title: Flat-Lens Focusing of Electron Beams in Graphene.
abstract: Coupling electron beams carrying information into electronic units is fundamental in microelectronics. This requires precision manipulation of electron beams through a coupler with a good focusing ability. In graphene, the focusing of wide electron beams has been successfully demonstrated by a circular p-n junction. However, it is not favorable for information coupling since the focal length is so small that the focal spot locates inside the circular gated region, rather than in the background region. Here, we demonstrate that an array of gate-defined quantum dots, which has gradually changing lattice spacing in the direction transverse to propagation, can focus electrons outside itself, providing a possibility to make a coupler in graphene. The focusing effect can be understood as due to the gradient change of effective refractive indices, which are defined by the local energy band in a periodic potential. The strong focusing can be achieved by suitably choosing the lattice gradient and the layer number in the incident direction, offering an effective solution to precision manipulation of electron beams with wide electron energy range and high angular tolerance.
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Tang
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Xiyuan
authors.initials: X
authors.lastname: Cao
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Ran
authors.initials: R
authors.lastname: Guo
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Yanyan
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Zhiyuan
authors.initials: Z
authors.lastname: Che
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Fouodji T
authors.initials: FT
authors.lastname: Yannick
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Weiping
authors.initials: W
authors.lastname: Zhang
authors.affiliation: Quantum Institute for Light and Atoms, Department of Physics, East China Normal University, Shanghai 200062, China.
authors.forename: Junjie
authors.initials: J
authors.lastname: Du