The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at the Fermi level, and few low-energy conduction electron states occur both in triangular and hexagonal flakes due to symmetry reasons. Armchair triangles can be used as building blocks for other types of flakes that support the ghost states. Edge roughness has only a small effect on the level structure of the triangular flakes, but the effect is considerably enhanced in the other types of flakes. In round flakes, the states near the Fermi level depend strongly on the flake radius, and they are always localized on the zigzag parts of the edge.
We investigate quantum transport properties of triangular graphene flakes with zigzag edges by using first principles calculations. Triangular graphene flakes have large magnetic moments which vary with the number of hydrogen atoms terminating its edge atoms and scale with its size. Electronic transmission and current-voltage characteristics of these flakes, when contacted with metallic electrodes, reveal spin valve and remarkable rectification features. The transition from ferromagnetic to antiferromagnetic state under bias voltage can, however, terminate the spin polarizing effects for speci…
Optical reflectivity contrast provides a simple, fast and noninvasive method for characterization of few monolayer samples of two-dimensional materials. Here we apply this technique to measure the thickness of thin flakes of hexagonal Boron Nitride (hBN), which is a material of increasing interest in nanodevice fabrication. The optical contrast shows a strong negative peak at short wavelengths and zero contrast at a thickness dependent wavelength. The optical contrast varies linearly for 1-80 layers of hBN, which permits easy calibration of thickness. We demonstrate the applicability of this q…
The electronic shell and supershell structure of triangular graphene quantum dots has been studied using density functional and tight-binding methods. The density functional calculations demonstrate that the electronic structure close to the Fermi energy is correctly described with a simple tight-binding model where only the p_z orbitals perpendicular to the graphene layer are included. The results show that (i) both at the bottom and at the top of the p_z band a supershell structure similar to that of free electrons confined in a triangular cavity is seen, (ii) close to the Fermi level the sh…
The electronic properties of a triaxially strained hexagonal graphene flake with either armchair or zig-zag edges are investigated using molecular dynamics simulations and tight-binding calculations. We found that: i) the pseudo-magnetic field in the strained graphene flakes is not uniform neither in the center nor at the edge of zig-zag terminated flakes, ii) the pseudo-magnetic field is almost zero in the center of armchair terminated flakes but increases dramatically near the edges, iii) the pseudo-magnetic field increases linearly with strain, for strains lower than 15$%$ while growing non…
We investigate the spin-dependent thermoelectric effect of graphene flakes with magnetic edges in the ballistic regime. Employing static, respectively, dynamic mean-field theory we first show that magnetism appears at the zigzag edges for a window of Coulomb interactions that increases significantly with increasing flake size. We then use the Landauer formalism in the framework of the non-equilibrium Green's function method to calculate the spin and charge currents in magnetic hexagonal graphene flakes by varying the temperature of the junction for different flake sizes. While in non-magnetic …
Hexagonal boron nitride (hBN)-long-known as a thermally stable ceramic-is now available as atomically smooth, single-crystalline flakes, revolutionizing its use in optoelectronics. For nanophotonics, these flakes offer strong nonlinearities, hyperbolic dispersion, and single-photon emission, providing unique properties for optical and quantum-optical applications. For nanoelectronics, their pristine surfaces, chemical stability, and wide bandgap have made them the key substrate, encapsulant, and gate dielectric for two-dimensional electronic devices. However, while exploring these advantages, …
We study fully hexagonal boron nitride (hBN)-encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes; thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from SiO2/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Furthe…
Hexagonal boron nitride (hBN) is the supporting substrate of choice for two-dimensional material devices because it is atomically flat and chemically inert. However, due to the small size of mechanically exfoliated hBN flakes, electronic structure studies of 2D materials supported by hBN using angle-resolved photoemission spectroscopy (ARPES) are challenging. Here we investigate the electronic band structure of a Bernal-stacked bilayer graphene sheet on a hexagonal boron nitride (BLG/hBN) flake using nanospot ARPES (nanoARPES). By fitting high-resolution energy vs. momentum electronic band spe…
Hexagonal boron nitride (hBN) is a wide bandgap van der Waals material that has recently emerged as promising platform for quantum photonics experiments. In this work we study the formation and localization of narrowband quantum emitters in large flakes (up to tens of microns wide) of hBN. The emitters can be activated in as-grown hBN by electron irradiation or high temperature annealing, and the emitter formation probability can be increased by ion implantation or focused laser irradiation of the as-grown material. Interestingly, we show that the emitters are always localized at edges of the …
Graphene nano-flakes (GNFs) are predicted to host spin-polarized metallic edge states, which are envisioned for exploration of spintronics at the nanometer scale. To date, experimental realization of GNFs is only in its infancy because of the limitation of precise cutting or synthesizing methods at the nanometer scale. Here, we use low temperature scanning tunneling microscope (STM) to manipulate coronene molecules on a Cu(111) surface to build artificial triangular and hexagonal GNFs with either zigzag or armchair type of edges. We observe that the metallic edge states only exist in the GNFs …
The effects of geometry on the hosting of Majorana zero modes are explored in core-shell nanowires with a hexagonal core and a triangular shell, and vice versa. The energy interval separating electronic states localized in the corners from states localized on the sides of the shell is shown to be larger for a triangular nanowire with a hexagonal core, than a triangular one. We build the topological phase diagram for both cases and compare them to earlier work on prismatic nanowires with the same core and shell geometry. We suggest that a dual core nanowire is needed to allow for a braiding ope…
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.
Applications of quantum science to computing, cryptography and imaging are on their way to becoming key next generation technologies. Owing to the high-speed transmission and exceptional noise properties of photons, quantum photonic architectures are likely to play a central role. A long-standing hurdle, however, has been the realization of robust, device-compatible single photon sources that can be activated and controlled on demand. Here we use strain engineering to create large arrays of quantum emitters in two-dimensional hexagonal boron nitride (hBN). The large energy gap inherent to this…
Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than to the energy level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy level structure. The susceptibility at charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structure…
Raman spectroscopy, a fast and nondestructive imaging method, can be used to monitor the doping level in graphene devices. We fabricated chemical vapor deposition (CVD) grown graphene on atomically flat hexagonal boron nitride (hBN) flakes and SiO$_2$ substrates. We compared their Raman response as a function of charge carrier density using an ion gel as a top gate. The G peak position, 2D peak position, 2D peak width and the ratio of the 2D peak area to the G peak area show a dependence on carrier density that differs for hBN compared to SiO$_2$. Histograms of two-dimensional mapping are used…
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…
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…
In this paper, we study topological phases in a 2D photonic crystal with broken time ($\mathcal{T}$) and parity ($\mathcal{P}$) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks $\mathcal{T}$ symmetry while the triangular rods breaks $\mathcal{P}$ symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases wit…
We use density functional theory to determine the equilibrium shape of graphene flakes, through the calculation of the edge orientation dependence of the edge energy and edge stress of graphene nanoribbons. The edge energy is a nearly linear function of edge orientation angle; increasing from the armchair orientation to the zigzag orientation. Reconstruction of the zigzag edge lowers its energy to less than that of the armchair edge. The edge stress for all edge orientations is compressive, however, reconstruction of the zigzag edge reduces this edge stress to near zero. Hydrogen adsorption is…
Graphene can develop large magnetic moments in custom crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nano-systems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulene-like graphene systems and demonstrate that they possess a spin $S=1$ ground state. Scanning tunnelling spectroscopy identifies the fingerprint of an underscreened $S=1$ Kondo state on \rev{these} flakes at low temperatu…
Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every angle is energetically favorable. Recent experiments on rotation-tunable electronics reveal the existence of a discrete set of angles at which the rotation-tunable electronics assume the most stable configurations. Nevertheless, a quantitative map for locating these intrinsically preferred twist angles in twisted bilayer system has not been available, posing challenges for the on-demand design of twisted electronics that are intrinsically stable at desired twist angles. Here …
Despite recent successes in the synthesis of boron nanotubes (BNTs), the atomic arrangement of their walls has not yet been determined and many questions about their basic properties do remain. Here, we unveil the dynamical stability of BNTs by means of first-principles molecular dynamics simulations. We find that free-standing, single-wall BNTs with diameters larger than 0.6 nm are thermally stable at the experimentally reported synthesis temperature of 870$^\circ$C and higher. The walls of thermally stable BNTs are found to have a variety of different mixed triangular-hexagonal morphologies.…
We have investigated atomic and electronic structure of grain boundaries in monolayer MoS2, where relative angles between two different grains are 0 and 60 degree. The grain boundaries with specific relative angle have been formed with chemical vapor deposition growth on graphite and hexagonal boron nitride flakes; van der Waals interlayer interaction between MoS2 and the flakes restricts the relative angle. Through scanning tunneling microscopy and spectroscopy measurements, we have found that the perfectly stitched structure between two different grains of MoS2 was realized in the case of th…
Controlling the size and shape of nanopores in two-dimensional materials is a key challenge in applications such as DNA sequencing, sieving, and quantum emission in artificial atoms. We here investigate experimentally and theoretically triangular vacancies in (unconventional) Bernal-stacked AB-h-BN formed using a high-energy electron beam. Due to the geometric configuration of AB-h-BN, triangular pores in different layers are aligned, and their sizes are controlled by the duration of the electron irradiation. Interlayer covalent bonding at the vacancy edge is not favored, as opposed to what oc…
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…
To grow precisely aligned graphene on h-BN without metal catalyst is extremely important, which allows for intriguing physical properties and devices of graphene/h-BN hetero-structure to be studied in a controllable manner. In this report, such hetero-structures were fabricated and investigated by atomic resolution scanning probe microscopy. Moirre patterns are observed and the sensitivity of moirre interferometry proves that the graphene grains can align precisely with the underlying h-BN lattice within an error of less than 0.05 degree. The occurrence of moirre pattern clearly indicates that…
Graphite is a well-studied material with known electronic and optical properties. Graphene, on the other hand, which is just one layer of carbon atoms arranged in a hexagonal lattice, has been studied theoretically for quite some time but has only recently become accessible for experiments. Here we demonstrate how single- and multi-layer graphene can be unambiguously identified using Raman scattering. Furthermore, we use a scanning Raman set-up to image few-layer graphene flakes of various heights. In transport experiments we measure weak localization and conductance fluctuations in a graphene…
Statistical distribution of energy levels for Dirac fermions confined in a quantum dot is studied numerically on the examples of triangular and hexagonal graphene flakes with random electrostatic potential landscape. When increasing the disorder strength, level distribution evolves from Poissonian to Wigner, indicating the transition to quantum chaos. The unitary ensemble (with the twofold valley degeneracy) is observed for triangular flakes with zigzag or Klein edges and potential varying smoothly on the scale of atomic separation. For small number of edge defects, the unitary-to-orthogonal s…
A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correc…
Graphite surfaces can be manipulated by several methods to create graphene structures of different shapes and sizes. Scanning tunneling microscopy (STM) can be used to create these structures either through mechanical contact between the tip and the surface or through electro-exfoliation. In the latter, the mechanisms involved in the process of exfoliation with an applied voltage are not fully understood. Here we show how a graphite surface can be locally exfoliated in a systematic manner by applying an electrostatic force with a STM tip at the edge of a terrace, forming triangular flakes seve…
Straintronic devices made of carbon-based materials have been pushed up due to the graphene high mechanical flexibility and the possibility of interesting changes in transport properties. Properly designed strained systems have been proposed to allow optimized transport responses that can be explored in experimental realizations. In multi-terminal systems, comparisons between schemes with different geometries are important to characterize the modifications introduced by mechanical deformations, specially if the deformations are localized at a central part of the system or extended in a large r…
Devices made from two-dimensional (2D) materials such as graphene or transition metal dichalcogenides possess interesting electronic properties that can become accessible to experimental probes when the samples are protected from deleterious environmental effects by encapsulating them between hexagonal boron nitride (hBN) layers. While the encapsulated flakes can be detected through post-processing of optical images or confocal Raman mapping, these techniques lack the sub-micrometer scale resolution to identify tears, structural defects or impurities, which is crucial for the fabrication of hi…
Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replica of the original Dirac cone and Hofstadter butterflies. Our large-scale tight binding simulation reveals an unexpected coexistence of a relativistic and non-relativistic Landau level structure. The presence of the zeroth Landau level and its associated butter…
In this letter, we examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate, graphene can develop gapped low energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time reversal symmetry and can be d…
