  In this letter we show that the zero-point motion of the vortex in
superconducting doped topological insulators leads to significant changes in
the electronic spectrum at the topological phase transition in this system.
This topological phase transition is tuned by the doping level and the
corresponding effects manifest in the density of states at energies which are
of the order of the fluctuations frequency. This frequency might be much larger
than the electronic energy gap in the spectrum generated by a stationary
vortex. As a result the quantum zero-point motion can move the spectral
signature of the topological vortex phase transition to energies which are well
within the resolution of scanning tunneling microscopy. Moreover, the phenomena
studied in this letter present novel effects of Magnus force on the vortex
spectrum which are not present in the ordinary s-wave superconductors. Our
results show that quantum zero point fluctuations can bring the fingerprints of
topological phase transitions to more experimentally accessible grounds and
point to the importance of study of quantum fluctuations in different
candidates for realizing topological phase transitions.
