Magnetic field dependence of the atomic collapse state in graphene

Quantum electrodynamics predicts that heavy atoms ($Z > Z_c \approx 170$) 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 ($Z_c \approx 1$) 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 $\sqrt{B}$ scaling of the Landau levels with regard to magnetic field strength

Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene

The remarkable electronic properties of graphene have fueled 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 its electronic properties and to control its charge carriers. 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 tunneling microscope (STM). The response of the conduction electrons in graphene to the local charge is monitored with scanning tunneling 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 6-11 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 (DOS) within a disc centered 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 off, providing a new mechanism to control and guide electrons in grapheneComment: 18 pages and 5 figures plus 14 pages and 15 figures of supplementary information. Nature Physics advance online publication, Feb 22 (2016

Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding

The motion of massless Dirac-electrons in graphene mimics the propagation of photons. This makes it possible to control the charge-carriers with components based on geometrical-optics and has led to proposals for an all-graphene electron-optics platform. An open question arising from the possibility of reducing the component-size to the nanometer-scale is how to access and understand the transition from optical-transport to quantum-confinement. Here we report on the realization of a circular p-n junction that can be continuously tuned from the nanometer-scale, where quantum effects are dominant, to the micrometer scale where optical-guiding takes over. We find that in the nanometer-scale junction electrons are trapped in states that resemble atomic-collapse at a supercritical charge. As the junction-size increases, the transition to optical-guiding is signaled by the emergence of whispering-gallery modes and Fabry-Perot interference. The creation of tunable junctions that straddle the crossover between quantum-confinement and optical-guiding, paves the way to novel design-architectures for controlling electronic transport.Comment: 16 pages, 4 figure