Evolution of density of states and spin-resolved checkerboard pattern associated with Majorana bound state

In terms of Bogoliubov-de Gennes approach, we investigate Majorana bound state (MBS) in vortex of proximity-induced superconductivity on the surface of topological insulator. Mapping out the local density of states (LDOS) of quasiparticle excitations as a function of energy and distance from vortex center, it is found that the spectral distribution evolves from V-shape to Y-shape with emergence of MBS upon variation of chemical potential, consistent with the STM/STS measurement in a very recent experiment [Xu et al., Phys. Rev. Lett. 114, 017001 (2015)] on Bi2Te3 thin layer on the top of NbSe2. Moreover, we demonstrate that there is a checkerboard pattern in the relative LDOS between spin up and down channels, which maps out directly the quantum mechanical wave function of MBS. Therefore, spin-resolved STM/STS technique is expected to be able to provide phase sensitive evidence for MBS in vortex core of topological superconductor.