Related papers: Quantum dot energy levels in bilayer graphene: Exa…
Considering the increasing number of experimental results in the manufacturing process of quantum dots with different geometries, and the fact that most numerical methods that can be used to investigate quantum dots with non-trivial…
We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within…
We demonstrate a method to determine energy level degeneracies using non-equilibrium electronic transport through voltage-biased quantum dots. We establish the general validity of this approach using single and double quantum dots in…
Graphene quantum dots (GQDs) represent single layers up to dozens of graphene layers smaller than 30 nm. GQDs are newish molecules that have aroused great interest in research because of their exceptional and manageable optical, electrical,…
The electronic properties of bilayer graphene with a magnetic quantum dot and a magnetic quantum ring are investigated. The eigenenergies and wavefunctions of quasiparticle states are calculated analytically by solving decoupled…
Quantum dots induced by a strong magnetic field applied to a single layer of graphene in the perpendicular direction are investigated. The dot is defined by a model potential which consists of a well of depth $\Delta V$ relative to a flat…
Multi-electron semiconductor quantum dots have found wide application in qubits, where they enable readout and enhance polarizability. However, coherent control in such dots has typically been restricted to only the lowest two levels, and…
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…
Within a minimal model, we present analytical expressions for the eigenstates and eigenvalues of carriers confined in quantum rings in monolayer and bilayer graphene. The calculations were performed in the context of the continuum model, by…
We present analytic estimates for the energy levels of N electrons (N = 2 - 5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a…
Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for $p_z$ electrons and long-range Coulomb interactions. By disentangling low-…
We present a systematic study of the energy levels of twisted bilayer graphene (tBLG) quantum dots (QD) and rings (QR) under an external perpendicular magnetic field. The confinement structures are modeled by a circular dot-like- and…
We set up and parametrize a Hubbard model for interacting quantum dots in bilayer graphene and study double dots as the smallest multi-dot system. We demonstrate the tunability of the spin and valley multiplets, Hubbard parameters, and…
The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron…
Laterally localized electronic states are identified on a single layer of graphene on ruthenium. The individual states are separated by 3 nm and comprise regions of about 90 carbon atoms. This constitutes a quantum dot array, evidenced by…
We describe the theory of few Coulomb-correlated electrons in a magnetic quantum dot formed in graphene. While the corresponding nonrelativistic (Schr\"odinger) problem is well understood, a naive generalization to graphene's "relativistic"…
We demonstrate here that a chain of Bilayer Graphene Quantum Dots (BLGQDs) can realize topological quantum matter by effectively simulating a spin-1 chain that hosts the Haldane phase within a specific range of parameters. We describe a…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…