  The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound
states in a one-dimensional topological superconductor has inspired many
proposals aiming at demonstrating this property in transport. In particular,
transport through the mode from a lead attached to the left bound state to a
lead attached to the right will result in current cross-correlations. For ideal
zero modes on a grounded superconductor, the cross-correlations are however
completely suppressed in favor of purely local Andreev reflection. In order to
obtain a non-vanishing cross-correlation, previous studies have required the
presence of an additional global charging energy. Adding nonlocal terms in the
form of a global charging energy to the Hamiltonian when testing the intrinsic
nonlocality of the Majorana modes seems to be conceptually troublesome. Here,
we show that a floating superconductor allows to observe nonlocal current
correlations in the absence of charging energy. We show that the
non-interacting and the Coulomb-blockade regime have the same peak conductance
$e^2/h$ but different shot-noise power; while the shot noise is sub-Poissonian
in the Coulomb-blockade regime in the large bias limit, Poissonian shot noise
is generically obtained in the non-interacting case.
