# Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions

## TL;DR

This study uses atomistic simulations to analyze magnetotransport in nanopatterned graphene, revealing that electron trajectories involve bound states around antidots, which explains commensurability peaks beyond simple orbit models.

## Contribution

It introduces a comprehensive atomistic simulation approach to interpret magnetoresistance peaks in perforated graphene, emphasizing bound states over classical skipping orbits.

## Key findings

- Magnetoresistance spectra match experimental results.
- Bound states around antidots explain commensurability peaks.
- Peak behavior depends on antidot size, magnetic field, and electron density.

## Abstract

Commensurability oscillations in the magnetotransport of periodically patterned systems, emerging from the interplay of cyclotron orbit and the pattern periodicity, are a benchmark of mesoscopic physics in electron gas systems. Exploiting similar effects in 2D materials would allow exceptional control of electron behaviour, but is hindered by the requirement to maintain ballistic transport over large length scales. Recent experiments have overcome this obstacle and observed distinct magnetoresistance commensurability peaks for perforated graphene sheets (antidot lattices). Interpreting the exact mechanisms behind these peaks is of key importance, particularly in graphene where a range of regimes are accessible by varying the electron density. In this work a fully atomistic, device-based simulation of magnetoresistance experiments allows us to analyse both the resistance peaks and the current flow at commensurability conditions. Magnetoresistance spectra are found in excellent agreement with experiment, but we show that a semi-classical analysis, in terms of simple skipping or pinned orbits, is insufficient to fully describe the corresponding electron trajectories. Instead, a generalised mechanism in terms of states bound to individual antidots, or to groups of antidots, is required. Commensurability features are shown to arise when scattering between such states is enhanced. The emergence and suppression of commensurability peaks is explored for different antidot sizes, magnetic field strengths and electron densities. The insights gained from our study will guide the design and optimization of future experiments with nanostructured graphene.