Observing Majorana Zero Modes in a $p_x+ip_y$ Superconductor at High Temperature by Tunneling Spectroscopy

Directly observing a zero energy Majorana state in the vortex core of a chiral superconductor by tunneling spectroscopy requires energy resolution better than the spacing between core states $\Delta^2_0/\epsilon_F$. We show\footnote{arXiv:0811.2557, Phys. Rev. Lett. in press} that nevertheless, its existence can be clearly detected by comparing the temperature broadened tunneling conductance of a vortex with that of an antivortex even at temperatures $T \gg \Delta^2_0/\epsilon_F$. The Bogoliubov-de-Gennes (BdG) equation of a $p_x+ip_y$ superconductor is solved numerically on a sphere with vortex-antivortex pair at the poles. The robustness of the exponentially Majorana mode energy is verified by including a moderate white noise potential.