Surface states around a vortex in topological superconductors: Intersection of a surface and a vortex

We numerically show that the zero-energy Majorana surface states are suppressed around a vortex in the three-dimensional topological superconductors such as Cu$_{x}$Bi$_{2}$Se$_{3}$ and Sn$_{1-x}$In$_{x}$Te. On the other hand, the zero-energy Majorana bound states along the vortex line are robust against cut by the surface. The suppression of the surface bound states is similar to that with a magnetic impurity on the surface of the topological insulator. The suppression of the surface-bound states around a vortex can be observed as the unconventional energy dependence of imaging of the scanning tunneling microscopy/spectroscopy.