# Scanning gate microscopy of magnetic focusing in graphene devices: quantum vs. classical simulation

## TL;DR

This paper compares classical and quantum models of electron transport in graphene magnetic focusing devices using scanning gate microscopy, revealing different regimes and explaining asymmetries in resistance maps.

## Contribution

It introduces a detailed comparison between classical and quantum simulations of SGM in graphene, highlighting the regimes and effects of probe positioning on electron trajectories.

## Key findings

- Identification of focusing, repelling, and mixed regimes in SGM measurements.
- Tip influences electrons passing directly underneath, creating trails of modified current density.
- Spatial asymmetry in resistance maps linked to probe configuration and edge effects.

## Abstract

We compare classical versus quantum electron transport in recently investigated magnetic focusing devices [S. Bhandari et al., Nano Lett. 16, 1690 (2016)] exposed to the perturbing potential of a scanning gate microscope (SGM). Using the Landauer-B\"uttiker formalism for a multi-terminal device, we calculate resistance maps that are obtained as the SGM tip is scanned over the sample. There are three unique regimes in which the scanning tip can operate (focusing, repelling, and mixed regime) which are investigated. Tip interacts mostly with electrons with cyclotron trajectories passing directly underneath it, leaving a trail of modified current density behind it. Other (indirect) trajectories become relevant when the tip is placed near the edges of the sample, and current is scattered between the tip and the edge. We also discuss possible explanations for spatial asymmetry of experimentally measured resistance maps, and connect it with specific configurations of the measuring probes.