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 nonrelativist (Schrödinger) 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.

• Received 10 August 2014
• Revised 14 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245107