  The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole
of the size of the coherence length is considered. While the neutral zero
energy Majorana core state remains intact due to its topological origin, the
energy of charged excitations is enhanced significantly compared to that in the
unpinned vortex. As a consequence of the pinning the minigap separating the
Majorana state from the charged levels increases to a signicant fraction of
superconducting gap. Suppression of the thermodynamic and kinetic effects of
the charged excitations allows to isolate the Majorana state so it can be used
for quantum computation. It is proposed that thermal conductivity along the
vortex cores is a sensitive method to demonstrate the minigap. We calculate,
using Butticker-Landauer-Kopnin formula, the thermal conductance beyond linear
response as function of the hole radius.
