# Klein Paradox in Chaotic Dirac Billiards

## TL;DR

This paper explores the universal behavior of chaotic Dirac billiards, revealing the Klein paradox and tunable conductance phenomena through numerical simulations of quantum resonant scattering.

## Contribution

It demonstrates the presence of Klein's paradox and tunable transport transitions in chaotic Dirac billiards, extending understanding of relativistic quantum systems.

## Key findings

- Universal conductance anomalies observed
- Klein paradox demonstrated in graphene billiards
- Tunable suppression and amplification transitions identified

## Abstract

We investigate the Schr\"odinger (non-relativistic) and the Dirac (``relativistic") billiards in the universal regime. The study is based on a non-ideal quantum resonant scattering numerical simulation. We show universal results that reveal anomalous behavior on the conductance, on the shot-noise power and on the respective eigenvalues distributions. In particular, we demonstrate the Klein's paradox in the graphene and tunable suppression/amplification transitions on the typical observables of the quantum dots.