# Magnetotransport in a perturbed periodic antidot superlattice

## TL;DR

This paper investigates how small perturbations in a 2D antidot superlattice affect electron trajectories, revealing a transition from ballistic to superdiffusive behavior characterized by Levy walks.

## Contribution

It introduces a quasiperiodic LG model derived from a 3D billiard model to analyze the impact of perturbations on electron transport in antidot superlattices.

## Key findings

- Infinite drifting trajectories disappear with perturbations.
- Particles exhibit Levy walks and superdiffusive behavior.
- Superdiffusive exponent correlates with duration of superdiffusion.

## Abstract

We study a 2-dimensional model for an antidot periodic superlattice with perturbed positions of the antidots. To do so we use a quasiperiodic LG model obtained from a 3-dimensional billiard model. Our results show that infinite drifting trajectories present in the periodic antidot models disappear, but if the perturbation is small enough, those trajectories remain for long times. The probability to visit the region of the phase space where electrons have ballistic behavior tends to $0$ as the length of the drifting trajectories tends to infinity, leading to separation of these regions in phase space. As a result, we infer that the particles follow Levy walks and the system has superdiffusive behavior for short times. The superdiffusive exponent is correlated to the length of time where the superdiffusive behavior is present.