# Dirac wave transmission in L\'evy disordered systems

## TL;DR

This paper explores how Dirac electrons behave in Le9vy-disordered systems, revealing a phase transition in localization regimes that differs from Schrf6dinger electrons, with implications for understanding wave transport in disordered materials.

## Contribution

It demonstrates a novel phase transition in Dirac wave localization due to Le9vy disorder, contrasting with traditional Schrf6dinger systems, and maps the phase diagram of localization regimes.

## Key findings

- Identifies a phase transition from anomalous to standard to anomalous localization with increasing energy.
- Provides a phase diagram of localization regimes based on incidence angle and energy.
- Shows that transmission fluctuations decrease sharply beyond a critical incidence angle.

## Abstract

We investigate the propagation of electronic waves described by the Dirac equation subject to a L\'evy-type disorder distribution. Our numerical calculations, based on the transfer matrix method, in a system with a distribution of potential barriers show that it presents a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schr\"odinger equation do not present such transitions. Moreover, we obtain the phase diagram delimiting anomalous and standard localization regimes, in the form of an incidence angle versus incidence energy diagram, and argue that transitions can also be characterized by the behavior of the dispersion of the transmission. We attribute this transition to an abrupt reduction in the transmittance of the system when the incidence angle is higher than a critical value which induces a decrease in the transmission fluctuations.