQ) to graphene by changing its electron-beam exposure dose. Using HSQ as the dopant, a fine-resolution electron-beam resist allows us to selectively dope graphene with an extremely high spatial resolution of a few nanometers. Therefore, we can design and demonstrate the single quantum dot (QD)-like transport in the graphene nanoribbon (GNR) with the opening of the energy gap. Moreover, we suggest a rough geometric design rule in which a relatively short and wide GNR is required for observing the single QD-like transport. We envisage that this method can be utilized for other materials and for other applications, such as p-n junctions and tunnel field-effect transistors.

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.

Bound state properties of ABC-stacked trilayer graphene quantum dots

The few-layer graphene quantum dot provides a promising platform for quantum computing with both spin and valley degrees of freedom. Gate-defined quantum dots in particular can avoid noise from edge disorders. In connection with the recent experimental efforts (Song et al 2016 Nano Lett. 16 6245), we investigate the bound state properties of trilayer graphene (TLG) quantum dots (QDs) through numerical simulations. We show that the valley degeneracy can be lifted by breaking the time reversal symmetry through the application of a perpendicular magnetic field. The spectrum under such a potential exhibits a transition from one group of Landau levels to another group, which can be understood analytically through perturbation theory. Our results provide insight into the transport property of TLG QDs, with possible applications to study of spin qubits and valleytronics in TLG QDs.

Coupling graphene nanomechanical motion to a single-electron transistor

Graphene-based electromechanical resonators have attracted great interest recently because of the outstanding mechanical and electrical properties of graphene and their various applications. However, the coupling between mechanical motion and charge transport has not been explored in graphene. Herein, we studied the mechanical properties of a suspended 50 nm wide graphene nanoribbon, which also acts as a single-electron transistor (SET) at low temperatures. Using the SET as a sensitive detector, we found that the resonance frequency could be tuned from 82 MHz to 100 MHz and the quality factor exceeded 30 000. The strong charge-mechanical coupling was demonstrated by observing the SET induced ∼140 kHz resonance frequency shifts and mechanical damping. We also found that the SET can enhance the nonlinearity of the resonator. Our SET-coupled graphene mechanical resonator could approach an ultra-sensitive mass resolution of ∼0.55 × 10^-21 g and a force sensitivity of ∼1.9 × 10^-19 N (Hz)^-1/2, and can be further improved. These properties indicate that our device is a good platform for both fundamental physical studies and potential applications.

Coulomb Oscillations in a Gate-Controlled Few-Layer Graphene Quantum Dot

Graphene quantum dots could be an ideal host for spin qubits and thus have been extensively investigated based on graphene nanoribbons and etched nanostructures; however, edge and substrate-induced disorders severely limit device functionality. Here, we report the confinement of quantum dots in few-layer graphene with tunable barriers, defined by local strain and electrostatic gating. Transport measurements unambiguously reveal that confinement barriers are formed by inducing a band gap via the electrostatic gating together with local strain induced constriction. Numerical simulations according to the local top-gate geometry confirm the band gap opening by a perpendicular electric field. We investigate the magnetic field dependence of the energy-level spectra in these graphene quantum dots. Experimental results reveal a complex evolution of Coulomb oscillations with the magnetic field, featuring kinks at level crossings. The simulation of energy spectrum shows that the kink features and the magnetic field dependence are consistent with experimental observations, implying the hybridized nature of energy-level spectrum of these graphene quantum dots.

Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime

We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.

A gate defined quantum dot on the two-dimensional transition metal dichalcogenide semiconductor WSe2

Two-dimensional layered materials, such as transition metal dichalcogenides (TMDCs), are promising materials for future electronics owing to their unique electronic properties. With the presence of a band gap, atomically thin gate defined quantum dots (QDs) can be achieved on TMDCs. Herein, standard semiconductor fabrication techniques are used to demonstrate quantum confined structures on WSe2 with tunnel barriers defined by electric fields, therefore eliminating the edge states induced by etching steps, which commonly appear in gapless graphene QDs. Over 40 consecutive Coulomb diamonds with a charging energy of approximately 2 meV were observed, showing the formation of a QD, which is consistent with the simulations. The size of the QD could be tuned over a factor of 2 by changing the voltages applied to the top gates. These results shed light on a way to obtain smaller quantum dots on TMDCs with the same top gate geometry compared to traditional GaAs/AlGaAs heterostructures with further research.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Suspending effect on low-frequency charge noise in graphene quantum dot

Charge noise is critical in the performance of gate-controlled quantum dots (QDs). Such information is not yet available for QDs made out of the new material graphene, where both substrate and edge states are known to have important effects. Here we show the 1/f noise for a microscopic graphene QD is substantially larger than that for a macroscopic graphene field-effect transistor (FET), increasing linearly with temperature. To understand its origin, we suspended the graphene QD above the substrate. In contrast to large area graphene FETs, we find that a suspended graphene QD has an almost-identical noise level as an unsuspended one. Tracking noise levels around the Coulomb blockade peak as a function of gate voltage yields potential fluctuations of order 1 μeV, almost one order larger than in GaAs/GaAlAs QDs. Edge states and surface impurities rather than substrate-induced disorders, appear to dominate the 1/f noise, thus affecting the coherency of graphene nano-devices.

Tuning inter-dot tunnel coupling of an etched graphene double quantum dot by adjacent metal gates

Graphene double quantum dots (DQDs) open to use charge or spin degrees of freedom for storing and manipulating quantum information in this new electronic material. However, impurities and edge disorders in etched graphene nano-structures hinder the ability to control the inter-dot tunnel coupling, tC, the most important property of the artificial molecule. Here we report measurements of tC in an all-metal-side-gated graphene DQD. We find that tC can be controlled continuously about a factor of four by employing a single gate. Furthermore, tC, can be changed monotonically about another factor of four as electrons are gate-pumped into the dot one by one. The results suggest that the strength of tunnel coupling in etched graphene DQDs can be varied in a rather broad range and in a controllable manner, which improves the outlook to use graphene as a base material for qubit applications.

Nanofabrication of gate-defined GaAs/AlGaAs lateral quantum dots

A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe.

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.

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.

Evidence for formation of multi-quantum dots in hydrogenated graphene

We report the experimental evidence for the formation of multi-quantum dots in a hydrogenated single-layer graphene flake. The existence of multi-quantum dots is supported by the low-temperature measurements on a field effect transistor structure device. The resulting Coulomb blockade diamonds shown in the color scale plot together with the number of Coulomb peaks exhibit the characteristics of the so-called 'stochastic Coulomb blockade'. A possible explanation for the formation of the multi-quantum dots, which is not observed in pristine graphene to date, was attributed to the impurities and defects unintentionally decorated on a single-layer graphene flake which was not treated with the thermal annealing process. Graphene multi-quantum dots developed around impurities and defect sites during the hydrogen plasma exposure process.

Large area extreme-UV lithography of graphene oxide via spatially resolved photoreduction

The ability to pattern graphene over large areas with nanometer resolution is the current request for nanodevice fabrication at the industrial scale. Existing methods do not match high throughput with nanometer resolution. We propose a high-throughput resistless extreme-UV (EUV) photolithographic approach operating with sub-micrometer resolution on large area (~10 mm(2)) graphene oxide (GO) films via spatially resolved photoreduction. The efficiency of EUV photoreduction is tested with 46.9 nm coherent light produced by a table top capillary discharge plasma source. Irradiated samples are studied by X-ray photoemission spectroscopy (XPS) and micro-Raman Spectroscopy (μRS). XPS data show that 200 mJ/cm(2) EUV dose produces, onto pristine GO, a 6% increase of sp(2) carbon bonds and a 20% decrease of C-O bonds. μRS data demonstrate a photoreduction efficiency 2 orders of magnitude higher than the one reported in the literature for UV-assisted photoreduction. GO patterning is obtained modulating the EUV dose with a Lloyd's interferometer. The lithographic features consist of GO stripes with modulated reduction degree. Such modulation is investigated and demonstrated by μRS on patterns with 2 μm periodicity.

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.

Electronic properties of graphene nanostructures

In this review, recent developments in the fabrication and understanding of the electronic properties of graphene nanostructures are discussed. After a brief overview of the structure of graphene and the two-dimensional transport properties, the focus is put on graphene constrictions, quantum dots and double quantum dots. For constrictions with a width below 100 nm, the current through the constriction is strongly suppressed for a certain back gate voltage range, related to the so-called transport gap. This transport gap is due to the formation of localized puddles in the constriction, and its size depends strongly on the constriction width. Such constrictions can be used to confine charge carriers in quantum dots, leading to Coulomb blockade effects.

Fabrication of quantum-dot devices in graphene

We describe our recent experimental results on the fabrication of quantum-dot devices in a graphene-based two-dimensional system. Graphene samples were prepared by micromechanical cleavage of graphite crystals on a SiO₂/Si substrate. We performed micro-Raman spectroscopy measurements to determine the number of layers of graphene flakes during the device fabrication process. By applying a nanofabrication process to the identified graphene flakes, we prepared a double-quantum-dot device structure comprising two lateral quantum dots coupled in series. Measurements of low-temperature electrical transport show the device to be a series-coupled double-dot system with varied interdot tunnel coupling, the strength of which changes continuously and non-monotonically as a function of gate voltage.