Theoretical investigation of the scanning tunneling microscopy of Majorana bound states in topological superconductor vortices.

Scanning tunneling microscopy (STM) is an indispensable tool in detecting Majorana bound states (MBSs) in vortices of topological superconductors. By reducing the computational complexity via non-uniform grids, we systematically study the tunnel coupling as well as the temperature dependence of the differential conductance of MBSs in two dimensional devices. Numerical results show that the conductance peak approaches the quantized value 2e /h in strong coupling limit at low temperatures which are characteristic features of MBSs. More interestingly, a conductance local minimum in the spatially scanning is observed when the STM tip is placed at the vortex center. The dip structure can be enhanced with increased temperature or enlarged vortex size. We ascribe this observation to the sensitivity of the Andreev reflection processes of carriers at the vortex center where the thermal energy could be comparable to the vanishing pair potential. We also investigate the STM of two-vortex systems where the hybridization of the vortices can lead to oscillatory behavior of the state energy. With small inter-vortex distances, the original MBSs in vortices can merge into topologically trivial states and the conductance peak can be significantly suppressed.