Imaging Cyclotron Orbits of Electrons in Graphene

Abstract

Electrons in graphene can travel for several microns without scattering at low temperatures, and their motion becomes ballistic, following classical trajectories. When a magnetic field B is applied perpendicular to the plane, electrons follow cyclotron orbits.Magnetic focusing occurs when electrons injected from one narrow contact focus onto a second contact located an integer number of cyclotron diameters away. By tuning the magnetic field B and electron density n in the graphene layer, we observe magnetic focusing peaks. We use a cooled scanning gate microscope to image cyclotron trajectories in graphene at 4.2 K. The tip creates a local change in density that casts a shadow by deflecting electrons flowing nearby; an image of flow can be obtained by measuring the transmission between contacts as the tip is raster scanned across the sample. On the first magnetic focusing peak, we image a cyclotron orbit that extends from one contact to the other. In addition, we study the geometry of orbits deflected into the second point contact by the tip. KEYWORDS:Graphene, scanning gate microscope, image cyclotron orbits, magnetic focusing. 2The unusual properties of graphene offer new approaches to electronics based on the ballistic motion of electrons. 14,16,17 Electrons that enter the graphene sheet at different angles all travel in a circle -as a consequence of this geometry, the electron flux peaks at a distance d c where circles overlap. As B is increased from zero, the electron transmission from one contact reaches the first magnetic focusing peak when d c = L. As the field continues to increase additional magnetic focusing peaks can occur when L is an integer multiple of d c , if the electron orbit bounces off the edge of the sample specularly. 16,[18][19][20] In this paper, we present images of the cyclotron orbits in graphene associated with the first magnetic focusing peak, recorded using a cooled SPM at 4.2 K with a tip that acts as a movable gate. [13][14][15][16][17] The sample is a high-mobility hBN-graphene-hBN sandwich patterned into a hall bar geometry using reactive ion etching with a mixture of CHF 3 and O (Fig. 1b) The first magnetic focusing peak is clearly shown in in Fig. 2a which presents experimental measurements of R m vs. B and n 1/2 at 4.2K with no tip present. As the density and magnetic field are increased, the transresistance peaks (red) along a track with B 1 ∝ n 1/2 as predicted by theory.At magnetic fields B along either side of the magnetic focusing peak, the transmission between the two contacts is reduced (blue), because cyclotron orbit trajectories are focused away from the receiving contact. Evidence for the second magnetic focusing peak with one bounce off the edge between contacts is seen (black) at magnetic fields B ~ 2B 1 . The intensity of the second peak is reduced by diffuse boundary scattering, which reduces the probability of specular reflection to 5 0.3 to 0.4 in magnetic focusing measurements 20 in graphene, and to almost zero in 1.0 µm wide ballistic graphene w...

Independent Band Modulation in 2D van der Waals Heterostructures via a Novel Device Architecture

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Analysis of Scanned Probe Images for Magnetic Focusing in Graphene

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Scanning gate microscopy of magnetic focusing in graphene devices: quantum versus classical simulation

“…[13][14][15][16]. Before, similar magnetic focusing measurements were performed on semiconductor two-dimensional electron gas (2DEG) in parallel with the scanning technique.…”

“…[13][14][15][16]. We consider both positively and negatively charged tip, as well as a tip acting in the mixed regime.…”