title: Electron optics with p-n junctions in ballistic graphene.
abstract: Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.
authors.affiliation: Department of Physics, Columbia University, New York, NY 10027, USA. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA.
authors.forename: Shaowen
authors.initials: S
authors.lastname: Chen
authors.affiliation: Department of Physics, Columbia University, New York, NY 10027, USA. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China.
authors.forename: Zheng
authors.initials: Z
authors.lastname: Han
authors.affiliation: Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA.
authors.forename: Mirza M
authors.initials: MM
authors.lastname: Elahi
authors.affiliation: Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA.
authors.forename: K M Masum
authors.initials: KM
authors.lastname: Habib
authors.affiliation: Department of Physics, Cornell University, Ithaca, NY 14853, USA.
authors.forename: Lei
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Physics, Columbia University, New York, NY 10027, USA. IBM Thomas J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, NY 10598, USA. USA.
authors.forename: Bo
authors.initials: B
authors.lastname: Wen
authors.affiliation: Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA.
authors.forename: Yuanda
authors.initials: Y
authors.lastname: Gao
authors.affiliation: National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0047, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Taniguchi
authors.affiliation: National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0047, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Watanabe
authors.affiliation: Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA.
authors.forename: James
authors.initials: J
authors.lastname: Hone
authors.affiliation: Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA.
authors.forename: Avik W
authors.initials: AW
authors.lastname: Ghosh
authors.affiliation: Department of Physics, Columbia University, New York, NY 10027, USA. cdean@phys.columbia.edu.
authors.forename: Cory R
authors.initials: CR
authors.lastname: Dean