  We address the question of probing the supercurrents in superconducting (SC)
samples on a local scale by performing Scanning Tunneling Spectroscopy (STS)
experiments with a SC tip. In this configuration, we show that the tunneling
conductance is highly sensitive to the Doppler shift term in the SC
quasiparticle spectrum of the sample, thus allowing the local study of the
superfluid velocity. Intrinsic screening currents, such as those surrounding
the vortex cores in a type II SC in a magnetic field, are directly probed. With
Nb tips, the STS mapping of the vortices, in single crystal 2H-NbSe_2, reveals
both the vortex cores, on the scale of the SC coherence length $\xi$, and the
supercurrents, on the scale of the London penetration length $\lambda$. A
subtle interplay between the SC pair potential and the supercurrents at the
vortex edge is observed. Our results open interesting prospects for the study
of screening currents in any superconductor.
