Symmetry-protected vortex phase transitions and anisotropic magnetic response in superconducting topological crystalline insulator SnTe

Topological crystalline insulator SnTe is known to support at most 2 Majorana zero modes (MZMs) at each end of a single vortex, their coexistence is protected by a magnetic mirror symmetry M_T. We study how a tilted magnetic field changes the topological classification of the vortex and calculate the local density of states (LDOS) which can be compared with experiments. When the Fermi level is deep inside the bulk states, the MZMs from opposite surfaces tunnel through and hybridize in a vortex phase transition. We find that if a magnetic glide symmetry G_T is broken, the vortex may feature only a single MZM between vortex phase transitions. Although resolving the MZMs in experiment is difficult since they are buried deep under other low-lying vortex bound states, the MZMs can be identified from the anisotropic magnetic response of the LDOS. For higher chemical potential when the vortex features MZMs, the zero bias peak elongates when the in-plane component of the magnetic field is along {110} direction preserving M_T, while it splits when M_T is broken or when the chemical potential is low so that all MZMs are hybridized.