Investigating the Transition Region in Scanned Probe Images of the Cyclotron Orbit in Graphene

TL;DR

This study uses scanning probe microscopy to image and analyze the transition region in magnetic focusing of electrons in graphene, revealing how this region shifts with electron density and magnetic field, and enabling measurement of cyclotron diameters.

Contribution

It introduces a method to identify the transition region in magnetic focusing images of graphene, linking the transition location to electron trajectories and cyclotron diameters.

Findings

Transition region shifts with electron density and magnetic field.

Cyclotron diameter can be extracted from transition region location.

Trends in inflection points correlate with electron trajectory behavior.

Abstract

A cooled scanning probe microscope (SPM) has been used to image cyclotron orbits of electrons through high-mobility graphene in a magnetic field.1-5 In a hBN-graphene-hBN device patterned into a hall bar geometry, the magnetic field focuses a current Ii injected from one narrow contact into another narrow contact located an integer number of cyclotron diameters away, creating a voltage Vc. The degree of focusing is measured by the transresistance Rm = Vc/Ii. In SPM, the tip can either enhance or decrease conductance in the sample by deflecting electrons into or away from the second contact, respectively.3,4 Our SPM images of magnetic focusing feature a region in which the tip transitions from enhancing to decreasing the conductance in the sample where the change in transresistance caused by the tip is equal to zero. In this paper, we investigate how the location of this region in the graphene sample changes as we modulate the electron density n and magnetic field B. By plotting line-cuts of the change in trans-resistance for different electron densities and magnetic fields, we identify trends in the inflection point where the tip changes from enhancing to decreasing the conductance in the sample. From the location of each transition region, we show that the cyclotron diameter of the electron trajectories can be obtained, and explain the trends in inflection point location for different electron densities and magnetic fields.