  The quest to discover exoplanets is one of the most important missions in
astrophysics, and is widely performed using the transit method, which allows
for the detection of exoplanets down to the size of Mercury. However, to
confirm these detections, additional vetting is mandatory. We selected six K2
targets from campaigns #1 to #8 that show transit light curves corresponding to
Earth-sized to Neptune-sized exoplanets. We aim to discard some scenarios that
could mimic an exoplanetary transit, leading to a misinterpretation of the
data. We performed direct imaging observations using the SPHERE/VLT instrument
to probe the close environment of these stars. For five of the K2 targets, we
report no detection and we give the detection limits. For EPIC 206011496, we
detect a 0.38 $\pm$ 0.06 $M_{\odot}$ companion at a separation of 977.12 $\pm$
0.73 mas (140.19 $\pm$ 0.11 au). The spectral analysis corresponds to an M4-7
star, and the analysis of the proper motion shows that it is bounded to the
primary star. EPIC 206011496 also hosts an Earth-like planetary candidate. If
it transits the primary star, its radius is consistent with that of a
super-Earth. However, if it transits the companion star, it falls into the
mini-Neptune regime.
