Shot noise cross-correlations in normal metal–superconductor–normal metal structures are discussed at arbitrary interface transparencies using both the scattering approach of Blonder, Tinkham, and Klapwik and a microscopic Green’s function approach. Surprisingly, negative crossed conductance in such setups [R. Mélin and D. Feinberg, Phys. Rev. B 70, 174509 (2004)] does not preclude the possibility of positive noise cross-correlations for almost transparent contacts. We conclude with a phenomenological discussion of interactions in the one-dimensional leads connected to the superconductor, which induce sign changes in the noise cross-correlations.

We propose a set of interferometric methods on how to detect Majorana bound states induced by a topological insulator. The existence of these states can be easily determined by the conductance oscillations as function of magnetic flux and/or electric voltage. We study the system in the presence and absence of Majorana bound states and observe strikingly different behaviors. Importantly, we show that the presence of coupled Majorana bound states can induce a persistent current in absence of any external magnetic field.

Shot-noise cross correlations across single layer graphene structures are calculated with insulators separating a superconducting region. A different feature of specular crossed Andreev reflection comes into play due to the unique band structure of graphene. This gives rise to a rich structure in the states of the electric current flowing across the graphene sheet. We identified a parametric regime where positive shot-noise cross correlations of the current appear signifying entanglement. In contrast to previous proposals the sign of the cross correlations can be easily tuned by the application of a gate voltage.