We investigate the vacancy effects on quasiparticle band structure of graphene near the Dirac point. It is found that each Dirac nodal point splits into two new nodal points due to the coherent scattering among vacancies. The splitting energy between
the two nodal points is proportional to the square root of vacancy concentration. In addition, an extra dispersionless impurity band of zero energy due to particle-hole symmetry is found. Our theory offers an excellent explanation to the recent experiments.
The puzzle of recently observed insulating phase of graphene at filling factor $ u=0$ in high magnetic field quantum Hall (QH) experiments is investigated. We show that the magnetic field driven Peierls-type lattice distortion (due to the Landau leve
l degeneracy) and random bond fluctuations compete with each other, resulting in a transition from a QH-metal state at relative low field to a QH-insulator state at high enough field at $ u=0$. The critical field that separates QH-metal from QH-insulator depends on the bond fluctuation. The picture explains well why the field required for observing the insulating phase is lower for a cleaner sample.
An accurate simulation of Greens function and self-energy function of non-interacting electrons in disordered graphenes are performed. Fundamental physical quantities such as the elastic relaxation time {tau}e, the phase velocity vp, and the group ve
locity vg are evaluated. New features around the Dirac point are revealed, showing hints that multi-scattering induced hybridization of Bloch states plays an important role in the vicinity of the Dirac point.
Density of states (DOS) of graphene under a high uniform magnetic field and white-noise random potential is numerically calculated. The disorder broadened zero-energy Landau band has a Gaussian shape whose width is proportional to the random potentia
l variance and the square root of magnetic field. Wegner-type calculation is used to justify the results.
In this paper, we numerically study the bound electron states induced by long range Coulomb impurity in gapped graphene and the quasi-bound states in supercritical region based on the lattice model. We present a detailed comparison between our numeri
cal simulations and the prediction of the continuum model which is described by the Dirac equation in (2+1)-dimensional Quantum Electrodynamics (QED). We also use the Fanos formalism to investigate the quasi-bound state development and design an accessible experiments to test the decay of the supercritical vacuum in the gapped graphene.
Stimulated by recent advances in isolating graphene, we discovered that quantum dot can be trapped in Z-shaped graphene nanoribbon junciton. The topological structure of the junction can confine electronic states completely. By varying junction lengt
h, we can alter the spatial confinement and the number of discrete levels within the junction. In addition, quantum dot can be realized regardless of substrate induced static disorder or irregular edges of the junction. This device can be used to easily design quantum dot devices. This platform can also be used to design zero-dimensional functional nanoscale electronic devices using graphene ribbons.
