Focusing Of Electron Waves By A Graded Array Of Gate-defined Quantum Dots In Graphene

Since it was first experimentally fabricated in 2004, graphene, as a new kind of two-dimensional topological carbon material, has attracted much attention because of so many extraordinary electronic transport properties. When near the Fermi energy band, the energy of electrons in graphene has an approximately linear relationship with the momentum. And because the effective mass of electrons can be viewed as 0 and electrons are governed by the Dirac Equation, electrons in graphene are also called as massless Dirac Fermions. Therefore, graphene compares favorably for electronic transport properties with traditional semi-conductor.It is shown in this thesis that electron waves in graphene can be focused by a quantum dot array with gradually changing lattice spacing in the direction transverse to the incident wave. The effect can be understood as the gradient change of the effective refractive index which is defined by the energy band structure in a periodic potential provided by a quantum dot. Electron waves can be even strongly focused by choosing the suitable lattice gradient and the layer number in the incident direction. The wide energy range spectrum and the acceptable angular tolerance might enable the design to be an excellent alternative in graphene-based electronics.