Majorana state on the surface of a disordered three-dimensional topological insulator

We study low-lying electron levels in an "antidot" capturing a coreless vortex on the surface of a three-dimensional topological insulator in the presence of disorder. The surface is covered with a superconductor film with a hole of size R larger than coherence length, which induces superconductivity via proximity effect. Spectrum of electron states inside the hole is sensitive to disorder, however, topological properties of the system give rise to a robust Majorana bound state at zero energy. We calculate the subgap density of states with both energy and spatial resolution using the supersymmetric sigma model method. We identify the presence of the Majorana fermion with symmetry class B. Tunneling into the hole region is sensitive to the Majorana level and exhibits resonant Andreev reflection at zero energy.