Anomalous Entanglement in Chaotic Dirac Billiards

We present analytical and numerical results that demonstrate the presence of anomalous entanglement behavior on the Dirac Billiards. We investigate the statistical distribution of the characteristic entangled measures, focusing on the mean, on the variance and on the quantum interference terms. We show a quite distinct behavior of the Dirac Billiard compared with the non-relativist (Schrodinger) ones. Particularly, we show a very plausible Bell state and a sharp amplitude of quantum interference term on entangled electrons left from the Dirac Billiards. The results have remarkable relevance to the novel quantum dots build of materials like graphene or topological insulators.