Annular Majorana mode in a superconducting topological insulator

When the surface states of a topological insulator becomes superconducting, topological superconductivity can be obtained, and each vortex on the surface can host one single Majorana zero-energy mode which is usually a wave packet decaying exponentially off the vortex core. Here, we predict stable Majorana zero-energy mode whose wave function is ring-shape, dubbed as annular Majorana mode, in the superconducting vortex in topological insulators respecting $3$-fold or $6$-fold rotational symmetry. Such topological insulators are featured with a single nonlinear Dirac cone located at $\bar{\Gamma}$ or three linear Dirac cones at $\bar{\text{M}}$ in the surface Brillouin zone. The annular Majorana mode originates from the effective chiral $f$-wave superconductivity on the nonlinear Dirac cone in the former case and the interference of the effective chiral $p$-wave superconductivity on the three linear Dirac cones in the latter. In both cases, the annular Majorana mode is stabilized by the rotational symmetry and the winding number $3$ carried by the surface states. Candidate materials supporting the annular Majorana mode are predicted. Our work provides new insights into the topological superconductivity in superconducting topological insulators.