Electrostatically Confined Monolayer Graphene Quantum Dots with Orbital and Valley Splittings

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules

Materials such as graphene and topological insulators host massless Dirac fermions that enable the study of relativistic quantum phenomena. Single quantum dots and coupled quantum dots formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique testbed to study atomic and molecular physics in the ultrarelativistic regime (particle speed close to the speed of light). Here we use a scanning tunnelling microscope to create and probe single and coupled electrostatically defined graphene quantum dots to unravel the magnetic-field responses of artificial relativistic nanostructures. We observe a giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV T^-1 and ~600μ_B (μ_B, Bohr magneton) in single graphene quantum dots. For coupled graphene quantum dots, Aharonov-Bohm oscillations and a strong Van Vleck paramagnetic shift of ~20 meV T^-2 are observed. Our findings provide fundamental insights into relativistic quantum dot states, which can be potentially leveraged for use in quantum information science.

Photoelectrical properties of integrated photodetectors based on bilayer graphene quantum dots with asymmetric metal contacts: a NEGF-DFT study

We propose investigating the electro-optical properties of photodetectors based on mono- and bilayer graphene quantum dots or nanodots (GNDs). These photodetectors consist of dissimilar metals (gold, silver and titanium) that are in contact with the GNDs. To obtain photoelectrical characteristics, we employed density functional theory to solve the non-equilibrium Green's function. Photo-responsivities and quantum efficiencies obtained for these nanostructures were far better than those for structures based on graphene nanoribbons. Among the proposed photodetectors, the best performance belonged to the bilayer structures illuminated by in-plane polarized incident light. The proposed photodetectors operate without a need for externally applied voltage and are suitable for parallel light propagation using directional couplers based on the evanescent field of incident light; hence, they have applications in optical integrated circuits.

Quantum Confinement of Electron-Phonon Coupling in Graphene Quantum Dots

On the basis of first-principles calculations and the special displacement method, we demonstrate the quantum confinement scaling law of the phonon-induced gap renormalization of graphene quantum dots (GQDs). We employ zigzag-edged GQDs with hydrogen passivation and embedded in hexagonal boron nitride. Our calculations for GQDs in the sub-10 nm region reveal strong quantum confinement of the zero-point renormalization ranging from 20 to 250 meV. To obtain these values we introduce a correction to the Allen-Heine theory of temperature-dependent energy levels that arises from the phonon-induced splitting of 2-fold degenerate edge states. This correction amounts to more than 50% of the gap renormalization. We also present momentum-resolved spectral functions of GQDs, which are not reported in previous contributions. Our results lay the foundation to systematically engineer temperature-dependent electronic structures of GQDs for applications in solar cells, electronic transport, and quantum computing devices.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Flat band carrier confinement in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twist angle variation which has been studied elsewhere. Here, by using low temperature scanning tunneling spectroscopy and planar tunneling junction measurements, we demonstrate that flat bands in twisted bilayer graphene can amplify small doping inhomogeneity that surprisingly leads to carrier confinement, which in graphene could previously only be realized in the presence of a strong magnetic field.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Gate-Tunable Optical Nonlinearities and Extinction in Graphene/LaAlO3/SrTiO3 Nanostructures

We explore the ultrafast optical response of graphene subjected to intense (∼10⁶ V/cm) local (∼10 nm) electric fields. Nanoscale gating of graphene is achieved using a voltage-biased, SrTiO₃-based conductive nanowire junction "written" directly under the graphene and isolated from it by an insulating ultrathin (<2 nm) LaAlO₃ barrier. Upon illumination with ultrafast visible-to-near-infrared (VIS-NIR) light pulses, the local field from the nanojunction creates a strong gate-tunable second-order nonlinearity in the graphene and produces a substantial difference-frequency (DFG) and sum-frequency generation (SFG) response detected by the nanojunction. Spectrally sharp, gate-tunable extinction features (>99.9%) are observed in the VIS-NIR and SFG spectral ranges, in parameter regimes that are positively correlated with the enhanced nonlinear response. The observed graphene-light interaction and nonlinear response are of fundamental interest and open the way for future exploitation in graphene-based optical devices such as phase shifters, modulators, and nanoscale THz sources.

Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference

Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2π. This nontrivial topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties. Here we show that the quantum interference due to intervalley scattering induced by single-atom vacancies or impurities provides insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct valleys with opposite chirality undergo a rotation of pseudospin that results in the Friedel oscillation with wavefront dislocations. The number of dislocations reflects the information about pseudospin texture and hence can be used to measure the Berry phase. As demonstrated both experimentally and theoretically, the Friedel oscillation, depending on the single-atom vacancy or impurity at different sublattices, can exhibit N=4, 2, or 0 additional wavefronts, characterizing the 2π Berry phase of the bilayer graphene. Our results provide a comprehensive study of the intervalley quantum interference in bilayer graphene and can be extended to multilayer graphene, shedding light on the pseudospin physics.

Scanned Single-Electron Probe inside a Silicon Electronic Device

Solid-state devices can be fabricated at the atomic scale, with applications ranging from classical logic to current standards and quantum technologies. Although it is very desirable to probe these devices and the quantum states they host at the atomic scale, typical methods rely on long-ranged capacitive interactions, making this difficult. Here, we probe a silicon electronic device at the atomic scale using a localized electronic quantum dot induced directly within the device at a desired location, using the biased tip of a low-temperature scanning tunneling microscope. We demonstrate control over short-ranged tunnel coupling interactions of the quantum dot with the device's source reservoir using sub-nanometer position control of the tip and the quantum dot energy level using a voltage applied to the device's gate reservoir. Despite the ∼1 nm proximity of the quantum dot to the metallic tip, we find that the gate provides sufficient capacitance to enable a high degree of electric control. Combined with atomic-scale imaging, we use the quantum dot to probe applied electric fields and charge in individual defects in the device. This capability is expected to aid in the understanding of atomic-scale devices and the quantum states realized in them.

Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene

Energy spectroscopy of strongly interacting phases requires probes which minimize screening while retaining spectral resolution and local sensitivity. Here, we demonstrate that such probes can be realized using atomic sized quantum dots bound to defects in hexagonal Boron Nitride tunnel barriers, placed at nanometric distance from graphene. With dot energies capacitively tuned by a planar graphite electrode, dot-assisted tunneling becomes highly sensitive to the graphene excitation spectrum. The spectra track the onset of degeneracy lifting with magnetic field at the ground state, and at unoccupied excited states, revealing symmetry-broken gaps which develop steeply with magnetic field - corresponding to Landé g factors as high as 160. Measured up to B = 33 T, spectra exhibit a primary energy split between spin-polarized excited states, and a secondary spin-dependent valley-split. Our results show that defect dots probe the spectra while minimizing local screening, and are thus exceptionally sensitive to interacting states.

Comprehensive Electrostatic Modeling of Exposed Quantum Dots in Graphene/Hexagonal Boron Nitride Heterostructures

Recent experimental advancements have enabled the creation of tunable localized electrostatic potentials in graphene/hexagonal boron nitride (hBN) heterostructures without concealing the graphene surface. These potentials corral graphene electrons yielding systems akin to electrostatically defined quantum dots (QDs). The spectroscopic characterization of these exposed QDs with the scanning tunneling microscope (STM) revealed intriguing resonances that are consistent with a tunneling probability of 100% across the QD walls. This effect, known as Klein tunneling, is emblematic of relativistic particles, underscoring the uniqueness of these graphene QDs. Despite the advancements with electrostatically defined graphene QDs, a complete understanding of their spectroscopic features still remains elusive. In this study, we address this lapse in knowledge by comprehensively considering the electrostatic environment of exposed graphene QDs. We then implement these considerations into tight binding calculations to enable simulations of the graphene QD local density of states. We find that the inclusion of the STM tip's electrostatics in conjunction with that of the underlying hBN charges reproduces all of the experimentally resolved spectroscopic features. Our work provides an effective approach for modeling the electrostatics of exposed graphene QDs. The methods discussed here can be applied to other electrostatically defined QD systems that are also exposed.

Quantitative study of electronic whispering gallery modes in electrostatic-potential induced circular graphene junctions

Electronic whispering gallery modes (EWGMs) have been recently observed in several circular graphene junctions, pn and pp', created in scanning tunneling microscopy experiments. By computing the local density of states within the Dirac-Weyl formalism for massless fermions we demonstrate that the EWGMs may really be emerged in any type of the electrostatic-potential induced circular graphene junctions, including uni-junctions (e.g. np- or pp'-junctions) as well as bipolar-junctions (e.g. pnp-heterojunctions). Surprisingly, quantitative analyses show that for all the EWGMs identified (regardless of junction types) the quality (Q) factors seem to be ≤10², very small compared to those in ordinary optical whispering gallery modes microresonators, while the corresponding mode radii may tunably be in nanometer-scale. Our theoretical results are in good agreement with existent experimental data, putting a question to the application potential of the EWGMs identified.

Movable Valley Switch Driven by Berry Phase in Bilayer-Graphene Resonators

Berry phase, the geometric phase accumulated over a closed loop in parameter space during an adiabatic cyclic evolution, has been demonstrated to play an important role in many quantum systems since its discovery. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2π, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene p-n junction resonators. In our experiment, the resonators are generated by combining the electric field of a scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2π continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer-graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.

Valley Polarization and Inversion in Strained Graphene via Pseudo-Landau Levels, Valley Splitting of Real Landau Levels, and Confined States

It is quite easy to control spin polarization and the spin direction of a system via magnetic fields. However, there is no such direct and efficient way to manipulate the valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. Pseudomagnetic fields, which are quite different from real magnetic fields, point in opposite directions at the two distinct valleys of graphene. Therefore, the coexistence of pseudomagnetic fields and real magnetic fields leads to imbalanced effective magnetic fields at two distinct valleys of graphene. This allows us to control the valley in graphene as conveniently as the electron spin. In this work, we report a consistent observation of valley polarization and inversion in strained graphene via pseudo-Landau levels, splitting of real Landau levels, and valley splitting of confined states using scanning tunneling spectroscopy. Our results highlight a pathway to valleytronics in strained graphene-based platforms.

Gate controlled valley polarizer in bilayer graphene

Sign reversal of Berry curvature across two oppositely gated regions in bilayer graphene can give rise to counter-propagating 1D channels with opposite valley indices. Considering spin and sub-lattice degeneracy, there are four quantized conduction channels in each direction. Previous experimental work on gate-controlled valley polarizer achieved good contrast only in the presence of an external magnetic field. Yet, with increasing magnetic field the ungated regions of bilayer graphene will transit into the quantum Hall regime, limiting the applications of valley-polarized electrons. Here we present improved performance of a gate-controlled valley polarizer through optimized device geometry and stacking method. Electrical measurements show up to two orders of magnitude difference in conductance between the valley-polarized state and gapped states. The valley-polarized state displays conductance of nearly 4e2/h and produces contrast in a subsequent valley analyzer configuration. These results pave the way to further experiments on valley-polarized electrons in zero magnetic field.

Tuning single-electron charging and interactions between compressible Landau level islands in graphene

Interacting and tunable quantum dots (QDs) have been extensively exploited in condensed matter physics and quantum information science. Using a low-temperature scanning tunneling microscope (STM), we both create and directly image a new type of coupled QD system in graphene, a highly interacting quantum relativistic system with tunable density. Using detailed scanning tunneling spectroscopy (STS) measurements, we show that Landau quantization inside a potential well enables novel electron confinement via the incompressible strips between partially filled Landau levels (LLs), forming isolated and concentric LL QDs. By changing the charge density and the magnetic field we can tune continuously between single- and double-concentric LL QD systems within the same potential well. In the concentric QD regime, single-electron charging peaks of the two dots intersect, displaying a characteristic avoidance pattern. At moderate fields, we observe an unconventional avoidance pattern that differs significantly from that observed in capacitively coupled double-QD systems. We find that we can reproduce in detail this anomalous avoidance pattern within the framework of the electrostatic double-QD model by replacing the capacitive interdot coupling with a phenomenological charge-counting system in which charges in the inner concentric dot are counted in the total charge of both islands. The emergence of such strange forms of interdot coupling in a single potential well, together with the ease of producing such charge pockets in graphene and other two-dimensional (2D) materials, reveals an intriguing testbed for the confinement of 2D electrons in customizable potentials.

Effective detection of spatio-temporal carrier dynamics by carrier capture

The spatio-temporal dynamics of electrons moving in a 2D plane is challenging to detect when the required resolution shrinks simultaneously to nanometer length and subpicosecond time scale. We propose a detection scheme relying on phonon-induced carrier capture from 2D unbound states into the bound states of an embedded quantum dot. This capture process happens locally and here we explore if this locality is sufficient to use the carrier capture process as detection of the ultrafast diffraction of electrons from an obstacle in the 2D plane. As an example we consider an electronic wave packet traveling in a semiconducting monolayer of the transition metal dichalcogenide MoSe₂, and we study the scattering-induced dynamics using a single particle Lindblad approach. Our results offer a new way to high resolution detection of the spatio-temporal carrier dynamics.

Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures

Quantum coherence and control is foundational to the science and engineering of quantum systems^1,2. In van der Waals materials, the collective coherent behaviour of carriers has been probed successfully by transport measurements^3-6. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit^7-9, whose spectrum reflects the electronic properties of massless Dirac fermions travelling ballistically^4,5. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying van der Waals materials using microwave photons in coherent quantum circuits.

Unique Spin Vortices and Topological Charges in Quantum Dots with Spin-orbit Couplings

Spin textures of one or two electrons in a quantum dot with Rashba or Dresselhaus spin-orbit couplings reveal several intriguing properties. We show here that even at the single-electron level stable spin vortices with tunable topological charges exist. These topological textures appear in the ground state of the dots. The textures are stabilized by time-reversal symmetry breaking and are robust against the eccentricity of the dot. The topological charge is directly related to the sign of the z component of the spin in a large dot, allowing a direct probe of its topological properties. This would clearly pave the way to possible future topological spintronics. The phenomenon of spin vortices persists for the interacting two-electron dot in the presence of a magnetic field.

Interaction-driven quantum Hall wedding cake-like structures in graphene quantum dots

Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels. We directly observe the development of a "wedding cake"-like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.

Confined states in graphene quantum blisters

Bilayer graphene samples may exhibit regions where the two layers are locally delaminated forming a so-called quantum blister in the graphene sheet. Electron and hole states can be confined in this graphene quantum blisters (GQB) by applying a global electrostatic bias. We scrutinize the electronic properties of these confined states under the variation of interlayer bias, coupling, and blister's size. The spectra display strong anti-crossings due to the coupling of the confined states on upper and lower layers inside the blister. These spectra are layer localized where the respective confined states reside on either layer or equally distributed. For finite angular momentum, this layer localization can be at the edge of the blister and corresponds to degenerate modes of opposite momenta. Furthermore, the energy levels in GQB exhibit electron-hole symmetry that is sensitive to the electrostatic bias. Finally, we demonstrate that confinement in GQB persists even in the presence of a variation in the inter-layer coupling.

Visualization and Control of Single-Electron Charging in Bilayer Graphene Quantum Dots

Graphene p-n junctions provide an ideal platform for investigating novel behavior at the boundary between electronics and optics that arise from massless Dirac Fermions, such as whispering gallery modes and Veselago lensing. Bilayer graphene also hosts Dirac Fermions, but they differ from single-layer graphene charge carriers because they are massive, can be gapped by an applied perpendicular electric field, and have very different pseudospin selection rules across a p-n junction. Novel phenomena predicted for these massive Dirac Fermions at p-n junctions include anti-Klein tunneling, oscillatory Zener tunneling, and electron cloaked states. Despite these predictions there has been little experimental focus on the microscopic spatial behavior of massive Dirac Fermions in the presence of p-n junctions. Here we report the experimental manipulation and characterization of massive Dirac Fermions within bilayer graphene quantum dots defined by circular p-n junctions through the use of scanning tunneling microscopy-based (STM) methods. Our p-n junctions are created via a flexible technique that enables realization of exposed quantum dots in bilayer graphene/hBN heterostructures. These quantum dots exhibit sharp spectroscopic resonances that disperse in energy as a function of applied gate voltage. Spatial maps of these features show prominent concentric rings with diameters that can be tuned by an electrostatic gate. This behavior is explained by single-electron charging of localized states that arise from the quantum confinement of massive Dirac Fermions within our exposed bilayer graphene quantum dots.

Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Coherent manipulation of the binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid-state systems, whereas exploitation of the valley has only recently been started, albeit without control at the single-electron level. Here, we show that van der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunnelling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits.

High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices

Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work hints at unexplored physics in Hofstadter butterfly systems at high temperatures.

Folic acid-functionalized graphene quantum dots with tunable fluorescence emission for cancer cell imaging and optical detection of Hg2+

Functional groups may alter the optical and electrical characteristics of graphene quantum dots and lead to unusual properties and related applications.

An ultrahigh-vacuum cryostat for simultaneous scanning tunneling microscopy and magneto-transport measurements down to 400 mK

We present the design and calibration measurements of a scanning tunneling microscope setup in a ³He ultrahigh-vacuum cryostat operating at 400 mK with a hold time of 10 days. With 2.70 m in height and 4.70 m free space needed for assembly, the cryostat fits in a one-story lab building. The microscope features optical access, an xy table, in situ tip and sample exchange, and enough contacts to facilitate atomic force microscopy in tuning fork operation and simultaneous magneto-transport measurements on the sample. Hence, it enables scanning tunneling spectroscopy on microstructured samples which are tuned into preselected transport regimes. A superconducting magnet provides a perpendicular field of up to 14 T. The vertical noise of the scanning tunneling microscope amounts to 1 pm_rms within a 700 Hz bandwidth. Tunneling spectroscopy using one superconducting electrode revealed an energy resolution of 120 μeV. Data on tip-sample Josephson contacts yield an even smaller feature size of 60 μeV, implying that the system operates close to the physical noise limit.

On the density of states of circular graphene quantum dots

We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings. Calculations performed for the graphene quantum dot studied in a recent scanning tunneling microscopy measurement (Gutierrez et al 2016 Nat. Phys. 12 1069-75) show an excellent experimental-theoretical agreement.

Electrotunable artificial molecules based on van der Waals heterostructures

Quantum confinement has made it possible to detect and manipulate single-electron charge and spin states. The recent focus on two-dimensional (2D) materials has attracted significant interests on possible applications to quantum devices, including detecting and manipulating either single-electron charging behavior or spin and valley degrees of freedom. However, the most popular model systems, consisting of tunable double-quantum-dot molecules, are still extremely difficult to realize in these materials. We show that an artificial molecule can be reversibly formed in atomically thin MoS₂ sandwiched in hexagonal boron nitride, with each artificial atom controlled separately by electrostatic gating. The extracted values for coupling energies at different regimes indicate a single-electron transport behavior, with the coupling strength between the quantum dots tuned monotonically. Moreover, in the low-density regime, we observe a decrease of the conductance with magnetic field, suggesting the observation of Coulomb blockade weak anti-localization. Our experiments demonstrate for the first time the realization of an artificial quantum-dot molecule in a gated MoS₂ van der Waals heterostructure, which could be used to investigate spin-valley physics. The compatibility with large-scale production, gate controllability, electron-hole bipolarity, and new quantum degrees of freedom in the family of 2D materials opens new possibilities for quantum electronics and its applications.

Localization of massless Dirac particles via spatial modulations of the Fermi velocity

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.

Quantum Dots in Graphene Nanoribbons

Graphene quantum dots (GQDs) hold great promise for applications in electronics, optoelectronics, and bioelectronics, but the fabrication of widely tunable GQDs has remained elusive. Here, we report the fabrication of atomically precise GQDs consisting of low-bandgap N = 14 armchair graphene nanoribbon (AGNR) segments that are achieved through edge fusion of N = 7 AGNRs. The so-formed intraribbon GQDs reveal deterministically defined, atomically sharp interfaces between wide and narrow AGNR segments and host a pair of low-lying interface states. Scanning tunneling microscopy/spectroscopy measurements complemented by extensive simulations reveal that their energy splitting depends exponentially on the length of the central narrow bandgap segment. This allows tuning of the fundamental gap of the GQDs over 1 order of magnitude within a few nanometers length range. These results are expected to pave the way for the development of widely tunable intraribbon GQD-based devices.

Intrinsic valley polarization of magnetic VSe2 monolayers

Intrinsic valley polarization can be obtained in VSe₂ monolayers with broken inversion symmetry and time reversal symmetry. First-principles investigations reveal that the magnitude of the valley splitting in magnetic VSe₂ induced by spin-orbit coupling reaches as high as 78.2 meV and can be linearly tuned by biaxial strain. Besides conventional polarized light, hole doping or illumination with light of proper frequency can offer effective routes to realize valley polarization. Moreover, spin-orbit coupling in monolayer VSe₂ breaks not only the valley degeneracy but also the three-fold rotational symmetry in band structure. The intrinsic and tunable valley splitting and the breaking of optical isotropy bring additional benefits to valleytronic and optoelectronic applications.

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.

Veselago lens and Klein collimator in disordered graphene

We simulate electron transport through graphene nanoribbons of realistic size containing a p-n junction patterned by electrostatic gates. For a sharp p-n interface, Klein tunneling leads to refocusing of a divergent beam forming a Veselago lens. Wider transition regions allow only electrons with near-perpendicular incidence to pass the junction, forming a Klein collimator. Using a third nearest neighbor tight binding description we explore the influence of interface roughness and bulk disorder on guiding properties. We provide bounds on disorder amplitudes and p-n junction properties to be satisfied in order to experimentally observe the focusing effect and compare our predictions to very recent realizations.

Helical Level Structure of Dirac Potential Wells

In graphene and other massless two-dimensional Dirac materials, Klein tunneling compromises electron confinement, and momentum-space contours can be assigned a Berry phase which is either zero or π. Consequently, in such systems the energy spectrum of circular potential wells exhibits an interesting discontinuity as a function of magnetic field B: for a given angular momentum the ladder of eigen-resonances is split at an energy-dependent critical field B c. Here we show that introducing a mass term Δ in the Hamiltonian bridges this discontinuity in such a way that states below B c are adiabatically connected to states above B c whose principal quantum number differs by unity depending on the sign of Δ. In the B-Δ plane, the spectrum of these circular resonators resembles a spiral staircase, in which a particle prepared in the ∣n, m⟩ resonance state can be promoted to the ∣n± 1, m⟩ state by an adiabatic circuit of the Hamiltonian about B c, the sign depending on the direction of the circuit. We explain the phenomenon in terms of the evolving Berry phase of the orbit, which in such a circuit changes adiabatically by 2π.