Related papers: Symmetry Classes in Graphene Quantum Dots: Univers…
In view of the many quantum field theoretical descriptions of graphene in $2+1$ dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in…
Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless…
We investigate the effects of wedge disclination on charge carriers in circular graphene quantum dots subjected to a magnetic flux. Using the asymptotic solutions of the energy spectrum for large arguments, we approximate the scattering…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
Electron scattering problem in the monolayer graphene with short-range impurities is considered. The main novel element in the suggested model is the band asymmetry of the defect potential in the 2+1-dimensional Dirac equation. This…
The relationship between the universal conductance fluctuation and the weak localization effect in monolayer graphene is investigated. By comparing experimental results with the predictions of the weak localization theory for graphene, we…
We analyze the bound-state spectra of mass-profile quantum dots in graphene, a system at current experimental reach. Homogeneous perpendicular magnetic fields are also considered which result in breaking the valley degeneracy. The spectra…
The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points…
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…
Renowned for its sensitivity to detect the presence of numerous substances, graphene is an excellent chemical sensor. Unfortunately, which general features a dopant must have in order to enter the list of substances detectable by graphene…
Measuring degeneracy and broken-symmetry states of a system at nanoscale requires extremely high energy and spatial resolution, which has so far eluded direct observation. Here, we realize measurement of the degeneracy and subtle…
We study the spectrum and stationary states in a ring-shaped lattice potential in the context of ultracold atoms with attractive interatomic interactions. We determine analytical solutions in the absence of a lattice by mapping them to…
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions…
Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials…
In this paper we exploit the technique used in \cite{A}-\cite{5b} to deal with delta interactions in a rigorous way in a curved spacetime represented by a cosmic string along the $z$ axis. This mathematical machinery is applied in order to…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…