Imaging electron flow from collimating contacts in graphene

Abstract

The ballistic motion of electrons in graphene encapsulated in hexagonal boron nitride (hBN) promises exciting opportunities for electron-optics devices. A narrow electron beam is desired, with both the mean free path and coherence length exceeding the device size. One can form a collimating contact in graphene by adding zigzag contacts on either side of the electron emitter that absorb stray electrons to form a collimated electron beam [23]. Here we provide images of electron flow from a collimating contact that directly show the width and shape of the electron beam, obtained using a Scanning Gate Microscope (SGM) cooled to 4.2 K. The device is a hBN-encapsulated graphene hall bar with narrow side contacts on either side of the channel that have an electron emitter at the end and absorbing zig-zag contacts at both side. To form an image of electron flow, the SGM tip is raster scanned at a constant height above the sample surface while the transmission to a receiving contact on opposite sides of the channel is measured. By displaying the change {\Delta}T vs. tip position, an image of ballistic flow is obtained. The angular width of the electron beam leaving the collimating contact is found by applying a perpendicular magnetic field B that bends electron paths into cyclotron orbits. SGM images reveal that electron flow from a collimating contact disappears quickly at B = 0.05T while the flow from a non-collimating contact persists up to B = 0.19 T. Ray tracing simulations agree well with the experimental images over a range of B and electron density n. By fitting the half-width at half-max (HWHM) of the magnitude of electron flow in the experimental SGM images, we find a narrow half angular width {\Delta}{\theta} = 9.2{\deg} for the electron flow from the collimating contact, compared with a wide flow {\Delta}{\theta} = 54{\deg} from the non-collimating contact.