Graphene's remarkable electronic properties have fuelled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor graphene's electronic properties and to control its charge carriers [1][2][3][4][5] . Here we show that a single-atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunnelling microscope. The response of the conduction electrons in graphene to the local charge is monitored with scanning tunnelling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime [6][7][8][9][10][11] where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states within a disc centred on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and o , providing a mechanism to control and guide electrons in graphene.Supercriticality in atoms occurs when the Coulomb coupling, β = Zα, exceeds a critical value of order unity, where Z is the atomic number and α ∼ 1/137 is the fine structure constant. In this regime the electronic orbitals, starting with the 1S state, sink into the Dirac continuum until Z is reduced to the critical value. This process, known as atomic collapse (AC), is accompanied by vacuum polarization and the spontaneous generation of positrons 12,13 . But accessing this new physics requires ultra-heavy nuclei which do not exist in nature. In graphene, where the effective fine structure constant, α g = α(c/ν F ) ∼ 2, is much larger, the critical coupling, β c = (Z c /κ)α g = 0.5, can be reached for a relatively modest charge [6][7][8][9][10] (c is the speed of light, ν F the Fermi velocity and κ the effective dielectric constant). The transition to the supercritical regime in graphene is marked by the emergence of a sequence of quasi-bound states which can trap electrons. However, because graphene is a good conductor it is difficult to deposit and maintain a charge on its surface. Attempts to create charge by ionizing adatoms or donors with a scanning tunnelling microscope (STM) tip 14 showed that the charge decays when the field is removed. Alternatively, ions can be deposited directly on graphene, but because the charge transfer is inefficient 15 , attaining the critical Z requires piling up many ions, which, in the absence of a controllable mechanism to overcome the Coulomb repulsion, is very challenging 11 .Here we show that a vacancy in graphene can stably host a positive charge. The charge is deposited by applying voltage pulses with an STM tip and its gradual build-up is monitored with scanning tun...

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The effect of strain in graphene is usually modeled by a pseudo-magnetic vector potential which is, however, derived in the limit of small strain. In realistic cases deviations are expected in view of graphene's very high strain tolerance, which can be up to 25%. Here we investigate the pseudomagnetic field generated by a Gaussian bump and we show that it exhibits significant differences with numerical tight-binding results. Furthermore, we calculate the electronic states in the strained region for a hexagon shaped flake with armchair edges. We find that the six-fold symmetry of the wave functions inside the Gaussian bump is directly related to the different effect of strain along the fundamental directions of graphene: zigzag and armchair. Low energy electrons are strongly confined in the armchair directions and are localized on the carbon atoms of a single sublattice.

The feasibility of Veselago lensing in graphene with a p-n junction is investigated numerically for realistic injection leads. Two different set-ups with two narrow leads are considered with absorbing or reflecting side edges. This allows us to separately determine the influence of scattering on electron focusing for the edges and the p-n interface. Both semiclassical and tight-binding simulations show a distinctive peak in the transmission probability that is attributed to the Veselago lensing effect. We investigate the robustness of this peak on the width of the injector, the position of the p-n interface and different gate potential profiles. Furthermore, the influence of scattering by both short-and long-range impurities is considered.

Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similar to the way spintronics uses electron spin. We show how a double barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is included the energy bands and energy gaps at the K and K' points are different and they can be tuned by changing the potential.Comment: 20 figure

Recently, black phosphorus quantum dots were fabricated experimentally. Motivated by these experiments, we theoretically investigate the electronic and optical properties of rectangular phosphorene quantum dots (RPQDs) in the presence of an in-plane electric field and a perpendicular magnetic field. The energy spectra and wave functions of RPQDs are obtained numerically using the tight-binding approach. We find edge states within the band gap of the RPQD which are well separated from the bulk states. In an undoped RPQD and for in-plane polarized light, due to the presence of well-defined edge states, we find three types of optical transitions which are between the bulk states, between the edge and bulk states, and between the edge states. The electric and magnetic fields influence the bulk-to-bulk, edge-to-bulk, and edge-to-edge transitions differently due to the different responses of bulk and edge states to these fields.

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Quantum electrodynamics predicts that heavy atoms (Z > Zc ≈ 170) will undergo the process of atomic collapse where electrons sink into the positron continuum and a new family of so-called collapsing states emerges. The relativistic electrons in graphene exhibit the same physics but at a much lower critical charge (Zc ≈ 1) which has made it possible to confirm this phenomenon experimentally. However, there exist conflicting predictions on the effect of a magnetic field on atomic collapse. These theoretical predictions are based on the continuum Dirac-Weyl equation, which does not have an exact analytical solution for the interplay of a supercritical Coulomb potential and the magnetic field. Approximative solutions have been proposed, but because the two effects compete on similar energy scales, the theoretical treatment varies depending on the regime which is being considered. These limitations are overcome here by starting from a tight-binding approach and computing exact numerical results. By avoiding special limit cases, we found a smooth evolution between the different regimes. We predict that the atomic collapse effect persists even after the magnetic field is activated and that the critical charge remains unchanged. We show that the atomic collapse regime is characterized: 1) by a series of Landau level anticrossings and 2) by the absence of √ B scaling of the Landau levels with regard to magnetic field strength.