Shot Noise for Entangled Electrons with Berry Phase

We study shot noise for entangled electrons in a 4-lead beam-splitter with one incoming lead driven by adiabatically rotating magnetic fields. We propose a setup of an adiabatically rotating magnetic field therefor, which is appropriate for an electron beam to transport through. Using the scattering matrix approach, we find that shot noise for the singlet and that for the entangled triplet oscillates between bunching and antibunching due to the influence of the Berry phase. It provides us a new approach for testing the Berry phase in electron transport on the basis of entanglement.