Andreev Bound-states of vortices and surfaces in topological superconductors

We propose an experimental way to determine the pairing states for the unconventional superconductor CuxBi2Se3. Using the spectral polynomial expansion method, we numerically calculate the local density of states (LDOS) in the multi-orbital tight-binding model and analytically obtain the zero-energy solution around a vortex. Both calculations reveal that a quantized vortex is spin-polarized for the gap function categorized by “pseudo scalar” which is the isotropic odd-parity order parameter. On the other hand, no clear spin-polarization around a vortex can observed for the gap function categorized by “polar vector” which breaks the rotational isotropy in the normal states.