  We study the Kondo physics of a quantum magnetic impurity in two-dimensional
topological superconductors (TSCs), either intrinsic or induced on the surface
of a bulk topological insulator, using a numerical renormalization group
technique. We show that, despite sharing the p + ip pairing symmetry, intrinsic
and extrinsic TSCs host different physical processes that produce distinct
Kondo signatures. Extrinsic TSCs harbor an unusual screening mechanism
involving both electron and orbital degrees of freedom that produces rich and
prominent Kondo phenomena, especially an intriguing pseudospin Kondo singlet
state in the superconducting gap and a spatially anisotropic spin correlation.
In sharp contrast, intrinsic TSCs support a robust impurity spin doublet ground
state and an isotropic spin correlation. These findings advance fundamental
knowledge of novel Kondo phenomena in TSCs and suggest experimental avenues for
their detection and distinction.
