Emergence of intraparticle entanglement and time-varying violation of Bell's inequality in Dirac matter

Abstract

We demonstrate the emergence and dynamics of intraparticle entanglement in massless Dirac fermions. This entanglement, generated by spin-orbit coupling, arises between the spin and sublattice pseudospin of electrons in graphene. The entanglement is a complex dynamic quantity but is generally large, independent of the initial state. Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intraparticle entanglement is a general feature of graphene on a substrate. These features are also expected to impact entanglement between pairs of particles, and may be detectable in experiments that combine Cooper pair splitting with nonlocal measurements of spin-spin correlation in mesoscopic devices based on Dirac materials. ; ICN2 is funded by the CERCA Programme/Generalitat de Catalunya, and is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). The authors acknowledge the European Union's Horizon 2020 research and innovation programme under Grants Agreement No. 785219 and No. 881603 (Graphene Flagship). B.G. deM. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754558 (PREBIST). ; Peer reviewed