In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations: (1) a central Coulomb potential and (2) a positively charged carbon vacancy. The tight binding (TB) and the half-filled extended Hubbard models are numerically solved and compared with each other in order to reveal the effect of electron interactions and system sizes. Numerical results point out that off-site Coulomb repulsion leads to an increase in the critical coupling constant to $β_{\text{c}}$ = 0.6 for a central Coulomb potential. This critical value of the $β$ is found to be independent of GQD size, reflecting its universality even in the presence of electron-electron interactions. In addition, a sudden downshift in the transmission peaks shows a clear signature of the transition from subcritical $β$ $<$ $β_{\text{c}}$ to supercritical $β$ $>$ $β_{\text{c}}$ regime. On the other hand, for a positively charged vacancy, the collapse of the lowest bound state occurs at $β_{\text{c}}$ = 0.7 for the interacting case. Interestingly, the local magnetic moment, induced by a bare carbon vacancy, is totally quenched when the vacancy is subcritically charged, whereas the valley splittings in electron and hole channels continue to exist in both regimes.
We report the fabrication details and low-temperature characteristics of the first carbon nanotube (CNT) quantum dots on flakes of hexagonal boron nitride (hBN) as substrate. We demonstrate that CNTs can be grown on hBN by standard chemical vapor deposition and that standard scanning electron microscopy imaging and lithography can be employed to fabricate nanoelectronic structures when using optimized parameters. This proof of concept paves the way to more complex devices on hBN, with more predictable and reproducible characteristics and electronic stability.
With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states.
The mean-field Hubbard model is used to investigate the formation of the antiferromagnetic phase in hexagonal graphene rings with inner zigzag edges. The outer edge of the ring was taken to be either zigzag or armchair, and we found that both types of structures can have a larger antiferromagnetic interaction as compared with hexagonal dots. This difference could be partially ascribed to the larger number of zigzag edges per unit area in rings than in dots. Furthermore, edge states localized on the inner ring edge are found to hybridize differently than the edge states of dots, which results i…
We report on the fabrication and characterization of etched graphene quantum dots (QDs) on hexagonal boron nitride (hBN) and SiO2 with different island diameters. We perform a statistical analysis of Coulomb peak spacings over a wide energy range. For graphene QDs on hBN, the standard deviation of the normalized peak spacing distribution decreases with increasing QD diameter, whereas for QDs on SiO2 no diameter dependency is observed. In addition, QDs on hBN are more stable under the influence of perpendicular magnetic fields up to 9T. Both results indicate a substantially reduced substrate in…
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.…
We have carried out first-principles calculations on electronic properties of graphene quantum dots embedded in hexagonal boron nitride monolayer sheets. The calculations with density functional theory show that the band gaps of quantum dots are determined by the quantum confinement effects and the hybridization of π orbitals from B, N and C atoms. The energy states near the Fermi level are found to be strongly localized within and in the vicinity of the quantum dots.
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single particle energy leve…
We characterize InSb quantum dots induced by bottom finger gates within a nanowire that is grown via the vapor-liquid-solid process. The gates are separated from the nanowire by an exfoliated 35\,nm thin hexagonal BN flake. We probe the Coulomb diamonds of the gate induced quantum dot exhibiting charging energies of $\sim 2.5\,\mathrm{meV}$ and orbital excitation energies up to $0.3\,\mathrm{meV}$. The gate hysteresis for sweeps covering 5 Coulomb diamonds reveals an energy hysteresis of only $60\mathrm{μeV}$ between upwards and downwards sweeps. Charge noise is studied via long-term measureme…
We study numerically the optical properties of low-buckled silicene and AB-stacked bilayer graphene quantum dots subjected to an external electric field, which is normal to their surface. Within the tight-binding model, the optical absorption is calculated for quantum dots, of triangular and hexagonal shapes, with zigzag and armchair edge terminations. We show that in triangular silicene clusters with zigzag edges a rich and widely tunable infrared absorption peak structure originates from transitions involving zero energy states. The edge of absorption in silicene quantum dots undergoes red s…
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…
The electronic energy gap and total dipole moment of chemically functionalized hexagonal and triangular graphene quantum dots are investigated by the density functional theory. It has been found that the energy gap can be efficiently tuned in the selected clusters by edge passivation with different elements or groups. Edge passivation with oxygen provides a considerable decrease of the large energy gap observed in hexagonal nanodots. The edge states and energy gap in triangular graphene quantum dots can also be manipulated by passivation with fluorine. The total dipole moment strongly depends …
We present here an atomistic theory of the electronic and optical properties of hexagonal InAsP quantum dots in InP nanowires in the wurtzite phase. These self-assembled quantum dots are unique in that their heights, shapes, and diameters are well known. Using a combined valence-force-field, tight-binding, and configuration-interaction approach we perform atomistic calculations of single-particle states and excitonic, biexcitonic and trion complexes as well as emission spectra as a function of the quantum dot height, diameter and As versus P concentration. The atomistic tight-binding parameter…
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 study the magnetization of square and hexagonal graphene dots. It is shown that two classes of hexagonal dots have a second order phase transition at a critical Hubbard energy $U$, whoose value is similar to the one in bulk graphene, albeit the dots do not have a density of states proportional to the absolute value of the energy, relatively to the Dirac point. Furthermore, we show that a particular class of hexagonal dots having zig-zag edges, does not exhibit zero energy edge states. We also study the effect of uniaxial strain on the evolution of the magnetization of square dots, and find …
The structure stability and electronic properties of edge carboxylated hexagonal and triangular graphene quantum dots are investigated by using density functional theory. The calculated binding energies show that the hexagonal clusters with armchair edges have the highest stability among all other flakes. The binding energy of carboxylated graphene quantum dots increases by increasing the number of attached carboxyl groups. Our study shows that the total dipole moment significantly increases by adding COOH with the highest values observed in triangular clusters. The edge states in triangular g…
We apply the recently introduced Hubbard model approach to quantitatively describe the experimental charge stability diagram and tunnel coupling of silicon double quantum dot systems. The results calculated from both the generalized Hubbard model and the microscopic theory are compared with existing experimental data, and excellent agreement between theory and experiment is found. The central approximation of our theory is a reduction of the full multi-electron multi-band system to an effective two-electron model, which is numerically tractable. In the microscopic theory we utilize the Hund-Mu…
We investigate the properties of electronic states and optical transitions in hexagonal GaAs quantum dots within AlGaAs nanowires. Such dots are particularly interesting due to their high degree of symmetry. A streamlined postsymmetrization technique based on class operators (PTCO) is developed which enables one to benefit in one run from the insight brought by the Maximal symmetrization and reduction of fields (MSRF) approach reported by Dalessi et al. [Phys. Rev. B 81, 125106 (2010)], after having solved the Schrödinger equation. Definite advantages of the PTCO are that it does not require h…
Electronic properties of triangular and hexagonal nano-scale quantum dots (QDs) of Silicene and bilayer graphene are studied. It is shown that the low-energy edge-localized electronic states, existing within the size-quantized gap are easily tunable by electric field. The appearance and field evolution of the electronic gap in these zero energy states (ZES) is shown to be very sensitive to QD geometry that permits to design the field-effect scalable QD devices with electronic properties on-demand.
Exchange interaction in gate-defined quantum dots beyond the Hubbard model
RWTH Aachen University（亚琛工业大学）；Forschungszentrum Jülich GmbH（于利希研究中心有限公司）；IMEC（比利时imec研究院）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）；School of Electrical Engineering and Telecommunication, UNSW Sydney（新南威尔士大学悉尼电气与电信工程学院）；Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所量子设备中心）；Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum（鲁尔大学波鸿分校应用固体物理学讲座）
Spins in gated semiconductor quantum dots (QDs) are a promising platform for Hubbard model simulation inaccessible to computation. Precise control of the tunnel couplings by tuning voltages on metallic gates is vital for a successful QD-based simulator. However, the number of tunable voltages and the complexity of the relationships between gate voltages and the parameters of the resulting Hubbard models quickly increase with the number of quantum dots. As a consequence, it is not known if and how a particular gate geometry yields a target Hubbard model. To solve this problem, we propose a hybr…
We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an extended mean-field Hubbard model. We observe that randomly distributed defects with concentrations between 1-5\% of the total number of atoms leads to localization alongside magnetic puddle-like structures. We show that localization lenght is not affected by magnetization if there is an even distribution of defects between the two sublattices of the honeycomb lat…
Density functional theory calculations are performed on phosphorene quantum dots having different shapes and edge terminations to investigate their structure stability, electronic properties, and gas sensing ability. All the selected phosphorene dots, namely hexagonal and triangular flakes with armchair and zigzag terminations, have positive binding energies which insure their stability even though the bond lengths are much longer than those in the infinite phosphorene layer. It is found that all the selected hydrogen passivated quantum dots have a wide energy gap. In contrast, the partial pas…
Electronic and magnetic properties of a system of two charged vacancies in hexagonal shaped graphene quantum dots are investigated using a mean-field Hubbard model as a function of the Coulomb potential strength $β$ of the charge impurities and the distance R between them. For $β=0$, the magnetic properties of the vacancies are dictated by Lieb's rules where the opposite (same) sub-lattice vacancies are coupled antiferromagnetically (ferromagnetically) and exhibit Fermi oscillations. Here, we demonstrate the emergence of a non-magnetic regime within the subcritical region: as the Coulomb poten…
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 …
Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these new structures is rich as novel phases are attainable. The spins spontaneously dimerize and, by using the Density Matrix Renormalization Group (DMRG), we show that the dimer state is robust to perturbations which break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.
Magnetic properties of two and three-dimensional clusters of quantum dots are studied with exact diagonalization of a generalized Hubbard model. We study the weak coupling limit, where the electrons interact only within a quantum dot and consider cases where the second or third harmonic oscillator shell is partially filled. The results show that in the case of half-filled shell the magnetism is determined by the antiferromagnetic Heisenberg model with spin 1/2, 1 or 3/2, depending on the number of electrons in the open shell. For other fillings the system in most cases favors a large total spi…
We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of quantum dots defined in a semiconductor two-dimensional electron gas system. Bands with energies above the lowest energy band are used to form the Hubbard model, which allows for an experimentally simpler realization of the device. We find that depending on average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the …
Using the tight-binding approximation we calculated the magnetic susceptibility of graphene quantum dots (GQD) of different geometrical shapes and sizes, smaller than the magnetic length, when the magnetic properties are governed by the electron edge states. Two types of edge states can be discerned: the zero-energy states (ZES) located exactly at the zero-energy Dirac point, and the dispersed edge states (DES) with the energy close, but not exactly equal to zero. DES are responsible for the temperature independent diamagnetic response, while ZES provide the temperature dependent spin Curie pa…
We investigated binding of hydrogen atoms to small Polycyclic Aromatic Hydrocarbons (PAHs) - i.e. graphene dots with hydrogen-terminated edges - using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with 3 to 7 hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We sho…
We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagneti…
We investigate the electron states and optical absorption in square- and hexagonal-shaped two-dimensional (2D) HgTe quantum dots and quantum rings in the presence of a perpendicular magnetic field. The electronic structure is modeled by means of the $sp^3d^5s^*$ tight-binding method within the nearest-neighbor approximation. Both bulklike and edge states appear in the energy spectrum. The bulklike states in quantum rings exhibit Aharonov-Bohm oscillations in magnetic field, whereas no such oscillations are found in quantum dots, which is ascribed to the different topology of the two systems. W…
We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. Imperfections in the graphene quantum dots are modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy a…
Using the tight-binding approach, we investigate the energy spectrum of square, triangular and hexagonal MoS$_2$ quantum dots (QDs) in the presence of a perpendicular magnetic field. Novel edge states emerge in MoS$_2$ QDs, which are distributed over the whole edge which we call ring states. The ring states are robust in the presence of spin-orbit coupling (SOC). The corresponding energy levels of the ring states oscillate as function of the perpendicular magnetic field which are related to Aharonov-Bohm oscillations. Oscillations in the magnetic field dependence of the energy levels and the p…
We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra; (ii) the range of validity…
We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonoga-Luttinger model. We analyze the spin-charge separation and transport property as the difference between the two tunneling parameter increases. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with t…
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…
The effects of edge hydrogenation and hydroxylation on the relative stability and electronic properties of hexagonal boron nitride quantum dots (h-BNQDs) are investigated. Zigzag edge hydroxylation is found to result in considerable energetic stabilization of h-BNQDs as well as a reduction of their electronic gap with respect to their hydrogenated counterparts. The application of an external in-plane electric field leads to a monotonous decrease of the gap. When compared to their edge-hydrogenated counterparts, significantly lower field intensities are required to achieve full gap closure of t…
The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian. Moreover, the high degree of tunability of these systems make them a powerful platform to simulate different regimes of the Hubbard model. However, most quantum dot array implementations have been limited to one-dimensional linear arrays. In this letter, we present a square lattice unit cell of 2$\times$2 quantum dots defined electrostatically in a AlGaAs/GaAs heterostructure using a double-layer gate technique. We probe the properties of the array using …
Using exact-diagonalization of small clusters and Dyson equation embedding techniques, the conductance $G$ of linear arrays of quantum dots is investigated. The Hubbard interaction induces Kondo peaks at low temperatures for an odd number of dots. Remarkably, the Kondo peak is split in half by a deep minimum, and the conductance vanishes at one value of the gate voltage. Tentative explanations for this unusual effect are proposed, including an interference process between two channels contributing to $G$, with one more and one less particle than the exactly-solved cluster ground-state. The Hub…
Despite a rich choice of two-dimensional materials, which exists these days, heterostructures, both vertical (van der Waals) and in-plane, offer an unprecedented control over the properties and functionalities of the resulted structures. Thus, planar heterostructures allow p-n junctions between different two-dimensional semiconductors and graphene nanoribbons with well-defined edges; and vertical heterostructures resulted in the observation of superconductivity in purely carbon-based systems and realisation of vertical tunnelling transistors. Here we demonstrate simultaneous use of in-plane an…
We investigate the dynamics of interacting electrons confined to two types of quantum dot system, when driven by an external AC field. We first consider a system of two electrons confined to a pair of coupled quantum dots by using an effective two-site model of Hubbard-type. Numerically integrating the Schroedinger equation in time reveals that for certain values of the strength and frequency of the field the tunneling between the dots can be destroyed, thus allowing the correlated two-electron states to be manipulated. We then show how Floquet theory can be used to predict the field parameter…
Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter. Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disord…
We investigate theoretically the magnetic levels and optical properties of zigzag- and armchair-edged hexagonal graphene quantum dots (GQDs) utilizing the tight-binding method. A new bound edge state at zero energy appears for the zigzag GQDs in the absence of a magnetic field. The magnetic levels of GQDs exhibit a Hofstadter-butterfly spectrum and approach the Landau levels of two-dimensional graphene as the magnetic field increases. The optical properties are tuned by the size, the type of the edge, and the external magnetic field.
We combine x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD) and x-ray magnetic linear dichroism (XMLD) data with first principles density functional theory (DFT) calculations and a multiorbital many body Hamiltonian approach to understand the electronic and magnetic properties of Co atoms adsorbed on h-BN/Ru(0001) and h-BN/Ir(111). The XAS line shape reveals, for both substrates, an electronic configuration close to $3d^8$, corresponding to a spin $S = 1$. Magnetic field dependent XMCD data show large (14 meV) out-of-plane anisotropy on h-BN/Ru(0001), while it is a…
Carbon (C) doped hexagonal boron nitride (hBN) has been experimentally reported to be ferromagnetic at room temperature. Substitution by C in hBN has been also reported to form islands of graphene. In this work we derive a mechanistic understanding of ferromagnetism with graphene islands in hBN from first principles and mean-field Hubbard model. We find a general property, that in bipartite lattices where the sublattices differ in on-site energies, as in hBN, the ordering between local magnetic moments can be substantial and predominantly anti-ferromagnetic (AFM) if they are embedded in the sa…
Quantum dots are considered building blocks for future quantum information circuits. We present here experimental results on a quantum dot circuit consisting of three quantum dots with controlled electron numbers down to one per dot and tunable coupling. We experimentally map out for the first time the stability diagram of the triatomic system and reveal the existence of quadruple points, a signature of the three dots being in resonance. In their vicinity we observe a surprising effect, a 'cloning' of charge transfer transitions related to charge and spin reconfigurations. The experimental res…
The presence of degenerate conduction band valleys and how they are mixed by interfaces play critical roles in determining electron interaction and spectrum in a silicon nanostructure. Here we investigate how the valley phases affect the exchange interaction in a symmetric two-electron silicon double quantum dot. Through a configuration interaction calculation, we find that exchange splitting is suppressed at a finite value of valley phase difference between the two dots, and reaches its minimum value ({\sim} 0) when the phase difference is π. Such a suppression can be explained using the Hubb…
Artificial lattices created by assembling atoms on a surface with scanning tunneling microscopy present a platform to create matter with tailored electronic, magnetic and topological properties. However, such artificial lattices studies to date have focused exclusively on surfaces with weak spin-orbit coupling. Here, we created artificial and coupled quantum dots by fabricating quantum corrals from iron atoms on the prototypical Rashba surface alloy, BiCu2, using low-temperature scanning tunneling microscopy. We quantified the quantum confinement of such quantum dots with various diameter and …
We present a general description of low temperature transport through a quantum dot with any number of electrons at filling factor $1<ν<2$. We provide a general description of a novel Kondo effect which is turned on by application of an appropriate magnetic field. The spin-flip scattering of carriers by the quantum dot only involves two states of the scatterer which may have a large spin. This process is described by spin-flip Hubbard operators, which change the angular momentum, leading to a Kondo Hamiltonian. We obtain antiferromagnetic exchange couplings depending on tunneling amplitudes an…
