Topologically protected chiral states at a mass-inverted quantum dot in graphene are studied by analyzing both tight-binding and kernal polynomial method calculations. The mass-inverted quantum dot is introduced by considering a heterojunction between two different mass domains, which is similar to the domain wall in bilayer graphene. The numerical results show emergent metallic channels across the mass gap when the signs of the mass terms are opposite. The eigenstates of the metallic channels are revealed to be doubly degenerate---each state propagates along opposite directions, maintaining the time-reversal symmetry of graphene. The robustness of the metallic channels is further examined, concluding with the fact that chiral states are secured unless atomic vacancies form near the domain wall. Such chiral states circulating along the topological defects may pave a novel route to engineering topological states based on graphene.
AB-stacked bilayer graphene with a tunable electronic bandgap in excess of the optical phonon energy presents an interesting active medium, and we consider such theoretical possibility in this work. We argue the possibility of a highly resonant optical gain in the vicinity of the asymmetry gap. Associated with this resonant gain are strongly amplified plasmons, plasmons with negative group velocity and superluminal effects, as well as directional leaky modes.
We investigate theoretically the electron states in HgTe quantum dots (QDs) with inverted band structures. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of HgTe quantum dot with an inverted band structure are fully spin-polarized, and show ring-like density distributions near the boundary of the QD and spin-angular momentum locking. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such QD structure and oscillate with increasing magnetic fields. This feature offers us a practical way to detect t…
Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs for sulfides and selenides, while it merges with the valence band for tellurides. In the former case the proximity-induced staggered potential gaps and spin-orbit couplings (all on the meV scale) of the Dirac electrons are established by fitting to a phenomenological effective Hamiltonian. While graphene on MoS$_2$, MoSe$_2$, and WS$_2$ has a topologically …
Integrating high-mobility graphene grown by chemical vapor deposition (CVD) into spin transport devices is one of the key tasks in graphene spintronics. We use a van der Waals pickup technique to transfer CVD graphene by hexagonal boron nitride (hBN) from the copper growth substrate onto predefined Co/MgO electrodes to build inverted spin valve devices. Two approaches are presented: (i) a process where the CVD-graphene/hBN stack is first patterned into a bar and then transferred by a second larger hBN crystal onto spin valve electrodes and (ii) a direct transfer of a CVD-graphene/hBN stack. We…
We study the scattering of Dirac electrons of circular graphene quantum dot with mass-inverted subject to electrostatic potential. The obtained solutions of the energy spectrum are used to determine the scattering coefficients at the interface of the two regions. Using the asymptotic solutions at large arguments, we explicitly determine the radial component of reflected current density and the scattering efficiency. It is found that the presence of a mass term outside in addition to another one inside the quantum dot strongly affects the scattering of electrons. In particular, a non-null squar…
The band modulation of the silicene and graphene quantum dots is investigated by a first-principles method. This study includes the ordinary silicene and graphene quantum dots and the embedded quantum dots in the hydrogenated silicene and graphene. The shapes and sizes of quantum dots are recognized as important factors for the electronic properties. We studied several types of quantum dots: triangular, parallelogram, rectangular, hexagonal dots. It demonstrates the energy gap of the quantum dot can be tuned by the dot size, the larger of the dot the smaller the energy gap. Moreover, the shape…
We present Coulomb blockade measurements in a graphene double dot system. The coupling of the dots to the leads and between the dots can be tuned by graphene in-plane gates. The coupling is a non-monotonic function of the gate voltage. Using a purely capacitive model, we extract all relevant energy scales of the double dot system.
This work investigates the electronic properties of the energy spectrum of a hybrid system composed of (i) a circular quantum dot of monolayer graphene surrounded by an infinite sheet of AA-stacked bilayer graphene and (ii) a circular quantum dot of AA-stacked graphene bilayer surrounded by infinite monolayer graphene. We establish analytical findings for the related energy levels and wave functions using the continuum model and the zigzag boundary conditions at the graphene monolayer-bilayer interface. We investigate the effects of perpendicular magnetic, dot radius, and electrical fields on …
Higher harmonic generation in plane graphene quantum dots initiated by intense coherent radiation is investigated, using dynamical Hartree-Fock mean-field theory. A microscopic theory describing the extreme nonlinear optical response of plane graphene quantum dots is developed. The closed set of differential equations for the single-particle density matrix at the graphene quantum dots-strong laser field multiphoton interaction is solved numerically. The obtained solutions indicate the significance of the type of edge and lateral size, and bandgap and laser field strength in the high harmonic g…
A double quantum dot is formed in a graphene nanoribbon device using three top gates. These gates independently change the number of electrons on each dot and tune the inter-dot coupling. Transport through excited states is observed in the weakly coupled double dot regime. We extract from the measurements all relevant capacitances of the double dot system, as well as the quantized level spacing.
We show measurements on a bilayer graphene quantum dot with an integrated charge detector. The focus lies on enabling charge detection with a 30 nm wide bilayer graphene nanoribbon located approximately 35 nm next to a bilayer graphene quantum dot with an island diameter of about 100 nm. Local resonances in the nanoribbon can be successfully used to detect individual charging events in the dot even in regimes where the quantum dot Coulomb peaks cannot be measured by conventional techniques.
We propose a new method to use gapped graphene as barrier to confine electrons in gapless graphene and form a good quantum dot, which can be realized on an oxygen-terminated $SiO_{2}$ substrate partly H-passivated. In particular, we use ferromagnetic insulators deposited on top of barrier which give rise to a spin related energy spectrum and transport properties. Compared to the complexity of etched quantum dots in graphene, the setup suggested here is a promising candidate for practical applications.
We propose how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with semiconducting armchair boundaries. For such a setup, we find the energies and the exact wave functions of bound states, which are required for localized qubits. Additionally, we show that spin qubits in graphene can not only be coupled between nearest neighbor quantum dots via Heisenberg exchange interaction but also over l…
We report measurements on a graphene quantum dot with an integrated graphene charge detector. The quantum dot device consists of a graphene island (diameter approx. 200 nm) connected to source and drain contacts via two narrow graphene constrictions. From Coulomb diamond measurements a charging energy of 4.3 meV is extracted. The charge detector is based on a 45 nm wide graphene nanoribbon placed approx. 60 nm from the island. We show that resonances in the nanoribbon can be used to detect individual charging events on the quantum dot. The charging induced potential change on the quantum dot c…
We present a theory of excitonic processes in gate controlled graphene quantum dots. The dependence of the energy gap on shape, size and edge for graphene quantum dots with up to a million atoms is predicted. Using a combination of tight-binding, Hartree-Fock and configuration interaction methods, we show that triangular graphene quantum dots with zigzag edges exhibit optical transitions simultaneously in the THz, visible and UV spectral ranges, determined by strong electron-electron and excitonic interactions. The relationship between optical properties and finite magnetic moment and charge d…
We report on a double quantum dot which is formed in a width-modulated etched bilayer graphene nanoribbon. A number of lateral graphene gates enable us to tune the quantum dot energy levels and the tunneling barriers of the device over a wide energy range. Charge stability diagrams and in particular individual triple point pairs allow to study the tunable capacitive inter-dot coupling energy as well as the spectrum of the electronic excited states on a number of individual triple points. We extract a mutual capacitive inter-dot coupling in the range of 2 - 6 meV and an inter-dot tunnel couplin…
We examine a graphene quantum dot formed by combining an electric and a uniform magnetic field. The electric field creates a smooth quantum well potential while the magnetic field induces an exponential tail to the dot states. The states peak in the well and the electrostatic barrier region as a result of the Klein tunneling effect. Coupling between dot states which peak in different regions can be achieved with the electric and magnetic fields. The tunability of this dot with moderate external fields could be used for designing quantum devices in monolayer graphene.
Graphene is an attractive material for broadband photodetection but suffers from weak light absorption. Coating graphene with quantum dots can significantly enhance light absorption and create extraordinarily high photo gain. This high gain is often explained by the classical gain theory which is unfortunately an implicit function and may even be questionable. In this work, we managed to derive explicit gain equations for hybrid graphene-quantum-dot photodetectors. Due to the work function mismatch, lead sulfide (PbS) quantum dots coated on graphene will form a surface depletion region near th…
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 [{\sl Gutierrez et al. Nat. Phys. \textbf{12}, 1069--1075 (2016)}] show an excellent experimental-theoretical agreement.
The $s_z=0$ spin configuration of two electrons confined at a double quantum dot (DQD) encodes the singlet-triplet qubit (STQ). We introduce the inverted STQ (ISTQ) that emerges from the setup of two quantum dots (QDs) differing significantly in size and out-of-plane magnetic fields. The strongly confined QD has a two-electron singlet ground state, but the weakly confined QD has a two-electron triplet ground state in the $s_z=0$ subspace. Spin-orbit interactions act nontrivially on the $s_z=0$ subspace and provide universal control of the ISTQ together with electrostatic manipulations of the c…
We analyze the single particle states at the edges of disordered graphene quantum dots. We show that generic graphene quantum dots support a number of edge states proportional to circumference of the dot over the lattice constant. Our analytical theory agrees well with numerical simulations. Perturbations breaking electron-hole symmetry like next-nearest neighbor hopping or edge impurities shift the edge states away from zero energy but do not change their total amount. We discuss the possibility of detecting the edge states in an antidot array and provide an upper bound on the magnetic moment…
We present transport measurements on quantum dots of sizes 45, 60 and 80 nm etched with an Ar/O2-plasma into a single graphene sheet, allowing a size comparison avoiding effects from different graphene flakes. The transport gaps and addition energies increase with decreasing dot size, as expected, and display a strong correlation, suggesting the same physical origin for both, i.e. disorder-induced localization in presence of a small confinement gap. Gate capacitance measurements indicate that the dot charges are located in the narrow device region as intended. A dominant role of disorder is fu…
We present graphene quantum dots endowed with addition energies as large as 1.6 eV, fabricated by the controlled rupture of a graphene sheet subjected to a large electron current in air. The size of the quantum dot islands is estimated to be in the 1 nm range. The large addition energies allow for Coulomb blockade at room temperature, with possible application to single-electron devices.
Graphene and bilayer graphene quantum dots are promising hosts for spin qubits with long coherence times. Although recent technological improvements make it possible to confine single electrons electrostatically in bilayer graphene quantum dots, and their spin and valley texture of the single particle spectrum has been studied in detail, their relaxation dynamics remains still unexplored. Here, we report on transport through a high-frequency gate controlled single-electron bilayer graphene quantum dot. By transient current spectroscopy of single-electron spin states, we extract a lower bound o…
In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.
We use numerically exact Chebyshev expansion and kernel polynomial methods to study transport through circular graphene quantum dots in the framework of a tight-binding honeycomb lattice model. Our focus lies on the regime where individual modes of the electrostatically defined dot dominate the charge carrier dynamics. In particular, we discuss the scattering of an injected Dirac electron wave packet for a single quantum dot, electron confinement in the dot, the optical excitation of dot-bound modes, and the propagation of an electronic excitation along a linear array of dots.
This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and will then discuss gate-tunable quantum dots in detail. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundary, (ii) a disc in single-layer graphene, and (iii) a disc i…
We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering efficiency of a single dot and demonstrate that for small-sized scatterers the cross-sections are dominated by quantum effects, where resonant scattering leads to a series of quasi-bound dot states. Calculating the conductance and the local density of states for quantum dot superlattices we show that the resonant carrier transport through such graphene-based nanos…
The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them experimentally in symmetrical heterostructures composed by segments of graphene ribbons with different widths forming a graphene quantum dot. We identify the existence of bound states in the continuum in these graphene quantum dot systems by means of local density of states and electronic conductance calculations.
We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of around 4.5 meV. We show the evolution of Coulomb resonances as a function of perp…
A study of previously overlooked structural and optical properties of InGaAs heterostructures grown on (111)B oriented GaAs substrates patterned with inverted 7.5 um pitch pyramidal recesses is presented. First, the composition of the confinement barrier material (GaAs in this work) and its growth temperature are shown as some of the key parameters that determine the main quantum dot properties, including nontrivial emission energy dependence, excitonic pattern and unusual photoluminescence energetic ordering of the InGaAs ensemble nanostructures. Secondly, the formation of a formerly unidenti…
We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a numerically exact kernel polynomial expansion technique. Analyzing the local density of states and the momentum resolved photoemission spectrum we find clear evidence for a series of quasi-bound states at the dots, which can be probed by optical measurements. We further analyze the interplay of the superlattice structure with dot localized modes on the electron ene…
We study and compare two analytic models of graphene quantum dots for calculating charge relaxation times due to electron-phonon interaction. Recently, charge relaxation processes in graphene quantum dots have been probed experimentally and here we provide a theoretical estimate of relaxations times. By comparing a model with pure edge confinement to a model with electrostatic confinement, we find that the latter features much larger relaxation times. Interestingly, relaxation times in electrostatically defined quantum dots are predicted to exceed the experimentally observed lower bound of ~10…
Stimulated by recent advances in isolating graphene, we discovered that quantum dot can be trapped in Z-shaped graphene nanoribbon junciton. The topological structure of the junction can confine electronic states completely. By varying junction length, we can alter the spatial confinement and the number of discrete levels within the junction. In addition, quantum dot can be realized regardless of substrate induced static disorder or irregular edges of the junction. This device can be used to easily design quantum dot devices. This platform can also be used to design zero-dimensional functional…
We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for graphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR) and the shot noise. It is shown that for certain sh…
We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a large electron current. This results in the in-situ formation of a clean and ultra-narrow constriction, which hosts one quantum dot, and occasionally a few quantum dots in series. Conductance spectroscopy indicates that individual quantum dots can possess an addition energy as large as 180 meV and a level spacing as large as 25 meV. Our technique has several assets: (i) the dot is suspended, thus the electrostatic …
We study the conductance spectrum of graphene quantum dots, both single and multiple cases. The single electron tunneling phenomenon is investigated and the periodicity, amplitude and line shape of the Coulomb blockade oscillations at low temperatures are obtained. Further, we discuss the transport behavior when multiple dots are assembled in array and find a phase transition of conductance spectra from individual Coulomb blockade to collective Coulomb blockade.
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 form 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 form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.
We investigate the application of nanoscale topgates on exfoliated bilayer graphene to define quantum dot devices. At temperatures below 500 mK the conductance underneath the grounded gates is suppressed, which we attribute to nearest neighbour hopping and strain-induced piezoelectric fields. The gate-layout can thus be used to define resistive regions by tuning into the corresponding temperature range. We use this method to define a quantum dot structure in bilayer graphene showing Coulomb blockade oscillations consistent with the gate layout.
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 tw…
We present an electronic transport experiment in graphene where both classical and quantum mechanical charge detector back-action on a quantum dot are investigated. The device consists of two stacked graphene quantum dots separated by a thin layer of boron nitride. This device is fabricated by van der Waals stacking and is equipped with separate source and drain contacts to both dots. By applying a finite bias to one quantum dot, a current is induced in the other unbiased dot. We present an explanation of the observed measurement-induced current based on strong capacitive coupling and energy d…
We present electronic structure and quantum transport calculations that predict conducting channels induced in graphene quantum dots by lines of adsorbed hydrogen atoms to function as highly efficient, experimentally realizable valley filters, accumulators and switches. The underlying physics is a novel property of graphene Dirac point resonances (DPRs) that is revealed here, namely, that an electric current passing through a DPR-mediated conducting channel in a given direction is carried by electrons of em only one of the two graphene valleys. Our predictions apply to lines of hydrogen atoms …
We study a graphene double quantum dot in different coupling regimes. Despite the strong capacitive coupling between the dots, the tunnel coupling is below the experimental resolution. We observe additional structures inside the finite-bias triangles, part of which can be attributed to electronic excited dot states, while others are probably due to modulations of the transmission of the tunnel barriers connecting the system to source and drain leads.
We study the transport through evanescent waves in graphene quantum dots of different geometries. The transmission is suppressed when the leads are attached to edges of the same majority sublattice. Otherwise, the transmission depends exponentially on the distance between leads in rectangular dots, and as a power law in circular dots. The transmission through junctions where the transmitted and reflected currents belong to the opposite valley as the incoming one depends on details of the lattice structure at distances comparable to the atomic spacing.
We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum states of the dot. Numerical results show the simultaneous presence of electron and hole confined states for certain doping profiles and a remarkable angular momentum dependence of the quantum dot spectrum which is in sharp contrast with that for conventional semiconductor quantum dots. We predict that the optical spectrum will consist of a series of non-equidis…
Graphene quantum dots are considered as promising alternatives to quantum dots in III-V semiconductors, e.g., for the use as spin qubits due to their consistency made of light atoms including spin-free nuclei which both imply relatively long spin decoherene times. However, this potential has not been realized in experiments so far, most likely, due to a missing control of the edge configurations of the quantum dots. Thus, a more fundamental investigation of Graphene quantum dots appears to be necessary including a full control of the wave function properties most favorably during transport spe…
We measure telegraph noise of current fluctuations in an electrostatically defined quantum dot in bilayer graphene by real-time detection of single electron tunneling with a capacitively coupled neighboring quantum dot. Suppression of the second and third cumulant (related to shot noise) in a tunable graphene quantum dot is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels. Furthermore, we use this method to investigate the first spin excited state, an essential prerequisite to measure spin relaxation.
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 ground state energy as a function of a magnetic field. For a magnetic field in-plane of the quantum dot the Zemann 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 for graphene.
We theoretically investigate the spectrum of a single electron double quantum dot, defined by top gates in a graphene with a substrate induced gap. We examine the effects of electric and magnetic fields on the spectrum of localized states, focusing on the tunability of the inter-dot coupling. We find that the substrate induced gap allows for electrostatic control, with some limitations that for a fixed inter-dot distance, the inter-dot coupling can not be made arbitrarily small due to the Klein tunneling. On the other hand, the proximity of the valence band in graphene allows for new regimes, …
Within the Landauer transport formalism we demonstrate that conductance zeroes are possible in bipartite systems at half-filling when leads are contacted to different sublattice sites. In particular, we investigate the application of this theory to graphene quantum dots with leads in the armchair configuration. The obtained conductance cancellation is robust in the presence of any single-site impurity.
Surface graphene guides were interfaced with an array of individual semiconductor quantum dots, whose position was commensurate with the optical guide modes. The surface guide served as a channel for a Field Effect Transistor (FET) while the dots were placed within the capacitor formed between the graphene channel and the gate electrode. We report on negative differential photo-related conductance under light and a diminishing fluorescence effect as a function of bias. We suggest that the quenched fluorescence may be hindered, to some degree, by incorporating the QD in a resonator, which is tu…
We study the electron propagation in a circular electrostatically defined quantum dot in graphene. Solving the scattering problem for a plane Dirac electron wave we identify different scattering regimes depending on the radius and potential of the dot as well as the electron energy. Thereby, our particular focus lies on resonant scattering and the temporary electron trapping in the dot.
The interaction between carbon nanostructures like quantum dots and radiation can generate different effects inside the nanomaterial, with the use of computational methods such effects can be predicted and optimize the material allowing a desired output. In this work, a theoretical model for pristine graphene quantum dots is studied, allowing to explain the shape and size dependence for the electronic properties and how the bandgap can be tuned with the functionalization of the nanostructure at the edges.
Newly synthesized nanostructures of graphene appear as a promising breeding ground for new technology. Therefore, it is important to identify the role played by the boundary conditions in their electronic features. In this contribution we use the non-equilibrium Green's function method coupled to tight-binding theory to calculate and compare the current patterns of hexagonal graphene quantum dots, with contacts placed at different edge locations. Our results reveal the formation of current vortices when the symmetry of the contact geometry is in conflict with the symmetries of the quantum dot.…
In recent work by Schnez et al. [PRB 78, 195427 (2008)], they studied the analytical model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field. In this comment we first point out that the results Eqs.(5), (6) and (11) presented by them in [1] are not reliable and then give our results.
