Magnification of signatures of topological phase transition by quantum zero point motion

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.