Majorana zero modes can be realized in vortices of superconducting topological insulators and topological crystalline insulators. We study when and how the existence of Majorana zero modes can be revealed by the local density of states on the surface which can be probed in scanning tunneling microscopy experiments. The Majorana zero modes in these systems can be destroyed by high chemical potential. As the chemical potential increases, the Majorana zero modes on opposite surfaces penetrate into the bulk and hybridize. This phase transition is associated with a change in the spatial distribution of vortex bound states on the surface. By calculating the local density of states, we find that this spatially extended zero-bias peak can indicate existence of Majorana zero modes in superconduc...[ Read more ]

Majorana zero modes can be realized in vortices of superconducting topological insulators and topological crystalline insulators. We study when and how the existence of Majorana zero modes can be revealed by the local density of states on the surface which can be probed in scanning tunneling microscopy experiments. The Majorana zero modes in these systems can be destroyed by high chemical potential. As the chemical potential increases, the Majorana zero modes on opposite surfaces penetrate into the bulk and hybridize. This phase transition is associated with a change in the spatial distribution of vortex bound states on the surface. By calculating the local density of states, we find that this spatially extended zero-bias peak can indicate existence of Majorana zero modes in superconducting vortices of topological insulators and topological crystalline insulators when the chemical potential is lower than the bulk gap. For vortices in topological crystalline insulators, the multiple Majorana zero modes are protected by magnetic mirror symmetry. When an in-plane magnetic field is applied, the local density of states differ significantly when the magnetic mirror symmetry is broken or preserved. And provide observable signatures for demonstrating the symmetry protection of the Majorana zero modes in experiment.