The presence of flat bands near Fermi level has been proposed as an explanation for high transition temperature superconductors. The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around 1.5\ifmmode^\circ\else\textdegree\fi{} and is related to a process of layer decoupling. We have performed ab initio calculations to develop a tight-binding model with an interaction Hamiltonian between layers that include the $\pi${} orbitals of all atoms and takes into account interactions up to third nearest neighbors within a layer.

We investigate the electronic transport properties of a bilayer graphene flake contacted by two monolayer nanoribbons. Such a finite-size bilayer flake can be built by overlapping two semi-infinite ribbons or by depositing a monolayer flake onto an infinite nanoribbon. These two structures have a complementary behavior that we study and analyze by means of a tight-binding method and a continuum Dirac model. We have found that for certain energy ranges and geometries, the conductance of these systems oscillates markedly between zero and the maximum value of the conductance, allowing for the design of electromechanical switches. Our understanding of the electronic transmission through bilayer flakes may provide a way to measure the interlayer hopping in bilayer graphene.

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twistedlike Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twistedlike Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.

Electronic and optical characteristic energies of semiconductor quantum rings in the presence of magnetic fields were determined by adopting distinct potential models to describe the ring confinement and considering different geometric confinement parameters defining the quantum ring. It was found that the ground-state energy becomes independent of the ring radius once the internal ring hole is present, because it is the strength of the lateral confinement that determines its subsequent behavior. The optical spectra for large and narrow quantum rings exhibit a set of resonances governed basically by the strength of the radial confinement. The presence of a magnetic field produces a notable enhancement of the resonance intensities.

A theoretical study of the photoluminescence peak energies in InAs self-assembled quantum dots embedded in a GaAs matrix in the presence of magnetic fields applied perpendicular to the sample plane is performed. The effective mass approximation and a parabolic potential cylinder-shaped model for the InAs quantum dots are used to describe the effects of magnetic field and hydrostatic pressure on the correlated electron-hole transition energies. Theoretical results are found in quite good agreement with available experimental measurements for InAs/GaAs self-assembled quantum dots.

The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them experimentally in symmetrical heterostructures composed by segments of graphene ribbons with different widths forming a graphene quantum dot. We identify the existence of bound states in the continuum in these graphene quantum dot systems by means of local density of states and electronic conductance calculations.