Isolating the vortex core Majorana state in p-wave superconductors

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.