We describe the theory of few Coulomb-correlated electrons in a magnetic quantum dot formed in graphene. While the corresponding nonrelativistic (Schrödinger) problem is well understood, a naive generalization to graphene's "relativistic" (Dirac-Weyl) spectrum encounters divergencies and is ill-defined. We employ Sucher's projection formalism to overcome these problems. Exact diagonalization results for the two-electron quantum dot, i.e., the artificial helium atom in graphene, are presented.
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…
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…
Trapping electrons in quantum dots and controlling their collective quantum states is crucial for converting semiconductor structures into bits of quantum information processing. Here, we study single- and two-particle states in quantum dots formed in gapped bilayer graphene (BLG), where the electron's valley states appear in pair with their spin quantum number and we analyse spin- and valley-singlet and triplet states for various BLG and dot parameters, as well as two-particle interaction strength and external magnetic field.
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 table-top prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we provide a spatial visualization of the interplay between spatial and magnetic confinement in a circular graphene resonator. We directly observe the development of a multi-tiered "wedding cake"-like structure of concentric regions of compressible/incompressible quantum Hall…
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…
Coulomb interaction is of central importance in localized energy levels (bound states) or electronic flat bands and could result in many exotic quantum phases, such as magnetic, superconducting, and topological phases in graphene systems1-14. In graphene monolayer, the relativistic massless Dirac fermion nature of the charge carriers enables us to realize unprecedented quasibound states, which are trapped temporarily via whispering-gallery modes (WGMs) with the lifetime (trapping time) of ~ 10 fs, in circular graphene quantum dots (GQDs)15-20. Here we show that Coulomb interaction still plays …
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…
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.
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 …
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 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.
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 …
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 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…
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…
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…
In the field of condensed matter, graphene plays a central role as an emerging material for nanoelectronics. Nevertheless, graphene is a semimetal, which constitutes a severe limitation for some future applications. Therefore, a lot of efforts are being made to develop semiconductor materials whose structure is compatible with the graphene lattice. In this perspective, little pieces of graphene represent a promising alternative. In particular, their electronic, optical and spin properties can be in principle controlled by designing their size, shape and edges. As an example, graphene nanoribbo…
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…
Considerable efforts have been made to trap massless Dirac fermions in graphene monolayer, but only quasi-bound states are realized in continuous graphene sheets up to now. Here, we demonstrate the realization of bound states in nanoscale graphene quantum dots (GQDs) in a continuous graphene sheet. The GQDs are electronically isolated from the surrounding continuous graphene sheet by circular boundaries, which are generated by strong coupling between graphene and substrate. By using scanning tunneling microscopy (STM), we observe single-electron charging states of the GQDs, seen as Coulomb osc…
Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and transmission at these novel potential barriers should affect the quantum interference of electronic wavefunctions near these boundaries. Here we report the use of scanning tunneling microscopy (STM) to map the electronic structure of Dirac fermions confined by circular graphene pn junctions. These effective quantum dots were fabricated using a new technique…
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 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…
Spin transitions driven by a periodically varying electric potential in dilute fluorinated graphene quantum dots are investigated. Flakes of monolayer graphene are considered as well as electrostatic electron traps induced in bilayer graphene. The stationary states are obtained within the tight-binding approach and are used to the basis of eigenstates to describe the system dynamics. The dilute fluorination of the top layer lifts the valley degeneracy of the confined states and attenuates the orbital magnetic dipole moments due to current circulation within the flake. Moreover, the spin-orbit …
