Analysis of Scanned Probe Images for Magnetic Focusing in Graphene

Abstract

We have used cooled scanning probe microscopy (SPM) to study electron motion in nanoscale devices. The charged tip of the microscope was rasterscanned at constant height above the surface as the conductance of the device was measured. The image charge scatters electrons away, changing the path of electrons through the sample. Using this technique, we imaged cyclotron orbits that flow between two narrow contacts in the magnetic focusing regime for ballistic hBN-graphene-hBN devices. We present herein an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge density dip on the motion of ballistic electrons. The density dip locally reduces the Fermi energy, creating a force that pushes electrons away from the tip. When the tip is above the cyclotron orbit, electrons are deflected away from the receiving contact, creating an image by reducing the transmission between contacts. The data and our analysis suggest that the graphene edge is rather rough, and electrons scattering off the edge bounce in random directions. However, when the tip is close to the edge, it can enhance transmission by bouncing electrons away from the edge, toward the receiving contact. Our results demonstrate that cooled SPM is a promising tool to investigate the motion of electrons in ballistic graphene devices.

Imaging electron flow from collimating contacts in graphene

“…We have developed a technique that uses a cooled SGM to image the flow of electrons through a 2DEG that we used for GaAs/AlGaAs heterostructures [16,[19][20][21] and graphene samples [18,29,31]. The charged tip creates an image charge in the 2DEG below (figure 1(c)) that deflects electrons away from their original paths, changing the transmission T between two contacts of a ballistic device.…”

“…As electrons accumulate, raising the electron density, the chemical potential increases, creating an opposing current that maintains zero net current flow. By measuring the voltage change ΔV or the transresistance change ΔR = ΔV/I at the receiving contact, the transmission change ΔT induced by the tip can be obtained [18,31]. For a collimated electron beam, the current is emitted from contact 1 to contact 2 in figure 1(a), while contacts 7 and 8 are grounded to collect sideways moving electrons.…”

Quantum imaging of current flow in graphene

“…Edge currents in graphene have been mapped in one dimension using superconducting interferometry, but extending the concept to 2D imaging is very challenging ( 10 ). Scanning gate microscopy has been used to map conductance fluctuations and even cyclotron orbits ( 11 – 14 ), but the invasive gating tip makes quantitative analysis difficult and limits the technique’s applicability ( 15 , 16 ). Scanning magnetometry based on a superconducting quantum interference device is typically limited to moderate spatial resolutions of several micrometers ( 17 ), despite holding great promise for improvement ( 18 ), and is restricted to low temperatures.…”

Electron beam splitting at topological insulator surface states and a proposal for electronic Goos-Hanchen shift measurement

“…We present a proposal for experimentally measuring the GH shift based on the transverse magnetic focusing (TMF) technique in which by applying a transverse magnetic field one can focus the motion of electrons/holes in the ballistic regime [50][51][52]. The TMF has been used to study the shape of Fermi surfaces [52], Andreev reflection [52,53], spin-orbit interaction [54], the angle-resolved transmission probability in graphene [55], imaging electron trajectories [53,[56][57][58], as well as proposing a method for measuring warping strength in TIs [16].…”